HeatConduction

diffusion_coefficient

Default:thermal_conductivity

C++ Type:MaterialPropertyName

Unit:(no unit assumed)

Controllable:No

Description:Property name of the diffusion coefficient

diffusion_coefficient_dT

Default:thermal_conductivity_dT

C++ Type:MaterialPropertyName

Unit:(no unit assumed)

Controllable:No

Description:Property name of the derivative of the diffusion coefficient with respect to the variable

(modules/heat_transfer/tutorials/introduction/therm_step02.i)

#
# Single block thermal input with boundary conditions
# https://mooseframework.inl.gov/modules/heat_transfer/tutorials/introduction/therm_step02.html
#

[Mesh]
  [generated]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 2
    ymax = 1
  []
[]

[Variables]
  [T]
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 45.0
  []
[]

[BCs]
  [t_left]
    type = DirichletBC
    variable = T
    value = 300
    boundary = 'left'
  []
  [t_right]
    type = FunctionDirichletBC
    variable = T
    function = '300+5*t'
    boundary = 'right'
  []
[]

[Executioner]
  type = Transient
  end_time = 5
  dt = 1
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/code_verification/spherical_test_no2.i)

# Problem III.2
#
# A spherical shell has a thermal conductivity that varies linearly
# with temperature. The inside and outside surfaces of the shell are
# exposed to constant temperatures.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    xmin = 0.2
    nx = 4
  [../]
  coord_type = RSPHERICAL
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./exact]
    type = ParsedFunction
    symbol_names = 'ri ro beta ki ko ui uo'
    symbol_values = '0.2 1.0 1e-3 5.3 5 300 0'
    expression = 'uo+(ko/beta)* ( ( 1 + beta*(ki+ko)*(ui-uo)*( (1/x-1/ro) / (1/ri-1/ro) )/(ko^2))^0.5 -1 )'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
[]

[BCs]
  [./ui]
    type = DirichletBC
    boundary = left
    variable = u
    value = 300
  [../]
  [./uo]
    type = DirichletBC
    boundary = right
    variable = u
    value = 0
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat'
    prop_values = '1.0 1.0'
  [../]
  [./thermal_conductivity]
    type = ParsedMaterial
    property_name = 'thermal_conductivity'
    coupled_variables = u
    expression = '5 + 1e-3 * (u-0)'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/meshed_gap_thermal_contact/meshed_annulus_thermal_contact.i)

[Mesh]
  [fmesh]
    type = FileMeshGenerator
    file = meshed_annulus.e
  []
  [rename]
    type = RenameBlockGenerator
    input = fmesh
    old_block = '1 2 3'
    new_block = '1 4 3'
  []
[]

[Variables]
  [./temp]
    block = '1 3'
    initial_condition = 1.0
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
    block = '1 3'
  [../]
  [./source]
    type = HeatSource
    variable = temp
    block = 3
    value = 10.0
  [../]
[]

[BCs]
  [./outside]
    type = DirichletBC
    variable = temp
    boundary = 1
    value = 1.0
  [../]
[]

[ThermalContact]
  [./gap_conductivity]
    type = GapHeatTransfer
    variable = temp
    primary = 2
    secondary = 3
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductivity = 0.5
  [../]
[]

[Materials]
  [./hcm]
    type = HeatConductionMaterial
    block = '1 3'
    temp = temp
    thermal_conductivity = 1
  [../]
[]

[Problem]
  type = FEProblem
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  [./out]
    type = Exodus
  [../]
[]

(modules/heat_transfer/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/perfect.i)

[Mesh]
  file = perfect.e
[]

[Variables]
  [./temp]
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temp
    boundary = leftleft
    value = 300
  [../]
  [./right]
    type = DirichletBC
    variable = temp
    boundary = rightright
    value = 400
  [../]
[]

[ThermalContact]
  [./left_to_right]
    secondary = leftright
    quadrature = true
    primary = rightleft
    emissivity_primary = 0
    emissivity_secondary = 0
    variable = temp
    type = GapHeatTransfer
  [../]
[]

[Materials]
  [./hcm]
    type = HeatConductionMaterial
    block = 'left right'
    specific_heat = 1
    thermal_conductivity = 1
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/tutorials/introduction/therm_step03.i)

#
# Single block thermal input with time derivative term
# https://mooseframework.inl.gov/modules/heat_transfer/tutorials/introduction/therm_step03.html
#

[Mesh]
  [generated]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 2
    ymax = 1
  []
[]

[Variables]
  [T]
    initial_condition = 300.0
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = T
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 45.0
    specific_heat = 0.5
  []
  [density]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = 8000.0
  []
[]

[BCs]
  [t_left]
    type = DirichletBC
    variable = T
    value = 300
    boundary = 'left'
  []
  [t_right]
    type = FunctionDirichletBC
    variable = T
    function = '300+5*t'
    boundary = 'right'
  []
[]

[Executioner]
  type = Transient
  end_time = 5
  dt = 1
[]

[VectorPostprocessors]
  [t_sampler]
    type = LineValueSampler
    variable = T
    start_point = '0 0.5 0'
    end_point = '2 0.5 0'
    num_points = 20
    sort_by = x
  []
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = therm_step03_out
    execute_on = final
  []
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_balance/large_gap_heat_transfer_test_rz_cylinder.i)

rpv_core_gap_size = 0.2

core_outer_radius = 2
rpv_inner_radius = '${fparse 2 + rpv_core_gap_size}'
rpv_outer_radius = '${fparse 2.5 + rpv_core_gap_size}'
rpv_width = '${fparse rpv_outer_radius - rpv_inner_radius}'

rpv_outer_htc = 10 # W/m^2/K
rpv_outer_Tinf = 300 # K

core_blocks = '1'
rpv_blocks = '3'

[Mesh]
  [gmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '${core_outer_radius} ${rpv_core_gap_size} ${rpv_width}'
    ix = '400 1 100'
    dy = 1
    iy = '5'
  []
  [set_block_id1]
    type = SubdomainBoundingBoxGenerator
    input = gmg
    bottom_left = '0 0 0'
    top_right = '${core_outer_radius} 1 0'
    block_id = 1
    location = INSIDE
  []
  [rename_core_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = set_block_id1
    primary_block = 1
    paired_block = 0
    new_boundary = 'core_outer'
  []
  [set_block_id3]
    type = SubdomainBoundingBoxGenerator
    input = rename_core_bdy
    bottom_left = '${rpv_inner_radius} 0 0'
    top_right = '${rpv_outer_radius} 1 0'
    block_id = 3
    location = INSIDE
  []
  [rename_inner_rpv_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = set_block_id3
    primary_block = 3
    paired_block = 0
    new_boundary = 'rpv_inner'
  []
  # comment out for test without gap
  [2d_mesh]
    type = BlockDeletionGenerator
    input = rename_inner_rpv_bdy
    block = 0
  []
  coord_type = RZ
[]

[Variables]
  [Tsolid]
    initial_condition = 500
  []
[]

[Kernels]
  [heat_source]
    type = CoupledForce
    variable = Tsolid
    block = '${core_blocks}'
    v = power_density
  []
  [heat_conduction]
    type = HeatConduction
    variable = Tsolid
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = Tsolid
    boundary = 'right' # outer RPV
    coefficient = ${rpv_outer_htc}
    T_infinity = ${rpv_outer_Tinf}
  []
[]

[ThermalContact]
  [RPV_gap]
    type = GapHeatTransfer
    gap_geometry_type = 'CYLINDER'
    emissivity_primary = 0.8
    emissivity_secondary = 0.8
    variable = Tsolid
    primary = 'core_outer'
    secondary = 'rpv_inner'
    gap_conductivity = 0.1
    quadrature = true
  []
[]

[AuxVariables]
  [power_density]
    block = '${core_blocks}'
    initial_condition = 50e3
  []
[]

[Materials]
  [simple_mat]
    type = HeatConductionMaterial
    thermal_conductivity = 34.6 # W/m/K
  []
[]

[Postprocessors]
  [Tcore_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Trpv_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = '${core_blocks}'
  []
  [rpv_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = Tsolid
    boundary = 'right' # outer RVP
    T_fluid = ${rpv_outer_Tinf}
    htc = ${rpv_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(rpv_convective_out - ptot) / ptot'
    pp_names = 'rpv_convective_out ptot'
  []
  [flux_from_core] # converges to ptot as the mesh is refined
    type = SideDiffusiveFluxIntegral
    variable = Tsolid
    boundary = core_outer
    diffusivity = thermal_conductivity
  []
  [flux_into_rpv] # converges to rpv_convective_out as the mesh is refined
    type = SideDiffusiveFluxIntegral
    variable = Tsolid
    boundary = rpv_inner
    diffusivity = thermal_conductivity
  []

[]

[Executioner]
  type = Steady
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_max_its = 100
  [Quadrature]
    # order = fifth
    side_order = seventh
  []
  line_search = none
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/functional_expansion_tools/examples/3D_volumetric_Cartesian_different_submesh/main.i)

# Derived from the example '3D_volumetric_Cartesian' with the following differences:
#
#   1) The number of x and y divisions in the sub app is not the same as the master app
#   2) The subapp mesh is skewed in x and z
[Mesh]
  type = GeneratedMesh
  dim = 3

  xmin = 0.0
  xmax = 10.0
  nx = 15

  ymin = 1.0
  ymax = 11.0
  ny = 25

  zmin = 2.0
  zmax = 12.0
  nz = 35
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./s_in] # Add in the contribution from the SubApp
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'top bottom left right front back'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3   4   5'
    physical_bounds = '0.0  10.0    1.0 11.0    2.0 12.0'
    x = Legendre
    y = Legendre
    z = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(modules/heat_transfer/test/tests/code_verification/spherical_test_no1.i)

# Problem III.1
#
# A spherical shell has a constant thermal conductivity k and internal
# heat generation q. It has inner radius ri and outer radius ro.
# Both surfaces are exposed to constant temperatures: u(ri) = ui and u(ro) = uo.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    xmin = 0.2
    nx = 4
  [../]
  coord_type = RSPHERICAL
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./exact]
    type = ParsedFunction
    symbol_names = 'ri ro ui uo'
    symbol_values = '0.2 1.0 300 0'
    expression = '( uo * (1/ri-1/x) - ui * (1/ro-1/x)) / (1/ri-1/ro)'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
[]

[BCs]
  [./ui]
    type = DirichletBC
    boundary = left
    variable = u
    value = 300
  [../]
  [./uo]
    type = DirichletBC
    boundary = right
    variable = u
    value = 0
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat thermal_conductivity'
    prop_values = '1.0 1.0 5.0'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_rz_cylinder.i)

rpv_core_gap_size = 0.2

core_outer_radius = 2
rpv_inner_radius = '${fparse 2 + rpv_core_gap_size}'
rpv_outer_radius = '${fparse 2.5 + rpv_core_gap_size}'
rpv_width = '${fparse rpv_outer_radius - rpv_inner_radius}'

rpv_outer_htc = 10 # W/m^2/K
rpv_outer_Tinf = 300 # K

core_blocks = '1'
rpv_blocks = '3'

[Mesh]
  [gmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '${core_outer_radius} ${rpv_core_gap_size} ${rpv_width}'
    ix = '400 1 100'
    dy = 1
    iy = '5'
  []
  [set_block_id1]
    type = SubdomainBoundingBoxGenerator
    input = gmg
    bottom_left = '0 0 0'
    top_right = '${core_outer_radius} 1 0'
    block_id = 1
    location = INSIDE
  []
  [rename_core_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = set_block_id1
    primary_block = 1
    paired_block = 0
    new_boundary = 'core_outer'
  []
  [set_block_id3]
    type = SubdomainBoundingBoxGenerator
    input = rename_core_bdy
    bottom_left = '${rpv_inner_radius} 0 0'
    top_right = '${rpv_outer_radius} 1 0'
    block_id = 3
    location = INSIDE
  []
  [rename_inner_rpv_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = set_block_id3
    primary_block = 3
    paired_block = 0
    new_boundary = 'rpv_inner'
  []
  # comment out for test without gap
  [2d_mesh]
    type = BlockDeletionGenerator
    input = rename_inner_rpv_bdy
    block = 0
  []
  allow_renumbering = false
  coord_type = RZ
[]

[Variables]
  [Tsolid]
    initial_condition = 500
  []
[]

[Kernels]
  [heat_source]
    type = CoupledForce
    variable = Tsolid
    block = '${core_blocks}'
    v = power_density
  []
  [heat_conduction]
    type = HeatConduction
    variable = Tsolid
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = Tsolid
    boundary = 'right' # outer RPV
    coefficient = ${rpv_outer_htc}
    T_infinity = ${rpv_outer_Tinf}
  []
[]

[ThermalContact]
  [RPV_gap]
    type = GapHeatTransfer
    gap_geometry_type = 'CYLINDER'
    emissivity_primary = 0.8
    emissivity_secondary = 0.8
    variable = Tsolid
    primary = 'core_outer'
    secondary = 'rpv_inner'
    gap_conductivity = 0.1
    quadrature = true
  []
[]

[AuxVariables]
  [power_density]
    block = '${core_blocks}'
    initial_condition = 50e3
  []
[]

[Materials]
  [simple_mat]
    type = HeatConductionMaterial
    thermal_conductivity = 34.6 # W/m/K
  []
[]

[Postprocessors]
  [Tcore_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Trpv_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = '${core_blocks}'
  []
  [rpv_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = Tsolid
    boundary = 'right' # outer RVP
    T_fluid = ${rpv_outer_Tinf}
    htc = ${rpv_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(rpv_convective_out - ptot) / ptot'
    pp_names = 'rpv_convective_out ptot'
  []
  [flux_from_core] # converges to ptot as the mesh is refined
    type = SideDiffusiveFluxIntegral
    variable = Tsolid
    boundary = core_outer
    diffusivity = thermal_conductivity
  []
  [flux_into_rpv] # converges to rpv_convective_out as the mesh is refined
    type = SideDiffusiveFluxIntegral
    variable = Tsolid
    boundary = rpv_inner
    diffusivity = thermal_conductivity
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = 'rpv_inner core_outer'
    variable = Tsolid
  []
[]

[Executioner]
  type = Steady
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_max_its = 100
  [Quadrature]
    # order = fifth
    side_order = seventh
  []
  line_search = none
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/combined/test/tests/nodal_patch_recovery/npr_with_lower_domains.i)

E_block = 1e7
E_plank = 1e7
elem = QUAD4
order = FIRST

[Mesh]
  patch_size = 80
  patch_update_strategy = auto
  [plank]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -0.3
    xmax = 0.3
    ymin = -10
    ymax = 10
    nx = 2
    ny = 67
    elem_type = ${elem}
    boundary_name_prefix = plank
  []
  [plank_id]
    type = SubdomainIDGenerator
    input = plank
    subdomain_id = 1
  []

  [block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0.31
    xmax = 0.91
    ymin = 7.7
    ymax = 8.5
    nx = 3
    ny = 4
    elem_type = ${elem}
    boundary_name_prefix = block
    boundary_id_offset = 10
  []
  [block_id]
    type = SubdomainIDGenerator
    input = block
    subdomain_id = 2
  []

  [combined]
    type = MeshCollectionGenerator
    inputs = 'plank_id block_id'
  []
  [block_rename]
    type = RenameBlockGenerator
    input = combined
    old_block = '1 2'
    new_block = 'plank block'
  []

  [secondary]
    input = block_rename
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'block_left'
    new_block_id = '30'
    new_block_name = 'frictionless_secondary_subdomain'
  []
  [primary]
    input = secondary
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'plank_right'
    new_block_id = '20'
    new_block_name = 'frictionless_primary_subdomain'
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Variables]
  [disp_x]
    order = ${order}
    block = 'plank block'
    scaling = '${fparse 2.0 / (E_plank + E_block)}'
  []
  [disp_y]
    order = ${order}
    block = 'plank block'
    scaling = '${fparse 2.0 / (E_plank + E_block)}'
  []
  [temp]
    order = ${order}
    block = 'plank block'
    scaling = 1e-1
  []
  [thermal_lm]
    order = ${order}
    block = 'frictionless_secondary_subdomain'
    scaling = 1e-7
  []
  [frictionless_normal_lm]
    order = ${order}
    block = 'frictionless_secondary_subdomain'
    use_dual = true
  []
[]

[AuxVariables]
  [stress_xx]
    order = FIRST
    family = MONOMIAL
    block = 'plank block'
  []
  [stress_yy]
    order = FIRST
    family = MONOMIAL
    block = 'plank block'
  []
  [stress_xx_recovered]
    order = FIRST
    family = LAGRANGE
    block = 'plank block'
  []
  [stress_yy_recovered]
    order = FIRST
    family = LAGRANGE
    block = 'plank block'
  []
[]

[AuxKernels]
  [stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
    execute_on = 'timestep_end'
    block = 'plank block'
  []
  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
    execute_on = 'timestep_end'
    block = 'plank block'
  []
  [stress_xx_recovered]
    type = NodalPatchRecoveryAux
    variable = stress_xx_recovered
    nodal_patch_recovery_uo = stress_xx_patch
    execute_on = 'TIMESTEP_END'
    block = 'plank block'
  []
  [stress_yy_recovered]
    type = NodalPatchRecoveryAux
    variable = stress_yy_recovered
    nodal_patch_recovery_uo = stress_yy_patch
    execute_on = 'TIMESTEP_END'
    block = 'plank block'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [action]
    generate_output = 'stress_zz vonmises_stress hydrostatic_stress strain_xx strain_yy strain_zz'
    block = 'plank block'
    use_automatic_differentiation = false
    strain = FINITE
  []
[]

[Kernels]
  [hc]
    type = HeatConduction
    variable = temp
    use_displaced_mesh = true
    block = 'plank block'
  []
[]

[UserObjects]
  [weighted_gap_uo]
    type = LMWeightedGapUserObject
    primary_boundary = plank_right
    secondary_boundary = block_left
    primary_subdomain = frictionless_primary_subdomain
    secondary_subdomain = frictionless_secondary_subdomain
    lm_variable = frictionless_normal_lm
    disp_x = disp_x
    disp_y = disp_y
  []
  [stress_xx_patch]
    type = NodalPatchRecoveryMaterialProperty
    patch_polynomial_order = FIRST
    property = 'stress'
    component = '0 0'
    execute_on = 'NONLINEAR TIMESTEP_END'
    block = 'plank block'
  []
  [stress_yy_patch]
    type = NodalPatchRecoveryMaterialProperty
    patch_polynomial_order = FIRST
    property = 'stress'
    component = '1 1'
    execute_on = 'NONLINEAR TIMESTEP_END'
    block = 'plank block'
  []
[]

[Constraints]
  [weighted_gap_lm]
    type = ComputeWeightedGapLMMechanicalContact
    primary_boundary = plank_right
    secondary_boundary = block_left
    primary_subdomain = frictionless_primary_subdomain
    secondary_subdomain = frictionless_secondary_subdomain
    variable = frictionless_normal_lm
    disp_x = disp_x
    disp_y = disp_y
    use_displaced_mesh = true
    weighted_gap_uo = weighted_gap_uo
  []
  [normal_x]
    type = NormalMortarMechanicalContact
    primary_boundary = plank_right
    secondary_boundary = block_left
    primary_subdomain = frictionless_primary_subdomain
    secondary_subdomain = frictionless_secondary_subdomain
    variable = frictionless_normal_lm
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = weighted_gap_uo
  []
  [normal_y]
    type = NormalMortarMechanicalContact
    primary_boundary = plank_right
    secondary_boundary = block_left
    primary_subdomain = frictionless_primary_subdomain
    secondary_subdomain = frictionless_secondary_subdomain
    variable = frictionless_normal_lm
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = weighted_gap_uo
  []
  [thermal_contact]
    type = GapConductanceConstraint
    variable = thermal_lm
    secondary_variable = temp
    k = 1
    use_displaced_mesh = true
    primary_boundary = plank_right
    primary_subdomain = frictionless_primary_subdomain
    secondary_boundary = block_left
    secondary_subdomain = frictionless_secondary_subdomain
    displacements = 'disp_x disp_y'
  []
[]

[BCs]
  [left_temp]
    type = DirichletBC
    variable = temp
    boundary = 'plank_left'
    value = 400
  []

  [right_temp]
    type = DirichletBC
    variable = temp
    boundary = 'block_right'
    value = 300
  []

  [left_x]
    type = DirichletBC
    variable = disp_x
    boundary = plank_left
    value = 0.0
  []
  [left_y]
    type = DirichletBC
    variable = disp_y
    boundary = plank_bottom
    value = 0.0
  []
  [right_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = block_right
    function = '-0.04*sin(4*(t+1.5))+0.02'
    preset = false
  []
  [right_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = block_right
    function = '-t'
    preset = false
  []
[]

[Materials]
  [plank]
    type = ComputeIsotropicElasticityTensor
    block = 'plank'
    poissons_ratio = 0.3
    youngs_modulus = ${E_plank}
  []
  [block]
    type = ComputeIsotropicElasticityTensor
    block = 'block'
    poissons_ratio = 0.3
    youngs_modulus = ${E_block}
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
    block = 'plank block'
  []

  [heat_plank]
    type = HeatConductionMaterial
    block = plank
    thermal_conductivity = 2
    specific_heat = 1
  []
  [heat_block]
    type = HeatConductionMaterial
    block = block
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options = '-snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -snes_max_it'
  petsc_options_value = 'lu       NONZERO               1e-15                   20'
  end_time = 0.4
  dt = 0.1
  dtmin = 0.1
  timestep_tolerance = 1e-6
  line_search = 'none'
[]

[Postprocessors]
  [nl_its]
    type = NumNonlinearIterations
  []
  [total_nl_its]
    type = CumulativeValuePostprocessor
    postprocessor = nl_its
  []
  [l_its]
    type = NumLinearIterations
  []
  [total_l_its]
    type = CumulativeValuePostprocessor
    postprocessor = l_its
  []
  [contact]
    type = ContactDOFSetSize
    variable = frictionless_normal_lm
    subdomain = frictionless_secondary_subdomain
  []
  [avg_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
    block = 'block'
  []
  [avg_temp]
    type = ElementAverageValue
    variable = temp
    block = 'block'
  []
  [max_hydro]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    block = 'block'
  []
  [min_hydro]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    block = 'block'
    value_type = min
  []
  [avg_vonmises]
    type = ElementAverageValue
    variable = vonmises_stress
    block = 'block'
  []
  [max_vonmises]
    type = ElementExtremeValue
    variable = vonmises_stress
    block = 'block'
  []
  [min_vonmises]
    type = ElementExtremeValue
    variable = vonmises_stress
    block = 'block'
    value_type = min
  []
  [stress_xx_recovered]
    type = ElementExtremeValue
    variable = stress_xx_recovered
    block = 'block'
    value_type = max
  []
  [stress_yy_recovered]
    type = ElementExtremeValue
    variable = stress_yy_recovered
    block = 'block'
    value_type = max
  []
[]

[Outputs]
  exodus = true
  [comp]
    type = CSV
    show = 'contact avg_temp'
  []
  [out]
    type = CSV
  []
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Debug]
  show_var_residual_norms = true
[]

(modules/heat_transfer/test/tests/convective_heat_flux/t_inf.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 10
[]

[Variables]
  [./temp]
    initial_condition = 200.0
  [../]
[]

[Kernels]
  [./heat_dt]
    type = TimeDerivative
    variable = temp
  [../]
  [./heat_conduction]
    type = HeatConduction
    variable = temp
    diffusion_coefficient = 1
  [../]
  [./heat]
    type = BodyForce
    variable = temp
    value = 0
  [../]
[]

[BCs]
  [./right]
    type = ConvectiveHeatFluxBC
    variable = temp
    boundary = 'right'
    T_infinity = 100.0
    heat_transfer_coefficient = 1
    heat_transfer_coefficient_dT = 0
  [../]
[]

[Postprocessors]
  [./left_temp]
    type = SideAverageValue
    variable = temp
    boundary = left
    execute_on = 'TIMESTEP_END initial'
  [../]
  [./right_temp]
    type = SideAverageValue
    variable = temp
    boundary = right
  [../]
  [./right_flux]
    type = SideDiffusiveFluxAverage
    variable = temp
    boundary = right
    diffusivity = 1
  [../]
[]

[Executioner]
  type = Transient

  num_steps = 10
  dt = 1e1

  nl_abs_tol = 1e-12
[]

[Outputs]
  # csv = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_radiation/sphere.i)

#
# This problem is one of radiation boundary conditions between two
# spherical surfaces.
#
#            S(T1^4 - T2^4)                         R1^2
# flux1 = - ----------------   and flux2 = -flux1 * ----
#           1    1 - e2   R1^2                      R2^2
#           -- + ------ * ----
#           e1     e2     R2^2
#
# where S is the Stefan Boltzmann constant         5.67e-8 W/m^2/K^4
#       T1 is the temperature on the left surface  278 K
#       T2 is the temperature on the right surface 333 K
#       e1 is the emissivity for the left surface  0.8
#       e2 is the emissivity for the left surface  0.9
#       R1 is the radius of the inner surface      0.1 m
#       R2 is the radius of the outer surface      0.11 m
#
# Flux1:
# Exact           Code
# -------------   -------------
# -267.21 W/m^2   -267.02 W/m^2
#
# Flux2:
# Exact           Code
# -------------   -------------
#  220.83 W/m^2    220.70 W/m^2
#

thick = 0.01
R1 = 0.1
R2 = 0.11

[GlobalParams]
  order = second
  family = lagrange
[]

[Mesh]
  coord_type = RSPHERICAL
  [mesh1]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = edge3
    nx = 4
    xmin = '${fparse R1 - thick}'
    xmax = '${R1}'
    boundary_name_prefix = left
  []
  [mesh2]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = edge3
    nx = 4
    ny = 1
    xmin = '${R2}'
    xmax = '${fparse R2 + thick}'
    boundary_id_offset = 4
    boundary_name_prefix = right
  []
  [final]
    type = CombinerGenerator
    inputs = 'mesh1 mesh2'
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temperature
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = temperature
    boundary = left_left
    value = 278
  []
  [right]
    type = DirichletBC
    variable = temperature
    boundary = right_right
    value = 333
  []
[]

[Materials]
  [heat]
    type = HeatConductionMaterial
    thermal_conductivity = 200 # W/m/K
    specific_heat = 4.2e5
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temperature
    primary = left_right
    secondary = right_left
    emissivity_primary = 0.8
    emissivity_secondary = 0.9
    quadrature = true
    gap_conductivity = 1e-40 # requires a positive value
    gap_geometry_type = sphere
  []
[]

[Functions]
  [analytic_flux_1]
    type = ParsedFunction
    symbol_names = 'S        T1  T2  e1  e2  R1    R2'
    symbol_values = '5.67e-8 278 333 0.8 0.9 ${R1} ${R2}'
    expression = 'T14 := T1*T1*T1*T1;
                  T24 := T2*T2*T2*T2;
                  S*(T14-T24)/(1/e1+(1-e2)/e2*R1*R1/R2/R2)'
  []
  [analytic_flux_2]
    type = ParsedFunction
    symbol_names = 'S        T1  T2  e1  e2  R1    R2'
    symbol_values = '5.67e-8 278 333 0.8 0.9 ${R1} ${R2}'
    expression = 'T14 := T1*T1*T1*T1;
                  T24 := T2*T2*T2*T2;
                  -S*(T14-T24)/(1/e1+(1-e2)/e2*R1*R1/R2/R2)*R1*R1/R2/R2'
  []
[]

[Postprocessors]
  [code_flux_1]
    type = SideDiffusiveFluxAverage
    variable = temperature
    boundary = left_right
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [analytic_flux_1]
    type = FunctionValuePostprocessor
    function = analytic_flux_1
    execute_on = 'initial timestep_end'
  []
  [error_1]
    type = ParsedPostprocessor
    pp_names = 'code_flux_1 analytic_flux_1'
    expression = '(analytic_flux_1 - code_flux_1)/analytic_flux_1*100'
    execute_on = 'initial timestep_end'
  []
  [code_flux_2]
    type = SideDiffusiveFluxAverage
    variable = temperature
    boundary = right_left
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [analytic_flux_2]
    type = FunctionValuePostprocessor
    function = analytic_flux_2
    execute_on = 'initial timestep_end'
  []
  [error_2]
    type = ParsedPostprocessor
    pp_names = 'code_flux_2 analytic_flux_2'
    expression = '(analytic_flux_2 - code_flux_2)/analytic_flux_2*100'
    execute_on = 'initial timestep_end'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = newton

  num_steps = 1
  dt = 1
  end_time = 1

  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-10
[]

[Outputs]
  csv = true
[]

(modules/combined/test/tests/adaptive_timestepping/adapt_tstep_function_force_step.i)

# This is a test designed to evaluate the cabability of the
# IterationAdaptiveDT TimeStepper to adjust time step size according to
# a function.  For example, if the power input function for a BISON
# simulation rapidly increases or decreases, the IterationAdaptiveDT
# TimeStepper should take time steps small enough to capture the
# oscillation.

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  volumetric_locking_correction = true
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  file = 1hex8_10mm_cube.e
[]

[Functions]
  [./Fiss_Function]
    type = PiecewiseLinear
    data_file = blip.csv
    format = columns
  [../]
[]

[Variables]
  [./disp_x]
  [../]

  [./disp_y]
  [../]

  [./disp_z]
  [../]

  [./temp]
    initial_condition = 300.0
  [../]
[]


[Physics/SolidMechanics/QuasiStatic]
  [./all]
    strain = FINITE
    incremental = true
    eigenstrain_names = thermal_expansion
    add_variables  = true
    generate_output = 'vonmises_stress'
    temperature = temp
  [../]
[]


[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]

  [./heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]

  [./heat_source]
     type = HeatSource
     variable = temp
     value = 1.0
     function = Fiss_Function
  [../]
[]

[BCs]
 [./bottom_temp]
   type = DirichletBC
   variable = temp
   boundary = 1
   value = 300
 [../]
 [./top_bottom_disp_x]
   type = DirichletBC
   variable = disp_x
   boundary = '1'
   value = 0
 [../]
 [./top_bottom_disp_y]
   type = DirichletBC
   variable = disp_y
   boundary = '1'
   value = 0
 [../]
 [./top_bottom_disp_z]
   type = DirichletBC
   variable = disp_z
   boundary = '1'
   value = 0
 [../]
[]

[Materials]
 [./thermal]
    type = HeatConductionMaterial
    temp = temp
    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 300e6
    poissons_ratio = .3
  [../]

  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]

  [./thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 5e-6
    stress_free_temperature = 300.0
    temperature = temp
    eigenstrain_name = thermal_expansion
  [../]

  [./density]
    type = Density
    density = 10963.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  verbose = true
  nl_abs_tol = 1e-10
  start_time = 0.0
  num_steps = 50000

  end_time = 5.1e3
  [./TimeStepper]
    type = IterationAdaptiveDT
    timestep_limiting_function = Fiss_Function
    max_function_change = 3e20
    force_step_every_function_point = true
    dt = 1e2
  [../]
[]

[Postprocessors]
  [./Temperature_of_Block]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./vonMises]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  [./out]
    type = Exodus
    elemental_as_nodal = true
  [../]
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(modules/combined/test/tests/umat/gap_heat_transfer_umat.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  temperature = temp
[]

[Mesh]
  file = gap_heat_transfer_mesh.e
[]

[Functions]
  [disp]
    type = PiecewiseLinear
    x = '0 2.0'
    y = '0 1.0'
  []
  [temp]
    type = PiecewiseLinear
    x = '0     1'
    y = '273 2000'
  []
  [pressure_function]
    type = PiecewiseLinear
    x = '0     1'
    y = '0 200'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [temp]
    initial_condition = 273
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 2
    secondary = 3
    emissivity_primary = 0
    emissivity_secondary = 0
  []
[]

[Physics/SolidMechanics/QuasiStatic/All]
  volumetric_locking_correction = true
  strain = FINITE
  generate_output = 'strain_yy stress_yy'
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
[]

[BCs]
  [move_right]
    type = FunctionDirichletBC
    boundary = '3'
    variable = disp_x
    function = disp
  []

  [fixed_x]
    type = DirichletBC
    boundary = '1'
    variable = disp_x
    value = 0
  []
  [fixed_y]
    type = DirichletBC
    boundary = '1 2 4'
    variable = disp_y
    value = 0
  []
  [fixed_z]
    type = DirichletBC
    boundary = '1 2 3 4'
    variable = disp_z
    value = 0
  []

  [temp_bottom]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  []
  [temp_top]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  []
  [Pressure]
    [example]
      boundary = 3
      function = pressure_function
    []
  []
[]

[Materials]
  # 1. Active for umat calculation
  [umat]
    type = AbaqusUMATStress
    constant_properties = '1.0e6 0.3'
    plugin = '../../../../solid_mechanics/test/plugins/elastic_temperature'
    num_state_vars = 0
    temperature = temp
    use_one_based_indexing = true
  []
  #  2. Active for reference MOOSE computations
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2'
    base_name = 'base'
    youngs_modulus = 1e6
    poissons_ratio = 0.3
  []
  [temp_dependent_elasticity_tensor]
    type = CompositeElasticityTensor
    block = '1 2'
    coupled_variables = temp
    tensors = 'base'
    weights = 'prefactor_material'
  []
  [prefactor_material_block]
    type = DerivativeParsedMaterial
    block = '1 2'
    property_name = prefactor_material
    coupled_variables = temp
    expression = '273/(temp)'
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2'
  []
  [heat]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 1.0
  []
  [density]
    type = Density
    block = '1 2'
    density = 1.0
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  start_time = 0.0
  dt = 0.1
  end_time = 2.0
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/heat_convection/heat_convection_rz_test.i)

# Test cases for convective boundary conditions. TKLarson, 11/01/11, rev. 0.
# Input file for htc_2dtest1

# TKLarson
# 11/01/11
# Revision 0
#
# Goals of this test are:
#  1) show that expected results ensue from application of convective boundary conditions
# Convective boundary condition:
#  q = h*A*(Tw - Tf)
#  where
#    q - heat transfer rate (w)
#    h - heat transfer coefficient (w/m^2-K)
#    A - surface area (m^2)
#    Tw - surface temperature (K)
#    Tf - fluid temperature adjacent to the surface (K)
# The heat transfer coefficient (h) is input as a variable called 'rate'
# Tf is a two valued function specified by 'initial' and 'final' along with a variable
#  called 'duration,' the length of time in seconds that it takes initial to linearly ramp
#  to 'final.'

# The mesh for this test case is based on an ASTM standard for the so-called Brazillian Cylinder test
# (ASTM International, Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete
# Specimens, C 496/C 496M-04, 2004) (because I already had a version of the model).  While the
# Brazillian Cylinder test is for dynamic tensile testing of concrete, the model works for the present
# purposes.  The model is 2-d RZ coordinates.
#
# Brazillian Cylinder sample dimensions:
#       L = 20.3 cm, 0.203 m, (8 in)
#       r = 5.08 cm, 0.0508 m, (2 in)

# Material properties are:
#   density = 2405.28 km/m^3
#   specific heat = 826.4 J/kg-K
#   thermal conductivity 1.937 w/m-K
#  alpha (thermal conductivity/(density*specific heat) is then 9.74e-7 m^2/s
#
# Initial cylinder temperature is room temperature 294.26 K (70 F)
# The initial fluid temperature is room temperature. We will ramp it to 477.6 K (400 F) in 10 minutes.
# We will use a natural convection h (284 w/m^2-K (50 BTU/hr-ft^2-F)) on all faces of the cylinder.
# This is akin to putting the cylinder in an oven (nonconvection type) and turning the oven on.

# What we expect for this problem:
#  1) Use of h = 284 should cause the cylinder to slowly warm up
#  2) The fluid temperature should rise from initial (294 K) to final (477 K) in 600 s.
#  3) 1) and 2) should cause the cylinder to become soaked at 477.6 K after sufficient time(i.e. ~ 1/2 hr).
# This is a simple thermal soak problem.

[Mesh]    # Mesh Start
# 10cm x 20cm cylinder not so detailed mesh, 2 radial, 6 axial nodes
# Only one block (Block 1), all concrete
# Sideset 1 - top of cylinder, Sideset 2 - length of cylinder, Sideset 3 - bottom of cylinder
  file = heat_convection_rz_mesh.e
  coord_type = RZ
[]    # Mesh END

[Variables]  # Variables Start
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 294.26 # Initial cylinder temperature
  [../]

[]    # Variables END


[Kernels]  # Kernels Start
  [./heat]
    type = HeatConduction
    variable = temp
  [../]

  [./heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]

[]    # Kernels END


[BCs]    # Boundary Conditions Start
# Heat transfer coefficient on outer cylinder radius and ends
  [./convective_clad_surface]    # Convective Start
         type = ConvectiveFluxBC  # Convective flux, e.g. q'' = h*(Tw - Tf)
         boundary = '1 2 3'    # BC applied on top, along length, and bottom
         variable = temp
   rate = 284.      # (w/m^2-K)[50 BTU/hr/-ft^2-F]
          # the above h is a reasonable natural convection value
         initial = 294.26    # initial ambient (lab or oven) temperature (K)
         final = 477.6      # final ambient (lab or oven) temperature (K)
   duration = 600.    # length of time in seconds that it takes the ambient
          #   temperature to ramp from initial to final
  [../]          # Convective End

[]    # BCs END

[Materials]    # Materials Start
  [./thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 826.4
#    thermal_conductivity = 1.937  # this makes alpha 9.74e-7 m^2/s
#    thermal_conductivity = 19.37  # this makes alpha 9.74e-6 m^2/s
          # thermal conductivity arbitrarily increased by a decade to
          #    make the cylinder thermally soak faster (only for the purposes
          #    of this test problem
    thermal_conductivity = 193.7  # this makes alpha 9.74e-5 m^2/s
          # thermal conductivity arbitrarily increased by 2 decade to
          #    make the cylinder thermally soak faster (only for the purposes
          #    of this test problem

  [../]
  [./density]
    type = Density
    block = 1
    density = 2405.28
  [../]

[]      # Materials END

[Executioner]    # Executioner Start
   type = Transient
#   type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'


   petsc_options = '-snes_ksp_ew '
   petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type'
   petsc_options_value = '70 hypre boomeramg'
   l_max_its = 60
   nl_rel_tol = 1e-8
   nl_abs_tol = 1e-10
   l_tol = 1e-5

   start_time = 0.0
  dt = 60.
  num_steps = 20  # Total run time 1200 s

[]      # Executioner END

[Outputs]    # Output Start
  # Output Start
  file_base = out_rz
  exodus = true
[]      # Output END
#      # Input file END

(modules/heat_transfer/tutorials/introduction/therm_step01.i)

#
# Initial single block thermal input
# https://mooseframework.inl.gov/modules/heat_transfer/tutorials/introduction/therm_step01.html
#

[Mesh]
  [generated]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 2
    ymax = 1
  []
[]

[Variables]
  [T]
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 45.0
  []
[]

[Executioner]
  type = Transient
  end_time = 5
  dt = 1
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/code_verification/cartesian_test_no1.i)

# Problem I.1
#
# An infinite plate with constant thermal conductivity k and
# internal heat generation q. It is exposed on each boundary
# to a constant temperature: u(0) = ui and u(L) = uo.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    nx = 1
  [../]
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./exact]
    type = ParsedFunction
    symbol_names = 'q L k ui uo'
    symbol_values = '1200 1 12 100 0'
    expression = 'ui + (uo-ui)*x/L + (q/k) * x * (L-x) / 2'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
  [./heatsource]
    type = HeatSource
    function = 1200
    variable = u
  [../]
[]

[BCs]
  [./ui]
    type = DirichletBC
    boundary = left
    variable = u
    value = 100
  [../]
  [./uo]
    type = DirichletBC
    boundary = right
    variable = u
    value = 0
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat thermal_conductivity'
    prop_values = '1.0 1.0 12.0'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/combined/test/tests/break_mesh_interface_contact/break_mesh_interface_contact.i)

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    nx = 5
    ny = 5
    dim = 2
  []
  [block1]
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '0 0 0'
    top_right = '0.5 1 0'
    input = gen
  []
  [block2]
    type = SubdomainBoundingBoxGenerator
    block_id = 2
    bottom_left = '0.5 0 0'
    top_right = '1 1 0'
    input = block1
  []
  [breakmesh]
    input = block2
    type = BreakMeshByBlockGenerator
    block_pairs = '1 2'
    split_interface = true
    add_interface_on_two_sides = true
  []
[]

[Variables]
  [temperature]
  []
  [disp_x]
  []
  [disp_y]
  []
[]

[Kernels]
  [thermal_cond]
    type = HeatConduction
    variable = temperature
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  generate_output = 'stress_xx stress_yy strain_xx strain_yy'
  add_variables = true
  strain = FINITE
  incremental = true
  [block1]
    block = 1
  []
  [block2]
    block = 2
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temperature
    primary = Block1_Block2
    secondary = Block2_Block1
    emissivity_primary = 0
    emissivity_secondary = 0
    quadrature = true
    gap_conductivity = 1
  []
[]

[Contact]
  [mechanical]
    primary = Block1_Block2
    secondary = Block2_Block1
    penalty = 1000
    model = coulomb
    friction_coefficient = 0.5
    formulation = tangential_penalty
    tangential_tolerance = 0.1
  []
[]

[BCs]
  [left_temp]
    type = DirichletBC
    value = 100
    variable = temperature
    boundary = left
  []
  [right_temp]
    type = DirichletBC
    value = 0
    variable = temperature
    boundary = right
  []
  [left_disp_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = left
    function = 0
  []
  [left_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = left
    value = 0.0
  []
  [right_disp_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = right
    function = '-t'
  []
  [right_disp_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = right
    function = '0'
  []
[]

[Materials]
  [thermal_cond]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = 1
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    poissons_ratio = 0.3
    youngs_modulus = 100
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Dampers]
  [contact_slip]
    type = ContactSlipDamper
    secondary = Block1_Block2
    primary = Block2_Block1
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu mumps'

  line_search = none

  nl_rel_tol = 1e-9
  nl_abs_tol = 1e-9

  l_tol = 1e-4
  l_max_its = 50

  nl_max_its = 20

  start_time = 0.0

  num_steps = 2

  dtmin = 1e-8
  dt = 1e-2
  automatic_scaling = true
[]

[Outputs]
  print_linear_residuals = false
  time_step_interval = 1
  csv = false
  perf_graph = false
  exodus = true
[]

(modules/combined/test/tests/stateful_mortar_constraints/stateful_mortar_npr.i)

E_block = 1e7
E_plank = 1e7
elem = QUAD4
order = FIRST

[Mesh]
  patch_size = 80
  patch_update_strategy = auto
  [plank]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -0.3
    xmax = 0.3
    ymin = -10
    ymax = 10
    nx = 2
    ny = 67
    elem_type = ${elem}
    boundary_name_prefix = plank
  []
  [plank_id]
    type = SubdomainIDGenerator
    input = plank
    subdomain_id = 1
  []
  [block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0.31
    xmax = 0.91
    ymin = 7.7
    ymax = 8.5
    nx = 3
    ny = 4
    elem_type = ${elem}
    boundary_name_prefix = block
    boundary_id_offset = 10
  []
  [block_id]
    type = SubdomainIDGenerator
    input = block
    subdomain_id = 2
  []

  [combined]
    type = MeshCollectionGenerator
    inputs = 'plank_id block_id'
  []
  [block_rename]
    type = RenameBlockGenerator
    input = combined
    old_block = '1 2'
    new_block = 'plank block'
  []

  [secondary]
    input = block_rename
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'block_left'
    new_block_id = '30'
    new_block_name = 'frictionless_secondary_subdomain'
  []
  [primary]
    input = secondary
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'plank_right'
    new_block_id = '20'
    new_block_name = 'frictionless_primary_subdomain'
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Variables]
  [disp_x]
    order = ${order}
    block = 'plank block'
    scaling = '${fparse 2.0 / (E_plank + E_block)}'
  []
  [disp_y]
    order = ${order}
    block = 'plank block'
    scaling = '${fparse 2.0 / (E_plank + E_block)}'
  []
  [temp]
    order = ${order}
    block = 'plank block'
    scaling = 1e-1
  []
  [thermal_lm]
    order = ${order}
    block = 'frictionless_secondary_subdomain'
    scaling = 1e-7
  []
  [frictionless_normal_lm]
    order = ${order}
    block = 'frictionless_secondary_subdomain'
    use_dual = true
  []
[]

[AuxVariables]
  [stress_xx]
    order = FIRST
    family = MONOMIAL
    block = 'plank block'
  []
  [stress_yy]
    order = FIRST
    family = MONOMIAL
    block = 'plank block'
  []
  [stress_xx_recovered]
    order = FIRST
    family = LAGRANGE
    block = 'plank block'
  []
  [stress_yy_recovered]
    order = FIRST
    family = LAGRANGE
    block = 'plank block'
  []
[]

[AuxKernels]
  [stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
    execute_on = 'timestep_end'
    block = 'plank block'
  []
  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
    execute_on = 'timestep_end'
    block = 'plank block'
  []
  [stress_xx_recovered]
    type = NodalPatchRecoveryAux
    variable = stress_xx_recovered
    nodal_patch_recovery_uo = stress_xx_patch
    execute_on = 'TIMESTEP_END'
    block = 'plank block'
  []
  [stress_yy_recovered]
    type = NodalPatchRecoveryAux
    variable = stress_yy_recovered
    nodal_patch_recovery_uo = stress_yy_patch
    execute_on = 'TIMESTEP_END'
    block = 'plank block'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [action]
    generate_output = 'stress_zz vonmises_stress hydrostatic_stress strain_xx strain_yy strain_zz'
    block = 'plank block'
    use_automatic_differentiation = false
    strain = FINITE
  []
[]

[Kernels]
  [hc]
    type = HeatConduction
    variable = temp
    use_displaced_mesh = true
    block = 'plank block'
  []
[]

[UserObjects]
  [weighted_gap_uo]
    type = LMWeightedGapUserObject
    primary_boundary = plank_right
    secondary_boundary = block_left
    primary_subdomain = frictionless_primary_subdomain
    secondary_subdomain = frictionless_secondary_subdomain
    lm_variable = frictionless_normal_lm
    disp_x = disp_x
    disp_y = disp_y
  []
  [stress_xx_patch]
    type = NodalPatchRecoveryMaterialProperty
    patch_polynomial_order = FIRST
    property = 'stress'
    component = '0 0'
    execute_on = 'NONLINEAR TIMESTEP_END'
    block = 'plank block'
  []
  [stress_yy_patch]
    type = NodalPatchRecoveryMaterialProperty
    patch_polynomial_order = FIRST
    property = 'stress'
    component = '1 1'
    execute_on = 'NONLINEAR TIMESTEP_END'
    block = 'plank block'
  []
[]

[Constraints]
  [weighted_gap_lm]
    type = ComputeWeightedGapLMMechanicalContact
    primary_boundary = plank_right
    secondary_boundary = block_left
    primary_subdomain = frictionless_primary_subdomain
    secondary_subdomain = frictionless_secondary_subdomain
    variable = frictionless_normal_lm
    disp_x = disp_x
    disp_y = disp_y
    use_displaced_mesh = true
    weighted_gap_uo = weighted_gap_uo
  []
  [normal_x]
    type = NormalMortarMechanicalContact
    primary_boundary = plank_right
    secondary_boundary = block_left
    primary_subdomain = frictionless_primary_subdomain
    secondary_subdomain = frictionless_secondary_subdomain
    variable = frictionless_normal_lm
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = weighted_gap_uo
  []
  [normal_y]
    type = NormalMortarMechanicalContact
    primary_boundary = plank_right
    secondary_boundary = block_left
    primary_subdomain = frictionless_primary_subdomain
    secondary_subdomain = frictionless_secondary_subdomain
    variable = frictionless_normal_lm
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = weighted_gap_uo
  []
  [thermal_contact]
    type = GapConductanceStatefulConstraint
    variable = thermal_lm
    secondary_variable = temp
    k = 0.0001
    use_displaced_mesh = true
    primary_boundary = plank_right
    primary_subdomain = frictionless_primary_subdomain
    secondary_boundary = block_left
    secondary_subdomain = frictionless_secondary_subdomain
    displacements = 'disp_x disp_y'
    stateful_variable = stress_xx_recovered
  []
[]

[BCs]
  [left_temp]
    type = DirichletBC
    variable = temp
    boundary = 'plank_left'
    value = 400
  []

  [right_temp]
    type = DirichletBC
    variable = temp
    boundary = 'block_right'
    value = 300
  []

  [left_x]
    type = DirichletBC
    variable = disp_x
    boundary = plank_left
    value = 0.0
  []
  [left_y]
    type = DirichletBC
    variable = disp_y
    boundary = plank_bottom
    value = 0.0
  []
  [right_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = block_right
    function = '-0.04*sin(4*(t+1.5))+0.02'
    preset = false
  []
  [right_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = block_right
    function = '-t'
    preset = false
  []
[]

[Materials]
  [plank]
    type = ComputeIsotropicElasticityTensor
    block = 'plank'
    poissons_ratio = 0.3
    youngs_modulus = ${E_plank}
  []
  [block]
    type = ComputeIsotropicElasticityTensor
    block = 'block'
    poissons_ratio = 0.3
    youngs_modulus = ${E_block}
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
    block = 'plank block'
  []

  [heat_plank]
    type = HeatConductionMaterial
    block = plank
    thermal_conductivity = 2
    specific_heat = 1
  []
  [heat_block]
    type = HeatConductionMaterial
    block = block
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options = '-snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -snes_max_it'
  petsc_options_value = 'lu       NONZERO               1e-15                   20'
  end_time = 0.5
  dt = 0.1
  dtmin = 0.1
  timestep_tolerance = 1e-6
  line_search = 'none'
[]

[Postprocessors]
  [avg_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
    block = 'block'
  []
  [avg_temp]
    type = ElementAverageValue
    variable = temp
    block = 'block'
  []
  [max_hydro]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    block = 'block'
  []
  [min_hydro]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    block = 'block'
    value_type = min
  []
  [avg_vonmises]
    type = ElementAverageValue
    variable = vonmises_stress
    block = 'block'
  []
  [max_vonmises]
    type = ElementExtremeValue
    variable = vonmises_stress
    block = 'block'
  []
  [min_vonmises]
    type = ElementExtremeValue
    variable = vonmises_stress
    block = 'block'
    value_type = min
  []
  [stress_xx_recovered]
    type = ElementExtremeValue
    variable = stress_xx_recovered
    block = 'block'
    value_type = max
  []
  [stress_yy_recovered]
    type = ElementExtremeValue
    variable = stress_yy_recovered
    block = 'block'
    value_type = max
  []
  [min_temperature]
    type = ElementExtremeValue
    variable = temp
    block = 'plank'
    value_type = min
  []
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
  []
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Debug]
  show_var_residual_norms = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/cyl3D.i)

#
# 3D Cylindrical Gap Heat Transfer Test.
#
# This test exercises 3D gap heat transfer for a constant conductivity gap.
#
# The mesh consists of an inner solid cylinder of radius = 1 unit, and outer
# hollow cylinder with an inner radius of 2. In other words, the gap between
# them is 1 radial unit in length.
#
# The conductivity of both cylinders is set very large to achieve a uniform
# temperature in each cylinder. The temperature of the center node of the
# inner cylinder is ramped from 100 to 200 over one time unit. The temperature
# of the outside of the outer, hollow cylinder is held fixed at 100.
#
# A simple analytical solution is possible for the integrated heat flux
# between the inner and outer cylinders:
#
#  Integrated Flux = (T_left - T_right) * (gapK/(r*ln(r2/r1))) * Area
#
# For gapK = 1 (default value)
#
# The area is taken as the area of the secondary (inner) surface:
#
# Area = 2 * pi * h * r, where h is the height of the cylinder.
#
# The integrated heat flux across the gap at time 1 is then:
#
# 2*pi*h*k*delta_T/(ln(r2/r1))
# 2*pi*1*1*100/(ln(2/1)) = 906.5 watts
#
# For comparison, see results from the integrated flux post processors.
# This simulation makes use of symmetry, so only 1/4 of the cylinders is meshed
# As such, the integrated flux from the post processors is 1/4 of the total,
# or 226.6 watts.
# The value coming from the post processor is slightly less than this
# but converges as mesh refinement increases.
#
# Simulating contact is challenging. Regression tests that exercise
# contact features can be difficult to solve consistently across multiple
# platforms. While designing these tests, we felt it worth while to note
# some aspects of these tests. The following applies to:
# sphere3D.i, sphere2DRZ.i, cyl2D.i, and cyl3D.i.
# 1. We decided that to perform consistently across multiple platforms we
# would use very small convergence tolerance. In this test we chose an
# nl_rel_tol of 1e-12.
# 2. Due to such a high value for thermal conductivity (used here so that the
# domains come to a uniform temperature) the integrated flux at time = 0
# was relatively large (the value coming from SideIntegralFlux =
#  -_diffusion_coef[_qp]*_grad_u[_qp]*_normals[_qp] where the diffusion coefficient
# here is thermal conductivity).
# Even though _grad_u[_qp] is small, in this case the diffusion coefficient
# is large. The result is a number that isn't exactly zero and tends to
# fail exodiff. For this reason the parameter execute_on = initial should not
# be used. That parameter is left to default settings in these regression tests.
#
 [GlobalParams]
  order = SECOND
  family = LAGRANGE
  []


[Mesh]
  file = cyl3D.e
[]

[Functions]

  [./temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  [../]
[]

[Variables]
  [./temp]
   initial_condition = 100
  [../]
[]

[AuxVariables]
  [./gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]


[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temp
  [../]
[]

[AuxKernels]
  [./gap_cond]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_conductance
    boundary = 2
  [../]
[]

[Materials]
  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 1000000.0
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductivity = 1
    quadrature = true
    gap_geometry_type = CYLINDER
    cylinder_axis_point_1 = '0 0 0'
    cylinder_axis_point_2 = '0 1 0'
  [../]
[]

[BCs]
  [./mid]
    type = FunctionDirichletBC
    boundary = 5
    variable = temp
    function = temp
  [../]
  [./temp_far_right]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
[]

[Executioner]
  type = Transient

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

  [./Quadrature]
     order = fifth
     side_order = seventh
  [../]

[]

[Outputs]
  exodus = true
   [./Console]
    type = Console
   [../]
[]

[Postprocessors]
  [./temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  [../]

  [./temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  [../]

  [./flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  [../]

  [./flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  [../]
[]

(modules/heat_transfer/test/tests/code_verification/cylindrical_test_no1.i)

# Problem II.1
#
# An infinitely long hollow cylinder has an inner radius ri and
# outer radius ro. It has a constant thermal conductivity k and
# internal heat generation q. It is allowed to reach thermal
# equilibrium while being exposed to constant temperatures on its
# inside and outside boundaries: u(ri) = ui and u(ro) = uo.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    xmin = 0.2
    nx = 4
  [../]
  coord_type = RZ
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./exact]
    type = ParsedFunction
    symbol_names = 'ri ro ui uo'
    symbol_values = '0.2 1.0 300 0'
    expression = '( uo * log(ri) - ui * log(ro) + (ui-uo) * log(x) ) / log(ri/ro)'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
[]

[BCs]
  [./ui]
    type = DirichletBC
    boundary = left
    variable = u
    value = 300
  [../]
  [./uo]
    type = DirichletBC
    boundary = right
    variable = u
    value = 0
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat thermal_conductivity'
    prop_values = '1.0 1.0 5.0'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/parallel_element_pps_test/parallel_element_pps_test.i)

[Mesh]
  file = block_map.e
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  active = 'heat ie'

  [./heat]
    type = HeatConduction
    variable = u
  [../]

  [./ie]
    type = SpecificHeatConductionTimeDerivative
    variable = u
  [../]
[]

[BCs]
  active = 'bottom top'

  [./bottom]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 0.0
  [../]

  [./top]
    type = DirichletBC
    variable = u
    boundary = 2
    value = 1.0
  [../]
[]

[Postprocessors]
   active = 'p_1 p_2 p_3 p_all'

  [./p_1]
    type = ElementIntegralVariablePostprocessor
    variable = u
    block = '1'
  [../]

  [./p_2]
    type = ElementIntegralVariablePostprocessor
    variable = u
    block = '2'
  [../]

  [./p_3]
    type = ElementIntegralVariablePostprocessor
    variable = u
    block = '3'
  [../]

  [./p_all]
    type = ElementIntegralVariablePostprocessor
    variable = u
    block = '1 2 3'
  [../]
[]


[Materials]
  [./constant]
    type = GenericConstantMaterial
    block = 1
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '1.0 1.0 1.0'
  [../]

  [./constant2]
    type = GenericConstantMaterial
    block = 2
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '0.8 0.8 0.8'
  [../]

  [./constant3]
    type = GenericConstantMaterial
    block = 3
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '5 5 5'
  [../]
[]


[Executioner]
  type = Transient

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'



  start_time = 0.0
  num_steps = 5
  dt = .1
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/combined/tutorials/introduction/thermal_mechanical_contact/thermomech_cont_step02.i)

#
# Three shell thermo mechanical contact
# https://mooseframework.inl.gov/modules/combined/tutorials/introduction/step02.html
#

[GlobalParams]
  displacements = 'disp_x disp_y'
  block = '0 1 2'
[]

[Mesh]
  # inner cylinder
  [inner]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 40
    xmax = 1
    ymin = -1.75
    ymax = 1.75
    boundary_name_prefix = inner
  []

  # middle shell with subdomain ID 1
  [middle_elements]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 40
    xmin = 1.1
    xmax = 2.1
    ymin = -2.5
    ymax = 2.5
    boundary_name_prefix = middle
    boundary_id_offset = 4
  []
  [middle]
    type = SubdomainIDGenerator
    input = middle_elements
    subdomain_id = 1
  []

  # outer shell with subdomain ID 2
  [outer_elements]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 48
    xmin = 2.2
    xmax = 3.2
    ymin = -3
    ymax = 3
    boundary_name_prefix = outer
    boundary_id_offset = 8
  []
  [outer]
    type = SubdomainIDGenerator
    input = outer_elements
    subdomain_id = 2
  []

  [collect_meshes]
    type = MeshCollectionGenerator
    inputs = 'inner middle outer'
  []

  # add set of 3 nodes to remove rigid body modes for y-translation in each block
  [pin]
    type = ExtraNodesetGenerator
    input = collect_meshes
    new_boundary = pin
    coord = '0 0 0; 1.6 0 0; 2.7 0 0'
  []

  patch_update_strategy = iteration

  # switch to an axisymmetric coordinate system
  coord_type = RZ
[]

[Variables]
  # temperature field variable (first order Lagrange by default)
  [T]
  []
  # temperature lagrange multipliers
  [Tlm1]
    block = 'inner_gap_secondary_subdomain'
  []
  [Tlm2]
    block = 'outer_gap_secondary_subdomain'
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
  [dTdt]
    type = HeatConductionTimeDerivative
    variable = T
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    strain = FINITE
    eigenstrain_names = thermal
    generate_output = 'vonmises_stress stress_xx strain_xx stress_yy strain_yy'
    volumetric_locking_correction = true
    temperature = T
  []
[]

[Contact]
  [inner_gap]
    primary = middle_left
    secondary = inner_right
    model = frictionless
    formulation = mortar
    c_normal = 1e+0
  []
  [outer_gap]
    primary = outer_left
    secondary = middle_right
    model = frictionless
    formulation = mortar
    c_normal = 1e+0
  []
[]

[Constraints]
  # thermal contact constraint
  [Tlm1]
    type = GapConductanceConstraint
    variable = Tlm1
    secondary_variable = T
    use_displaced_mesh = true
    k = 1e-1
    primary_boundary = middle_left
    primary_subdomain = inner_gap_secondary_subdomain
    secondary_boundary = inner_right
    secondary_subdomain = inner_gap_primary_subdomain
  []
  [Tlm2]
    type = GapConductanceConstraint
    variable = Tlm2
    secondary_variable = T
    use_displaced_mesh = true
    k = 1e-1
    primary_boundary = outer_left
    primary_subdomain = outer_gap_secondary_subdomain
    secondary_boundary = middle_right
    secondary_subdomain = outer_gap_primary_subdomain
  []
[]

[BCs]
  [center_axis_fix]
    type = DirichletBC
    variable = disp_x
    boundary = 'inner_left'
    value = 0
  []
  [y_translation_fix]
    type = DirichletBC
    variable = disp_y
    boundary = 'pin'
    value = 0
  []
  [heat_center]
    type = FunctionDirichletBC
    variable = T
    boundary = 'inner_left'
    function = t*40
  []
  [cool_right]
    type = DirichletBC
    variable = T
    boundary = 'outer_right'
    value = 0
  []
[]

[Materials]
  [eigen_strain_inner]
    type = ComputeThermalExpansionEigenstrain
    eigenstrain_name = thermal
    temperature = T
    thermal_expansion_coeff = 1e-3
    stress_free_temperature = 0
    block = 0
  []
  [eigen_strain_middle]
    type = ComputeThermalExpansionEigenstrain
    eigenstrain_name = thermal
    temperature = T
    thermal_expansion_coeff = 2e-4
    stress_free_temperature = 0
    block = 1
  []
  [eigen_strain_outer]
    type = ComputeThermalExpansionEigenstrain
    eigenstrain_name = thermal
    temperature = T
    thermal_expansion_coeff = 1e-5
    stress_free_temperature = 0
    block = 2
  []

  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
  []

  # thermal properties
  [thermal_conductivity_0]
    type = HeatConductionMaterial
    thermal_conductivity = 50
    specific_heat = 1
    block = 0
  []
  [thermal_conductivity_1]
    type = HeatConductionMaterial
    thermal_conductivity = 5
    specific_heat = 1
    block = 1
  []
  [thermal_conductivity_2]
    type = HeatConductionMaterial
    thermal_conductivity = 1
    specific_heat = 1
    block = 2
  []
  [density]
    type = Density
    density = 1
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

# [Debug]
#   show_var_residual_norms = true
# []

[Executioner]
  type = Transient
  solve_type = PJFNK
  line_search = none
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       nonzero              '
  snesmf_reuse_base = false
  end_time = 7
  dt = 0.05

  nl_rel_tol = 1e-08
  nl_abs_tol = 1e-50

  [Predictor]
    type = SimplePredictor
    scale = 0.5
  []
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
  perf_graph = true
[]

(tutorials/tutorial03_verification/app/test/tests/step03_analytical/1d_analytical.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 1
    xmax = 0.03
    nx = 200
  []
[]

[Variables]
  [T]
  []
[]

[ICs]
  [T_O]
    type = ConstantIC
    variable = T
    value = 300
  []
[]

[Kernels]
  [T_time]
    type = HeatConductionTimeDerivative
    variable = T
    density_name = 7800
    specific_heat = 450
  []
  [T_cond]
    type = HeatConduction
    variable = T
    diffusion_coefficient = 80.2
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = T
    boundary = left
    value = 7e5
  []
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = NEWTON
  dt = 0.01
  end_time = 1
[]

[Outputs]
  exodus = true
  csv = true
[]

[Functions]
  [T_exact]
    type = ParsedFunction
    symbol_names = 'k    rho  cp  T0  qs'
    symbol_values = '80.2 7800 450 300 7e5'
    expression = 'T0 + '
            'qs/k*(2*sqrt(k/(rho*cp)*t/pi)*exp(-x^2/(4*k/(rho*cp)*(t+1e-50))) - '
            'x*(1-erf(x/(2*sqrt(k/(rho*cp)*(t+1e-50))))))'
  []
[]

[Postprocessors]
  [error]
    type = NodalL2Error
    variable = T
    function = T_exact
  []
  [h]
    type = AverageElementSize
  []
[]


[VectorPostprocessors]
  [T_exact]
    type = LineFunctionSampler
    functions = T_exact
    start_point = '0 0 0'
    end_point = '0.03 0 0'
    num_points = 200
    sort_by = x
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [T_simulation]
    type = LineValueSampler
    variable = T
    start_point = '0 0 0'
    end_point = '0.03 0 0'
    num_points = 200
    sort_by = x
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(modules/combined/test/tests/inelastic_strain/creep/creep_nl1.i)

#
# Test for effective strain calculation.
# Boundary conditions from NAFEMS test NL1
#
# This is not a verification test. This is the creep analog of the same test
# in the elas_plas directory. Instead of using the IsotropicPlasticity
# material model this test uses the PowerLawCreep material model.
#
[GlobalParams]
  temperature = temp
  order = FIRST
  family = LAGRANGE
  volumetric_locking_correction = true
  displacements = 'disp_x disp_y'
[]

[Mesh]
  file = one_elem2.e
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./temp]
    initial_condition = 600.0
  [../]
[]

[AuxVariables]
  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./vonmises]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./pressure]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./elastic_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./elastic_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./creep_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./tot_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./tot_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./tot_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./eff_creep_strain]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./TensorMechanics]
    use_displaced_mesh = true
    decomposition_method = EigenSolution
  [../]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]
[]

[AuxKernels]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  [../]
  [./stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
    execute_on = timestep_end
  [../]
  [./vonmises]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = vonmises
    scalar_type = VonMisesStress
    execute_on = timestep_end
  [../]
  [./pressure]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = pressure
    scalar_type = Hydrostatic
    execute_on = timestep_end
  [../]
  [./elastic_strain_xx]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  [../]
  [./elastic_strain_yy]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  [../]
  [./elastic_strain_zz]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  [../]
  [./creep_strain_xx]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  [../]
  [./creep_strain_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  [../]
  [./creep_strain_zz]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  [../]
  [./tot_strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = tot_strain_xx
    index_i = 0
    index_j = 0
  [../]
  [./tot_strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = tot_strain_yy
    index_i = 1
    index_j = 1
  [../]
  [./tot_strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = tot_strain_zz
    index_i = 2
    index_j = 2
  [../]
  [./eff_creep_strain]
    type = MaterialRealAux
    property = effective_creep_strain
    variable = eff_creep_strain
  [../]
[]

[Functions]
  [./appl_dispy]
    type = PiecewiseLinear
    x = '0     1.0     2.0'
    y = '0.0 0.25e-4 0.50e-4'
  [../]
[]

[BCs]
  [./side_x]
    type = DirichletBC
    variable = disp_x
    boundary = 101
    value = 0.0
  [../]
  [./origin_x]
    type = DirichletBC
    variable = disp_x
    boundary = 103
    value = 0.0
  [../]
  [./bot_y]
    type = DirichletBC
    variable = disp_y
    boundary = 102
    value = 0.0
  [../]
  [./origin_y]
    type = DirichletBC
    variable = disp_y
    boundary = 103
    value = 0.0
  [../]
  [./top_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 1
    function = appl_dispy
  [../]
  [./temp_fix]
    type = DirichletBC
    variable = temp
    boundary = '1 2'
    value = 600.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 250e9
    poissons_ratio = 0.25
  [../]
  [./strain]
    type = ComputePlaneFiniteStrain
    block = 1
  [../]
  [./radial_return_stress]
    type = ComputeMultipleInelasticStress
    block = 1
    inelastic_models = 'powerlawcrp'
  [../]
  [./powerlawcrp]
    type = PowerLawCreepStressUpdate
    block = 1
    coefficient = 3.125e-14
    n_exponent = 5.0
    m_exponent = 0.0
    activation_energy = 0.0
  [../]
  [./thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 1.0
    thermal_conductivity = 100.
  [../]
  [./density]
    type = Density
    block = 1
    density = 1.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-12
  l_tol = 1e-6
  l_max_its = 100
  nl_max_its = 20

  dt = 1.0
  start_time = 0.0
  num_steps = 100
  end_time = 2.0
[]

[Postprocessors]
  [./stress_xx]
    type = ElementAverageValue
    variable = stress_xx
  [../]
  [./stress_yy]
    type = ElementAverageValue
    variable = stress_yy
  [../]
  [./stress_zz]
    type = ElementAverageValue
    variable = stress_zz
  [../]
  [./stress_xy]
    type = ElementAverageValue
    variable = stress_xy
  [../]
  [./vonmises]
    type = ElementAverageValue
    variable = vonmises
  [../]
  [./pressure]
    type = ElementAverageValue
    variable = pressure
  [../]
  [./el_strain_xx]
    type = ElementAverageValue
    variable = elastic_strain_xx
  [../]
  [./el_strain_yy]
    type = ElementAverageValue
    variable = elastic_strain_yy
  [../]
  [./el_strain_zz]
    type = ElementAverageValue
    variable = elastic_strain_zz
  [../]
  [./crp_strain_xx]
    type = ElementAverageValue
    variable = creep_strain_xx
  [../]
  [./crp_strain_yy]
    type = ElementAverageValue
    variable = creep_strain_yy
  [../]
  [./crp_strain_zz]
    type = ElementAverageValue
    variable = creep_strain_zz
  [../]
  [./eff_creep_strain]
    type = ElementAverageValue
    variable = eff_creep_strain
  [../]
  [./tot_strain_xx]
    type = ElementAverageValue
    variable = tot_strain_xx
  [../]
  [./tot_strain_yy]
    type = ElementAverageValue
    variable = tot_strain_yy
  [../]
  [./tot_strain_zz]
    type = ElementAverageValue
    variable = tot_strain_zz
  [../]
  [./disp_x1]
    type = NodalVariableValue
    nodeid = 0
    variable = disp_x
  [../]
  [./disp_x4]
    type = NodalVariableValue
    nodeid = 3
    variable = disp_x
  [../]
  [./disp_y1]
    type = NodalVariableValue
    nodeid = 0
    variable = disp_y
  [../]
  [./disp_y4]
    type = NodalVariableValue
    nodeid = 3
    variable = disp_y
  [../]
  [./_dt]
    type = TimestepSize
  [../]
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    output_linear = true
  [../]
[]

(modules/combined/test/tests/adaptive_timestepping/adapt_tstep_function_change.i)

# This is a test designed to evaluate the cabability of the
# IterationAdaptiveDT TimeStepper to adjust time step size according to
# a function.  For example, if the power input function for a BISON
# simulation rapidly increases or decreases, the IterationAdaptiveDT
# TimeStepper should take time steps small enough to capture the
# oscillation.

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  file = 1hex8_10mm_cube.e
[]

[Functions]
  [./Fiss_Function]
    type = PiecewiseLinear
    x = '0 1e6  2e6  2.001e6 2.002e6'
    y = '0 3e8  3e8  12e8    0'
  [../]
[]

[Variables]
  [./disp_x]
  [../]

  [./disp_y]
  [../]

  [./disp_z]
  [../]

  [./temp]
    initial_condition = 300.0
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  [./all]
    strain = FINITE
    volumetric_locking_correction = true
    incremental = true
    eigenstrain_names = thermal_expansion
    decomposition_method = EigenSolution
    add_variables  = true
    generate_output = 'vonmises_stress'
    temperature = temp
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]

  [./heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]

  [./heat_source]
     type = HeatSource
     variable = temp
     value = 1.0
     function = Fiss_Function
  [../]
[]

[BCs]
  [./bottom_temp]
    type = DirichletBC
    variable = temp
    boundary = 1
    value = 300
  [../]
  [./top_bottom_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = '1'
    value = 0
  [../]
  [./top_bottom_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = '1'
    value = 0
  [../]
  [./top_bottom_disp_z]
    type = DirichletBC
    variable = disp_z
    boundary = '1'
    value = 0
  [../]
[]

[Materials]
 [./thermal]
    type = HeatConductionMaterial
    temp = temp
    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 300e6
    poissons_ratio = .3
  [../]

  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]

  [./thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 5e-6
    stress_free_temperature = 300.0
    temperature = temp
    eigenstrain_name = thermal_expansion
  [../]

  [./density]
    type = Density
    density = 10963.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  verbose = true
  nl_abs_tol = 1e-10
  start_time = 0.0
  num_steps = 50000
  end_time = 2.002e6
  [./TimeStepper]
    type = IterationAdaptiveDT
    timestep_limiting_function = Fiss_Function
    max_function_change = 3e7
    dt = 1e6
  [../]
[]

[Postprocessors]
  [./Temperature_of_Block]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./vonMises]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  [./out]
    type = Exodus
    elemental_as_nodal = true
  [../]
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(modules/combined/test/tests/reference_residual/reference_residual_perfgraph.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 4
  ny = 4
  nz = 4
[]

[Problem]
  type = ReferenceResidualProblem
  extra_tag_vectors = 'ref'
  reference_vector = 'ref'
[]

[Variables]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]

  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]

  [./disp_z]
    order = FIRST
    family = LAGRANGE
  [../]

  [./temp]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./saved_x]
  [../]
  [./saved_y]
  [../]
  [./saved_z]
  [../]
  [./saved_t]
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  [./all]
    volumetric_locking_correction = true
    incremental = true
    save_in = 'saved_x saved_y saved_z'
    eigenstrain_names = thermal_expansion
    strain = FINITE
    decomposition_method = EigenSolution
    extra_vector_tags = 'ref'
    temperature = temp
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
    save_in = saved_t
    extra_vector_tags = 'ref'
  [../]
[]

[Functions]
  [./pull]
    type = PiecewiseLinear
    x = '0 1 2'
    y = '0 1 1'
    scale_factor = 0.1
  [../]
[]

[BCs]
  [./bottom_x]
    type = DirichletBC
    variable = disp_x
    boundary = bottom
    value = 0.0
  [../]

  [./bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]

  [./bottom_z]
    type = DirichletBC
    variable = disp_z
    boundary = bottom
    value = 0.0
  [../]

  [./top_x]
    type = DirichletBC
    variable = disp_x
    boundary = top
    value = 0.0
  [../]

  [./top_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = top
    function = pull
  [../]

  [./top_z]
    type = DirichletBC
    variable = disp_z
    boundary = top
    value = 0.0
  [../]

  [./bottom_temp]
    type = DirichletBC
    variable = temp
    boundary = bottom
    value = 10.0
  [../]

  [./top_temp]
    type = DirichletBC
    variable = temp
    boundary = top
    value = 20.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 0
    youngs_modulus = 1.0
    poissons_ratio = 0.3
  [../]
  [./stress]
    type = ComputeFiniteStrainElasticStress
    block = 0
  [../]

  [./thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = 0
    eigenstrain_name = thermal_expansion
    temperature = temp
    thermal_expansion_coeff = 1e-5
    stress_free_temperature = 0.0
  [../]

  [./heat1]
    type = HeatConductionMaterial
    block = 0
    specific_heat = 1.0
    thermal_conductivity = 1e-3 #Tuned to give temperature reference resid close to that of solidmech
  [../]

  [./density]
    type = Density
    block = 0
    density = 1.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  nl_rel_tol = 1e-10
  l_tol = 1e-3
  l_max_its = 100
  dt = 1.0
  end_time = 2.0
[]

[Postprocessors]
  [./res_calls]
    type = PerfGraphData
    section_name = "ReferenceResidualProblem::computeResidualInternal"
    data_type = calls
  [../]
  [./elapsed]
    type = PerfGraphData
    section_name = "Root"
    data_type = total
  [../]
[]

[Outputs]
  csv = true
[]

(modules/combined/examples/optimization/thermomechanical/thermal_sub.i)

vol_frac = 0.4

power = 2.0

E0 = 1.0e-6
E1 = 1.0

rho0 = 0.0
rho1 = 1.0

C0 = 1.0e-6
C1 = 1.0

TC0 = 1.0e-16
TC1 = 1.0

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 40
    ny = 40
    xmin = 0
    xmax = 40
    ymin = 0
    ymax = 40
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push_left]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push_left
    coord = '16 0 0'
  []
  [push_center]
    type = ExtraNodesetGenerator
    input = push_left
    new_boundary = push_center
    coord = '24 0 0'
  []
  [extra]
    type = SideSetsFromBoundingBoxGenerator
    input = push_center
    bottom_left = '-0.01 17.999  0'
    top_right = '5 22.001  0'
    boundary_new = n1
    included_boundaries = left
  []
  [dirichlet_bc]
    type = SideSetsFromNodeSetsGenerator
    input = extra
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 100.0
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [Cc]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [Tc]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [Cost]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = FIRST
    initial_condition = ${vol_frac}
  []
[]

[AuxKernels]
  [Cost]
    type = MaterialRealAux
    variable = Cost
    property = Cost_mat
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
    diffusion_coefficient = thermal_cond
  []
  [heat_source]
    type = HeatSource
    value = 1e-2 # W/m^3
    variable = temp
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_x_symm]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [left_n1]
    type = DirichletBC
    variable = temp
    boundary = n1
    value = 0.0
  []
  [top]
    type = NeumannBC
    variable = temp
    boundary = top
    value = 0
  []
  [bottom]
    type = NeumannBC
    variable = temp
    boundary = bottom
    value = 0
  []
  [right]
    type = NeumannBC
    variable = temp
    boundary = right
    value = 0
  []
  [left]
    type = NeumannBC
    variable = temp
    boundary = left
    value = 0
  []
[]

[NodalKernels]
  [push_left]
    type = NodalGravity
    variable = disp_y
    boundary = push_left
    gravity_value = 0.0 # -1e-8
    mass = 1
  []
  [push_center]
    type = NodalGravity
    variable = disp_y
    boundary = push_center
    gravity_value = 0.0 # -1e-8
    mass = 1
  []
[]

[Materials]
  [thermal_cond]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${TC0}-${TC1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${TC0}-A1*${rho0}^${power}; TC1:=A1*mat_den^${power}+B1; TC1"
    coupled_variables = 'mat_den'
    property_name = thermal_cond
    outputs = 'exodus'
  []
  [thermal_compliance]
    type = ThermalCompliance
    temperature = temp
    thermal_conductivity = thermal_cond
    outputs = 'exodus'
  []
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; E1"
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [Cost_mat]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${C0}-${C1})/(${rho0}^(1/${power})-${rho1}^(1/${power})); "
                 "B1:=${C0}-A1*${rho0}^(1/${power}); C1:=A1*mat_den^(1/${power})+B1; C1"
    coupled_variables = 'mat_den'
    property_name = Cost_mat
  []
  [CostDensity]
    type = ParsedMaterial
    property_name = CostDensity
    coupled_variables = 'mat_den Cost'
    expression = 'mat_den*Cost'
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
  [cc]
    type = CostSensitivity
    design_density = mat_den
    cost = Cost_mat
    outputs = 'exodus'
  []
  [tc]
    type = ThermalSensitivity
    design_density = mat_den
    thermal_conductivity = thermal_cond
    temperature = temp
    outputs = 'exodus'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 0.1
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_cost]
    type = RadialAverage
    radius = 0.1
    weights = linear
    prop_name = cost_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_thermal]
    type = RadialAverage
    radius = 0.1
    weights = linear
    prop_name = thermal_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  # Provides Dc
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Cc
  [calc_sense_cost]
    type = SensitivityFilter
    density_sensitivity = Cc
    design_density = mat_den
    filter_UO = rad_avg_cost
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Tc
  [calc_sense_thermal]
    type = SensitivityFilter
    density_sensitivity = Tc
    design_density = mat_den
    filter_UO = rad_avg_thermal
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-12
  dt = 1.0
  num_steps = 500
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [right_flux]
    type = SideDiffusiveFluxAverage
    variable = temp
    boundary = right
    diffusivity = 10
  []
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
  [cost_sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = cost_sensitivity
  []
  [cost]
    type = ElementIntegralMaterialProperty
    mat_prop = CostDensity
  []
  [cost_frac]
    type = ParsedPostprocessor
    expression = 'cost / mesh_volume'
    pp_names = 'cost mesh_volume'
  []
  [objective]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [objective_thermal]
    type = ElementIntegralMaterialProperty
    mat_prop = thermal_compliance
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(modules/heat_transfer/test/tests/code_verification/spherical_test_no4.i)

# Problem III.4
#
# A spherical shell has thermal conductivity k and heat generation q.
# It has an inner radius ri and outer radius ro. A constant heat flux is
# applied to the inside surface qin and the outside surface is exposed
# to a fluid temperature uf and heat transfer coefficient h.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    xmin = 0.2
    nx = 4
  [../]
  coord_type = RSPHERICAL
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./exact]
    type = ParsedFunction
    symbol_names = 'qin q k ri ro uf h'
    symbol_values = '100 1200 1.0 0.2 1 100 10'
    expression = 'uf+ (q/(6*k)) * ( ro^2-x^2 + 2*k*(ro^3-ri^3)/(h*ro^2) + 2 * ri^3 * (1/ro-1/x) ) + (1/x-1/ro+k/(h*ro^2)) * qin * ri^2 / k'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
  [./heatsource]
    type = HeatSource
    function = 1200
    variable = u
  [../]
[]

[BCs]
  [./ui]
    type = NeumannBC
    boundary = left
    variable = u
    value = 100
  [../]
  [./uo]
    type = CoupledConvectiveHeatFluxBC
    boundary = right
    variable = u
    htc = 10.0
    T_infinity = 100
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat thermal_conductivity'
    prop_values = '1.0 1.0 1.0'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/three_materials_thermal.i)

vol_frac = 0.4
cost_frac = 0.4

power = 4

# Stiffness (not optimized in this test)
E0 = 1.0e-6
E1 = 0.2
E2 = 0.6
E3 = 1.0

# Densities
rho0 = 1.0e-6
rho1 = 0.4
rho2 = 0.7
rho3 = 1.0

# Costs
C0 = 1.0e-6
C1 = 0.5
C2 = 0.8
C3 = 1.0

# Thermal conductivity
TC0 = 1.0e-6
TC1 = 0.2
TC2 = 0.6
TC3 = 1.0

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 40
    ny = 40
    xmin = 0
    xmax = 40
    ymin = 0
    ymax = 40
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push_left]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push_left
    coord = '20 0 0'
  []
  [push_center]
    type = ExtraNodesetGenerator
    input = push_left
    new_boundary = push_center
    coord = '40 0 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 100.0
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [Cc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [Tc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [Cost]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [thermal_compliance]
    order = CONSTANT
    family = MONOMIAL
  []
[]

# [ICs]
#   [mat_den]
#     type = RandomIC
#     seed = 4
#     variable = mat_den
#     max = '${fparse vol_frac+0.25}'
#     min = '${fparse vol_frac-0.25}'
#   []
# []

[AuxKernels]
  [Cost]
    type = MaterialRealAux
    variable = Cost
    property = Cost_mat
  []
  [thermal_compliance]
    type = MaterialRealAux
    property = thermal_compliance
    variable = thermal_compliance
    execute_on = timestep_end
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
    diffusion_coefficient = thermal_cond
  []
  [heat_source]
    type = HeatSource
    value = 1e-2 # W/m^3
    variable = temp
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_x_symm]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [top]
    type = DirichletBC
    variable = temp
    boundary = top
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = temp
    boundary = bottom
    value = 0
  []
  [right]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 0
  []
  [left]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 0
  []
[]

[NodalKernels]
  [push_left]
    type = NodalGravity
    variable = disp_y
    boundary = push_left
    gravity_value = -1e-6 # -3
    mass = 1
  []
  [push_center]
    type = NodalGravity
    variable = disp_y
    boundary = push_center
    gravity_value = -1e-6 # -3
    mass = 1
  []
[]

[Materials]
  [thermal_cond]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${TC0}-${TC1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${TC0}-A1*${rho0}^${power}; TC1:=A1*mat_den^${power}+B1; "
                 "A2:=(${TC1}-${TC2})/(${rho1}^${power}-${rho2}^${power}); "
                 "B2:=${TC1}-A2*${rho1}^${power}; TC2:=A2*mat_den^${power}+B2; "
                 "A3:=(${TC2}-${TC3})/(${rho2}^${power}-${rho3}^${power}); "
                 "B3:=${TC2}-A3*${rho2}^${power}; TC3:=A3*mat_den^${power}+B3; "
                 "if(mat_den<${rho1},TC1,if(mat_den<${rho2},TC2,TC3))"
    coupled_variables = 'mat_den'
    property_name = thermal_cond
  []
  [thermal_compliance]
    type = ThermalCompliance
    temperature = temp
    thermal_conductivity = thermal_cond
  []
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; "
                 "A2:=(${E1}-${E2})/(${rho1}^${power}-${rho2}^${power}); "
                 "B2:=${E1}-A2*${rho1}^${power}; E2:=A2*mat_den^${power}+B2; "
                 "A3:=(${E2}-${E3})/(${rho2}^${power}-${rho3}^${power}); "
                 "B3:=${E2}-A3*${rho2}^${power}; E3:=A3*mat_den^${power}+B3; "
                 "if(mat_den<${rho1},E1,if(mat_den<${rho2},E2,E3))"
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [Cost_mat]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${C0}-${C1})/(${rho0}^(1/${power})-${rho1}^(1/${power})); "
                 "B1:=${C0}-A1*${rho0}^(1/${power}); C1:=A1*mat_den^(1/${power})+B1; "
                 "A2:=(${C1}-${C2})/(${rho1}^(1/${power})-${rho2}^(1/${power})); "
                 "B2:=${C1}-A2*${rho1}^(1/${power}); C2:=A2*mat_den^(1/${power})+B2; "
                 "A3:=(${C2}-${C3})/(${rho2}^(1/${power})-${rho3}^(1/${power})); "
                 "B3:=${C2}-A3*${rho2}^(1/${power}); C3:=A3*mat_den^(1/${power})+B3; "
                 "if(mat_den<${rho1},C1,if(mat_den<${rho2},C2,C3))"
    coupled_variables = 'mat_den'
    property_name = Cost_mat
  []
  [CostDensity]
    type = ParsedMaterial
    property_name = CostDensity
    coupled_variables = 'mat_den Cost'
    expression = 'mat_den*Cost'
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
  [cc]
    type = CostSensitivity
    design_density = mat_den
    cost = Cost_mat
  []
  [tc]
    type = ThermalSensitivity
    design_density = mat_den
    thermal_conductivity = thermal_cond
    temperature = temp
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 4
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_cost]
    type = RadialAverage
    radius = 4
    weights = linear
    prop_name = cost_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_thermal]
    type = RadialAverage
    radius = 4
    weights = linear
    prop_name = thermal_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [update]
    type = DensityUpdateTwoConstraints
    density_sensitivity = Dc
    cost_density_sensitivity = Cc
    cost = Cost
    cost_fraction = ${cost_frac}
    design_density = mat_den
    volume_fraction = ${vol_frac}

    bisection_lower_bound = 0
    bisection_upper_bound = 1.0e12 # 100

    use_thermal_compliance = true
    thermal_sensitivity = Tc
    # Only account for thermal optimizxation
    weight_mechanical_thermal = '0 1'

    relative_tolerance = 1.0e-8
    bisection_move = 0.05
    adaptive_move = false
    execute_on = TIMESTEP_BEGIN
  []
  # Provides Dc
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Cc
  [calc_sense_cost]
    type = SensitivityFilter
    density_sensitivity = Cc
    design_density = mat_den
    filter_UO = rad_avg_cost
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Tc
  [calc_sense_thermal]
    type = SensitivityFilter
    density_sensitivity = Tc
    design_density = mat_den
    filter_UO = rad_avg_thermal
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-10
  dt = 1.0
  num_steps = 12
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [right_flux]
    type = SideDiffusiveFluxAverage
    variable = temp
    boundary = right
    diffusivity = 10
  []
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
  [cost_sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = cost_sensitivity
  []
  [cost]
    type = ElementIntegralMaterialProperty
    mat_prop = CostDensity
  []
  [cost_frac]
    type = ParsedPostprocessor
    expression = 'cost / mesh_volume'
    pp_names = 'cost mesh_volume'
  []
  [objective]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [objective_thermal]
    type = ElementIntegralMaterialProperty
    mat_prop = thermal_compliance
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/gap_heat_transfer_sphere3D_mortar.i)

sphere_outer_htc = 10 # W/m^2/K
sphere_outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Problem]
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = sphere3D.e
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '2'
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    input = file
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '3'
    new_block_id = 10000
    new_block_name = 'primary_lower'
    input = secondary
  []
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
  [lm]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  []
[]

[AuxVariables]
  # [gap_conductance]
  #   order = CONSTANT
  #   family = MONOMIAL
  # []
  [power_density]
    block = 'fuel'
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
    block = '1 2'
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = 'fuel'
    v = power_density
  []
[]

# [AuxKernels]
#   [gap_cond]
#     type = MaterialRealAux
#     property = gap_conductance
#     variable = gap_conductance
#     boundary = 2
#   []
# []

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[UserObjects]
  [radiation]
    type = GapFluxModelRadiation
    temperature = temp
    boundary = 2
    primary_emissivity = 0.0
    secondary_emissivity = 0.0
  []
  [conduction]
    type = GapFluxModelConduction
    temperature = temp
    boundary = 2
    gap_conductivity = 5.0
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = temp
    primary_boundary = 3
    primary_subdomain = 10000
    secondary_boundary = 2
    secondary_subdomain = 10001
    gap_flux_models = 'radiation conduction'
    gap_geometry_type = SPHERE
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = '4' # outer RPV
    coefficient = ${sphere_outer_htc}
    T_infinity = ${sphere_outer_Tinf}
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7
[]

[Outputs]
  exodus = true
  csv = true
  [Console]
    type = Console
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  []
  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 'fuel'
  []
  [sphere_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = '4' # outer RVP
    T_fluid = ${sphere_outer_Tinf}
    htc = ${sphere_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(sphere_convective_out - ptot) / ptot'
    pp_names = 'sphere_convective_out ptot'
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = '2 3'
    variable = temp
  []
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/planar_xz.i)

# 1-D Gap Heat Transfer Test without mechanics
#
# This test exercises 1-D gap heat transfer for a constant conductivity gap.
#
# The mesh consists of two element blocks in the x-z plane.  Each element block
# is a square. They sit next to one another with a unit between them.
#
# The conductivity of both blocks is set very large to achieve a uniform temperature
# across each block. The temperature of the far bottom boundary
# is ramped from 100 to 200 over one time unit.  The temperature of the far top
# boundary is held fixed at 100.
#
# A simple analytical solution is possible for the heat flux between the blocks:
#
# Flux = (T_left - T_right) * (gapK/gap_width)
#
# The gap conductivity is specified as 1, thus
#
# gapK(Tavg) = 1.0*Tavg
#
# The heat flux across the gap at time = 1 is then:
#
# Flux = 100 * (1.0/1.0) = 100
#
# For comparison, see results from the flux post processors.  These results
# are the same as for the unit 1-D gap heat transfer between two unit cubes.

[Mesh]
  [file]
    type = FileMeshGenerator
    file = simple_2D.e
  []
  [./rotate]
    type = TransformGenerator
    transform = ROTATE
    vector_value = '0 90 0'
    input = file
  [../]
[]

[Functions]
  [./temp]
    type = PiecewiseLinear
    x = '0   1   2'
    y = '100 200 200'
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
  [../]
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  [../]
[]

[AuxVariables]
  [./gap_cond]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]


[BCs]
  [./temp_far_bottom]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  [../]
  [./temp_far_top]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
[]

[AuxKernels]
  [./conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 2
  [../]
[]

[Materials]
  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 100000000.0
  [../]
  [./density]
    type = GenericConstantMaterial
    block = '1 2'
    prop_names = 'density'
    prop_values = '1.0'
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'
  nl_rel_tol = 1e-12
  l_tol = 1e-3
  l_max_its = 100

  dt = 1e-1
  end_time = 1.0
[]

[Postprocessors]
  [./temp_bottom]
    type = SideAverageValue
    boundary = 2
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./temp_top]
    type = SideAverageValue
    boundary = 3
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./flux_bottom]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  [../]

  [./flux_top]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_balance/large_gap_heat_transfer_test_cylinder.i)

rpv_core_gap_size = 0.15

core_outer_radius = 2
rpv_inner_radius = ${fparse 2 + rpv_core_gap_size}
rpv_outer_radius = ${fparse 2.5 + rpv_core_gap_size}

rpv_outer_htc = 10 # W/m^2/K
rpv_outer_Tinf = 300 # K

core_blocks = '1'
rpv_blocks = '3'

[Mesh]
  [core_gap_rpv]
    type = ConcentricCircleMeshGenerator
    num_sectors = 10
    radii = '${core_outer_radius} ${rpv_inner_radius} ${rpv_outer_radius}'
    rings = '2 1 2'
    has_outer_square = false
    preserve_volumes = true
    portion = full
  []
  [rename_core_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = core_gap_rpv
    primary_block = 1
    paired_block = 2
    new_boundary = 'core_outer'
  []
  [rename_inner_rpv_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = rename_core_bdy
    primary_block = 3
    paired_block = 2
    new_boundary = 'rpv_inner'
  []
  [2d_mesh]
    type = BlockDeletionGenerator
    input = rename_inner_rpv_bdy
    block = 2
  []
[]

[Variables]
  [Tsolid]
    initial_condition = 500
  []
[]

[Kernels]
  [heat_source]
    type = CoupledForce
    variable = Tsolid
    block = '${core_blocks}'
    v = power_density
  []
  [heat_conduction]
    type = HeatConduction
    variable = Tsolid
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = Tsolid
    boundary = 'outer' # outer RPV
    coefficient = ${rpv_outer_htc}
    T_infinity = ${rpv_outer_Tinf}
  []
[]

[ThermalContact]
  [RPV_gap]
    type = GapHeatTransfer
    gap_geometry_type = 'CYLINDER'
    emissivity_primary = 0.8
    emissivity_secondary = 0.8
    variable = Tsolid
    primary = 'core_outer'
    secondary = 'rpv_inner'
    gap_conductivity = 0.1
    quadrature = true
    cylinder_axis_point_1 = '0 0 0'
    cylinder_axis_point_2 = '0 0 5'
  []
[]

[AuxVariables]
  [power_density]
    block = '${core_blocks}'
    initial_condition = 50e3
  []
[]

[Materials]
  [simple_mat]
    type = HeatConductionMaterial
    thermal_conductivity = 34.6 # W/m/K
  []
[]

[Postprocessors]
  [Tcore_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Trpv_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = '${core_blocks}'
  []
  [rpv_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = Tsolid
    boundary = 'outer' # outer RVP
    T_fluid = ${rpv_outer_Tinf}
    htc = ${rpv_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(rpv_convective_out - ptot) / ptot'
    pp_names = 'rpv_convective_out ptot'
  []
[]

[Executioner]
  type = Steady
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_max_its = 100

  [Quadrature]
    side_order = seventh
  []
  line_search = none
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/heat_transfer/test/tests/thin_layer_heat_transfer/steady_2d.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    nx = 10
    ny = 10
    dim = 2
  []
  [block1]
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '0 0 0'
    top_right = '0.5 1 0'
    input = gen
  []
  [block2]
    type = SubdomainBoundingBoxGenerator
    block_id = 2
    bottom_left = '0.5 0 0'
    top_right = '1 1 0'
    input = block1
  []
  [breakmesh]
    input = block2
    type = BreakMeshByBlockGenerator
    block_pairs = '1 2'
    split_interface = true
    add_interface_on_two_sides = true
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [thermal_cond]
    type = HeatConduction
    variable = temperature
  []
[]

[InterfaceKernels]
  [thin_layer]
    type = ThinLayerHeatTransfer
    thermal_conductivity = thermal_conductivity_layer
    thickness = 0.01
    variable = temperature
    neighbor_var = temperature
    boundary = Block1_Block2
  []
[]

[BCs]
  [left_temp]
    type = DirichletBC
    value = 100
    variable = temperature
    boundary = left
  []
  [right_temp]
    type = DirichletBC
    value = 0
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [thermal_cond]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '1'
  []
  [thermal_cond_layer]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity_layer'
    prop_values = '0.05'
    boundary = Block1_Block2
  []
[]
[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10

  dt = 0.05
  num_steps = 1
[]


[Outputs]
  print_linear_residuals = false
  exodus = true
[]

(modules/heat_transfer/test/tests/truss_heat_conduction/rectangle_w_line.i)

[Mesh]
  parallel_type = 'replicated'
  [rectangle]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 50
    xmin = -0.5
    xmax = 0.5
    ymin = -1.25
    ymax = 1.25
    boundary_name_prefix = rectangle
  []
  [rectangle_id]
    type = SubdomainIDGenerator
    input = rectangle
    subdomain_id = 1
  []
  [line]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = -0.5
    xmax = 0.5
    nx = 10
    boundary_name_prefix = line
    boundary_id_offset = 10
  []
  [line_id]
    type = SubdomainIDGenerator
    input = line
    subdomain_id = 2
  []
  [combined]
    type = MeshCollectionGenerator
    inputs = 'rectangle_id line_id'
  []
  [blcok_rename]
    type = RenameBlockGenerator
    input = combined
    old_block = '1 2'
    new_block = 'rectangle line'
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = temperature
    block = 'rectangle'
  []
  [heat_conduction]
    type = HeatConduction
    variable = temperature
    block = 'rectangle'
  []
  [time_derivative_line]
    type = TrussHeatConductionTimeDerivative
    variable = temperature
    area = area
    block = 'line'
  []
  [heat_conduction_line]
    type = TrussHeatConduction
    variable = temperature
    area = area
    block = 'line'
  []
[]

[AuxVariables]
  [area]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [area]
    type = ConstantAux
    variable = area
    value = 0.1 # strip thickness
    execute_on = 'initial timestep_begin'
  []
[]

[Constraints]
  [equalvalue]
    type = EqualValueEmbeddedConstraint
    secondary = 'line'
    primary = 'rectangle'
    penalty = 1e6
    formulation = kinematic
    primary_variable = temperature
    variable = temperature
  []
[]

[Materials]
  [rectangle]
    type = GenericConstantMaterial
    block = 'rectangle'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
  [line]
    type = GenericConstantMaterial
    block = 'line'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '10.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
[]

[BCs]
  [right]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'rectangle_right line_right'
    function = '10*t'
  []
[]

[VectorPostprocessors]
  [x_n0_25]
    type = LineValueSampler
    start_point = '-0.25 0 0'
    end_point = '-0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
  [x_0_25]
    type = LineValueSampler
    start_point = '0.25 0 0'
    end_point = '0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1
  end_time = 1
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'csv/rectangle_w_line'
    time_data = true
  []
[]

(modules/heat_transfer/test/tests/truss_heat_conduction/rectangle_w_strip.i)

[Mesh]
  [rectangle]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 50
    xmin = -0.5
    xmax = 0.5
    ymin = -1.25
    ymax = 1.25
  []
  [strip]
    type = SubdomainBoundingBoxGenerator
    input = rectangle
    bottom_left = '-0.5 -0.05 0'
    top_right = '0.5 0.05 0'
    block_id = 2
    block_name = 'strip'
    location = INSIDE
  []
  [top_bottom_layers]
    type = SubdomainBoundingBoxGenerator
    input = strip
    bottom_left = '-0.5 -0.05 0'
    top_right = '0.5 0.05 0'
    block_id = 1
    block_name = 'rectangle'
    location = OUTSIDE
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat_conduction]
    type = HeatConduction
    variable = temperature
  []
[]

[Materials]
  [block]
    type = GenericConstantMaterial
    block = 'rectangle'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
  [strip]
    type = GenericConstantMaterial
    block = 'strip'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '10.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
[]

[BCs]
  [right]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'right'
    function = '10*t'
  []
[]

[VectorPostprocessors]
  [x_n0_25]
    type = LineValueSampler
    start_point = '-0.25 0 0'
    end_point = '-0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
  [x_0_25]
    type = LineValueSampler
    start_point = '0.25 0 0'
    end_point = '0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1
  end_time = 1
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'csv/rectangle_w_strip'
    time_data = true
  []
[]

(modules/functional_expansion_tools/examples/3D_volumetric_Cartesian/main.i)

# Basic example coupling a master and sub app in a 3D Cartesian volume.
#
# The master app provides field values to the sub app via Functional Expansions, which then performs
# its calculations. The sub app's solution field values are then transferred back to the master app
# and coupled into the solution of the master app solution.
#
# This example couples Functional Expansions via AuxVariable.
#
# Note: this problem is not light, and may take a few minutes to solve.
[Mesh]
  type = GeneratedMesh
  dim = 3

  xmin = 0.0
  xmax = 10.0
  nx = 15

  ymin = 1.0
  ymax = 11.0
  ny = 25

  zmin = 2.0
  zmax = 12.0
  nz = 35
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./s_in] # Add in the contribution from the SubApp
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'top bottom left right front back'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3   4   5'
    physical_bounds = '0.0  10.0    1.0 11.0    2.0 12.0'
    x = Legendre
    y = Legendre
    z = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(python/peacock/tests/common/transient_heat_test.i)

[Mesh]
  file = cube.e
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]

  [./ie]
    type = SpecificHeatConductionTimeDerivative
    variable = u
  [../]
[]

[BCs]
  [./bottom]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 0.0
  [../]

  [./top]
    type = DirichletBC
    variable = u
    boundary = 2
    value = 1.0
  [../]
[]

[Materials]
  [./constant]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1
    specific_heat = 1
  [../]
  [./density]
    type = Density
    block = 1
    density = 1
  [../]
[]

[Executioner]
  type = Transient

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'



  start_time = 0.0
  num_steps = 5
  dt = .1
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/sphere3D.i)

#
# 3D Spherical Gap Heat Transfer Test.
#
# This test exercises 3D gap heat transfer for a constant conductivity gap.
#
# The mesh consists of an inner solid sphere of radius = 1 unit, and outer
# hollow sphere with an inner radius of 2. In other words, the gap between
# them is 1 radial unit in length.
#
# The conductivity of both spheres is set very large to achieve a uniform
# temperature in each sphere. The temperature of the center node of the
# inner sphere is ramped from 100 to 200 over one time unit. The
# temperature of the outside of the outer, hollow sphere is held fixed
# at 100.
#
# A simple analytical solution is possible for the integrated heat flux
# between the inner and outer spheres:
#
#  Integrated Flux = (T_left - T_right) * (gapK/(r^2*((1/r1)-(1/r2)))) * Area
#
# For gapK = 1 (default value)
#
# The area is taken as the area of the secondary (inner) surface:
#
# Area = 4 * pi * 1^2 (4*pi*r^2)
#
# The integrated heat flux across the gap at time 1 is then:
#
# 4*pi*k*delta_T/((1/r1)-(1/r2))
# 4*pi*1*100/((1/1) - (1/2)) =  2513.3 watts
#
# For comparison, see results from the integrated flux post processors.
# This simulation makes use of symmetry, so only 1/8 of the spheres is meshed
# As such, the integrated flux from the post processors is 1/8 of the total,
# or 314.159 watts... i.e. 100*pi.
# The value coming from the post processor is slightly less than this
# but converges as mesh refinement increases.
#
# Simulating contact is challenging. Regression tests that exercise
# contact features can be difficult to solve consistently across multiple
# platforms. While designing these tests, we felt it worth while to note
# some aspects of these tests. The following applies to:
# sphere3D.i, sphere2DRZ.i, cyl2D.i, and cyl3D.i.
# 1. We decided that to perform consistently across multiple platforms we
# would use very small convergence tolerance. In this test we chose an
# nl_rel_tol of 1e-12.
# 2. Due to such a high value for thermal conductivity (used here so that the
# domains come to a uniform temperature) the integrated flux at time = 0
# was relatively large (the value coming from SideIntegralFlux =
#  -_diffusion_coef[_qp]*_grad_u[_qp]*_normals[_qp] where the diffusion coefficient
# here is thermal conductivity).
# Even though _grad_u[_qp] is small, in this case the diffusion coefficient
# is large. The result is a number that isn't exactly zero and tends to
# fail exodiff. For this reason the parameter execute_on = initial should not
# be used. That parameter is left to default settings in these regression tests.
#
[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  file = sphere3D.e
[]

[Functions]
  [./temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  [../]
[]

[Variables]
  [./temp]
   initial_condition = 100
  [../]
[]

[AuxVariables]
  [./gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temp
  [../]
[]


[AuxKernels]
  [./gap_cond]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_conductance
    boundary = 2
  [../]
[]

[Materials]
  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 100000000.0
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductivity = 1
    quadrature = true
    gap_geometry_type = SPHERE
    sphere_origin = '0 0 0'
  [../]
[]

[BCs]
  [./mid]
    type = FunctionDirichletBC
    boundary = 5
    variable = temp
    function = temp
  [../]
  [./temp_far_right]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

  [./Quadrature]
     order = fifth
     side_order = seventh
  [../]
[]

[Outputs]
  exodus = true
  [./Console]
    type = Console
  [../]
[]

[Postprocessors]
  [./temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  [../]

  [./temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  [../]

  [./flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  [../]

  [./flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  [../]
[]

(modules/combined/test/tests/elastic_thermal_patch/ad_elastic_thermal_weak_plane_stress_jacobian.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
  temperature = temp
  out_of_plane_strain = strain_zz
[]

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./strain_zz]
  [../]
  [./temp]
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  [./plane_stress]
    planar_formulation = WEAK_PLANE_STRESS
    strain = SMALL
    eigenstrain_names = thermal_eigenstrain
    use_automatic_differentiation = true
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
    use_displaced_mesh = false
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    poissons_ratio = 0.0
    youngs_modulus = 1
  [../]
  [./thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 1e-5
    stress_free_temperature = 0
    eigenstrain_name = thermal_eigenstrain
  [../]
  [./stress]
    type = ADComputeLinearElasticStress
  [../]

  [./conductivity]
    type = HeatConductionMaterial
    thermal_conductivity = 1
    use_displaced_mesh = false
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON

  petsc_options_iname = '-ksp_type -pc_type -snes_type'
  petsc_options_value = 'bcgs bjacobi test'

  end_time = 1.0
[]

(modules/combined/test/tests/thermo_mech/thermo_mech_smp.i)

[GlobalParams]
  temperature = temp
  volumetric_locking_correction = true
[]

[Mesh]
  file = cube.e
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]

  [./temp]
  [../]
[]

[Kernels]
  [./TensorMechanics]
    displacements = 'disp_x disp_y disp_z'
  [../]

  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./bottom_x]
    type = DirichletBC
    variable = disp_x
    boundary = 1
    value = 0.0
  [../]
  [./bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = 1
    value = 0.0
  [../]
  [./bottom_z]
    type = DirichletBC
    variable = disp_z
    boundary = 1
    value = 0.0
  [../]

  [./bottom_temp]
    type = DirichletBC
    variable = temp
    boundary = 1
    value = 10.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1.0
    poissons_ratio = 0.3
  [../]
  [./strain]
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y disp_z'
    eigenstrain_names = eigenstrain
  [../]
  [./thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    stress_free_temperature = 0.0
    thermal_expansion_coeff = 1e-5
    eigenstrain_name = eigenstrain
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]

  [./heat]
    type = HeatConductionMaterial
    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./density]
    type = Density
    density = 1.0
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  nl_rel_tol = 1e-14
  l_tol = 1e-3

  l_max_its = 100

  dt = 1.0
  end_time = 1.0
[]

[Outputs]
  file_base = thermo_mech_smp_out
  [./exodus]
    type = Exodus
    execute_on = 'initial timestep_end nonlinear'
    nonlinear_residual_dt_divisor = 100
  [../]
[]

(modules/combined/test/tests/heat_convection/heat_convection_rz_tf_test.i)

# Test cases for convective boundary conditions. TKLarson, 11/01/11, rev. 0.
# Input file for htc_2dtest0

# TKLarson
# 11/01/11
# Revision 0
#
# Goals of this test are:
#  1) show that the 'fluid' temperature for convective boundary condition
#    is behaving as expected/desired
#  2) show that expected results ensue from application of convective boundary conditions
# Convective boundary condition:
#  q = h*A*(Tw - Tf)
#  where
#    q - heat transfer rate (w)
#    h - heat transfer coefficient (w/m^2-K)
#    A - surface area (m^2)
#    Tw - surface temperature (K)
#    Tf - fluid temperature adjacent to the surface (K)
# The heat transfer coefficient (h) is input as a variable called 'rate'
# Tf is a two valued function specified by 'initial' and 'final' along with a variable
#  called 'duration,' the length of time in seconds that it takes initial to linearly ramp
#  to 'final.'

# The mesh for this test case is based on an ASTM standard for the so-called Brazillian Cylinder test
# (ASTM International, Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete
# Specimens, C 496/C 496M-04, 2004) (because I already had a version of the model).  While the
# Brazillian Cylinder test is for dynamic tensile testing of concrete, the model works for the present
# purposes.  The model is 2-d RZ coordinates.
#
# Brazillian Cylinder sample dimensions:
#       L = 20.3 cm, 0.203 m, (8 in)
#       r = 5.08 cm, 0.0508 m, (2 in)

# Material properties are:
#   density = 2405.28 km/m^3
#   specific heat = 826.4 J/kg-K
#   thermal conductivity 1.937 w/m-K
#  alpha (thermal conductivity/(density*specific heat) is then 9.74e-7 m^2/s
#
# Initial cylinder temperature is room temperature 294.26 K (70 F)
# The initial fluid temperature is room temperature. We will ramp it to 477.6 K (400 F) in 10 minutes.
# We will use a very large h (1000000) to make the surface temperature mimick the fluid temperature.

# What we expect for this problem:
#  1) Use of h = 1000000 should cause the cylinder surface temperature to track the fluid temperature
#  2) The fluid temperature should rise from initial (294.26 K) to final (477.6 K) in 600 s.
#  3) 1) and 2) should prove that the Tf boundary condition is ramping as desired.
# Note, we do the above because there is no way to plot a variable that is not on a mesh node!

[Mesh]    # Mesh Start
# 10cm x 20cm cylinder not so detailed mesh, 2 radial, 6 axial nodes
# Only one block (Block 1), all concrete
# Sideset 1 - top of cylinder, Sideset 2 - length of cylinder, Sideset 3 - bottom of cylinder
  file = heat_convection_rz_mesh.e
  coord_type = RZ
[]    # Mesh END

[Variables]  # Variables Start
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 294.26 # Initial cylinder temperature
  [../]

[]    # Variables END


[Kernels]  # Kernels Start
  [./heat]
    type = HeatConduction
    variable = temp
  [../]

  [./heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]

[]    # Kernels END


[BCs]    # Boundary Conditions Start
# Heat transfer coefficient on outer cylinder radius and ends
  [./convective_clad_surface]    # Convective Start
         type = ConvectiveFluxBC        # Convective flux, e.g. q'' = h*(Tw - Tf)
         boundary = '1 2 3'    # BC applied on top, along length, and bottom
         variable = temp
   rate = 1000000.   # convective heat transfer coefficient (w/m^2-K)[176000 "]
#         #  the above h is ~ infinity for present purposes
         initial = 294.26         # initial ambient (lab or oven) temperature (K)
         final = 477.6            # final ambient (lab or oven) temperature (K)
   duration = 600.   # length of time in seconds that it takes the ambient
         #     temperature to ramp from initial to final
  [../]          # Convective End

[]    # BCs END

[Materials]    # Materials Start
  [./thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 826.4
    thermal_conductivity = 1.937  # this makes alpha 9.74e-7 m^2/s
  [../]
  [./density]
    type = Density
    block = 1
    density = 2405.28
  [../]
[]      # Materials END

[Executioner]    # Executioner Start
   type = Transient
#   type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'


   petsc_options = '-snes_ksp_ew '
   petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type'
   petsc_options_value = '70 hypre boomeramg'
   l_max_its = 60
   nl_rel_tol = 1e-8
   nl_abs_tol = 1e-10
   l_tol = 1e-5

   start_time = 0.0
  dt = 60.
  num_steps = 20  # Total run time 1200 s

[]      # Executioner END

[Outputs]    # Output Start
  # Output Start
  file_base = out_rz_tf
  exodus = true
[]      # Output END
#      # Input file END

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/planar_xy.i)

# 1-D Gap Heat Transfer Test without mechanics
#
# This test exercises 1-D gap heat transfer for a constant conductivity gap.
#
# The mesh consists of two element blocks in the x-y plane.  Each element block
# is a square. They sit next to one another with a unit between them.
#
# The conductivity of both blocks is set very large to achieve a uniform temperature
# across each block. The temperature of the far bottom boundary
# is ramped from 100 to 200 over one time unit.  The temperature of the far top
# boundary is held fixed at 100.
#
# A simple analytical solution is possible for the heat flux between the blocks:
#
# Flux = (T_left - T_right) * (gapK/gap_width)
#
# The gap conductivity is specified as 1, thus
#
# gapK(Tavg) = 1.0*Tavg
#
# The heat flux across the gap at time = 1 is then:
#
# Flux = 100 * (1.0/1.0) = 100
#
# For comparison, see results from the flux post processors.  These results
# are the same as for the unit 1-D gap heat transfer between two unit cubes.



[Mesh]
  file = simple_2D.e
[]

[Functions]
  [./temp]
    type = PiecewiseLinear
    x = '0   1   2'
    y = '100 200 200'
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
  [../]
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  [../]
[]

[AuxVariables]
  [./gap_cond]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]


[BCs]
  [./temp_far_bottom]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  [../]
  [./temp_far_top]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
[]

[AuxKernels]
  [./conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 2
  [../]
[]

[Materials]
  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 100000000.0
  [../]
  [./density]
    type = GenericConstantMaterial
    block = '1 2'
    prop_names = 'density'
    prop_values = '1.0'
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'
  nl_rel_tol = 1e-14
  l_tol = 1e-3
  l_max_its = 100

  dt = 1e-1
  end_time = 1.0
[]

[Postprocessors]
  [./temp_bottom]
    type = SideAverageValue
    boundary = 2
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./temp_top]
    type = SideAverageValue
    boundary = 3
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./flux_bottom]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  [../]

  [./flux_top]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/heat_conduction/3d_quadrature_gap_heat_transfer/second.i)

[Mesh]
  file = nonmatching.e
  second_order = true
[]

[Variables]
  [./temp]
    order = SECOND
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temp
    boundary = leftleft
    value = 1000
  [../]
  [./right]
    type = DirichletBC
    variable = temp
    boundary = rightright
    value = 400
  [../]
[]

[ThermalContact]
  [./left_to_right]
    secondary = leftright
    quadrature = true
    primary = rightleft
    variable = temp
    emissivity_primary = 0
    emissivity_secondary = 0
    type = GapHeatTransfer
    order = SECOND
  [../]
[]

[Materials]
  [./hcm]
    type = HeatConductionMaterial
    block = 'left right'
    specific_heat = 1
    thermal_conductivity = 1
  [../]
[]

[Postprocessors]
  [./left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = leftright
    diffusivity = thermal_conductivity
  [../]
  [./right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = rightleft
    diffusivity = thermal_conductivity
  [../]
[]

[Executioner]
  type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/ref.i)

[Mesh]
  file = 3blk.e
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    block = '1 2 3'
  [../]
[]

[Materials]
  [./left]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1000
    specific_heat = 1
  [../]

  [./right]
    type = HeatConductionMaterial
    block = 2
    thermal_conductivity = 500
    specific_heat = 1
  [../]

  [./middle]
    type = HeatConductionMaterial
    block = 3
    thermal_conductivity = 100
    specific_heat = 1
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
    use_displaced_mesh = false
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temp
    boundary = 'left'
    value = 1
  [../]

  [./right]
    type = DirichletBC
    variable = temp
    boundary = 'right'
    value = 0
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  nl_rel_tol = 1e-11
  l_tol = 1e-11
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/radiation_transfer_action/cavity_with_pillar_vf.i)

[Mesh]
  [cartesian]
    type = CartesianMeshGenerator
    dim = 3
    dx = '0.1 0.3 0.4 0.3 0.1'
    ix = '  1  3  4  3   1'
    dy = '0.1 0.3 0.4 0.3 0.1'
    iy = '  1  3  4  3   1'
    dz = '0.1 0.8 0.2 0.1'
    iz = ' 1   8   2   1'
    subdomain_id = '1 1 1 1 1
                    1 15 15 15 1
                    1 15 1 15 1
                    1 15 15 15 1
                    1 1 1 1 1

                    1 12 12 12 1
                    11 0 103 0  14
                    11 104 2 102  14
                    11 0 101 0  14
                    1 13 13 13 1

                    1 12 12 12 1
                    11 0 0 0  14
                    11 0 105 0  14
                    11 0 0 0  14
                    1 13 13 13 1

                    1 1 1 1 1
                    1 16 16 16 1
                    1 16 16 16 1
                    1 16 16 16 1
                    1 1 1 1 1'
  []

  [left_interior]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 11
    paired_block = '0 101 102 103 104 105'
    new_boundary = left_interior_wall
    input = cartesian
  []

  [right_interior]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 14
    paired_block = '0 101 102 103 104 105'
    new_boundary = right_interior_wall
    input = left_interior
  []

  [bottom_interior]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 12
    paired_block = '0 101 102 103 104 105'
    new_boundary = bottom_interior_wall
    input = right_interior
  []

  [top_interior]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 13
    paired_block = '0 101 102 103 104 105'
    new_boundary = top_interior_wall
    input = bottom_interior
  []

  [front_interior]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 15
    paired_block = '0 101 102 103 104 105'
    new_boundary = front_interior_wall
    input = top_interior
  []

  [back_interior]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 16
    paired_block = '0 101 102 103 104 105'
    new_boundary = back_interior_wall
    input = front_interior
  []

  [pillar_left]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 2
    paired_block = 104
    new_boundary = pillar_left
    input = 'back_interior'
  []

  [pillar_right]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 2
    paired_block = 102
    new_boundary = pillar_right
    input = 'pillar_left'
  []

  [pillar_bottom]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 2
    paired_block = 103
    new_boundary = pillar_bottom
    input = 'pillar_right'
  []

  [pillar_top]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 2
    paired_block = 101
    new_boundary = pillar_top
    input = 'pillar_bottom'
  []

  [pillar_back]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 2
    paired_block = 105
    new_boundary = pillar_back
    input = 'pillar_top'
  []

  [rename_block]
    type = RenameBlockGenerator
    old_block = '2 11 12 13 14 15 16 101 102 103 104 105'
    new_block = '2 1  1  1  1  1  1  0   0   0   0   0'
    input = 'pillar_back'
  []
[]

[GrayDiffuseRadiation]
  [cavity]
    sidesets = '6 7 8 9 10 11 12 13 14 15 16'
    emissivity = '0.8 0.8 0.8 0.8 0.8 eps_fn 0.8 0.8 0.8 0.8 0.8'
    n_patches = '5 5 5 5 5 5 5 5 5 5 5'
    partitioners = 'metis metis metis metis metis metis metis metis metis metis metis'
    temperature = temperature
    ray_tracing_face_order = SECOND
  []
[]

[Functions]
  [eps_fn]
    type = ConstantFunction
    value = 0.8
  []
[]

[Variables]
  [temperature]
    initial_condition = 300
    block = '1 2'
  []
[]

[Kernels]
  [hc]
    type = HeatConduction
    variable = temperature
    block = '1 2'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 500
  []

  [front]
    type = DirichletBC
    variable = temperature
    boundary = front
    value = 300
  []
[]

[Materials]
  [hcmat]
    type = HeatConductionMaterial
    thermal_conductivity = 25.0
    specific_heat = 490.0
    block = '1 2'
  []

  [density]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = '80'
    block = '1 2'
  []
[]

[Executioner]
  type = Steady
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/code_verification/cylindrical_test_no3.i)

# Problem II.3
#
# The thermal conductivity of an infinitely long hollow cylinder varies
# linearly with temperature: k = k0(1+beta*u). The tube inside radius is ri and
# outside radius is ro. It has a constant internal heat generation q and
# is exposed to the same constant temperature on both surfaces: u(ri) = u(ro) = uo.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    xmin = 0.2
    nx = 4
  [../]
  coord_type = RZ
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./exact]
    type = ParsedFunction
    symbol_names = 'q k0 ri ro beta u0'
    symbol_values = '1200 1 0.2 1.0 1e-3 0'
    expression = 'u0+(1/beta)*( ( 1 + 0.5*beta*((ro^2-x^2)-(ro^2-ri^2) * log(ro/x)/log(ro/ri))*q/k0 )^0.5  - 1)'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
  [./heatsource]
    type = HeatSource
    function = 1200
    variable = u
  [../]
[]

[BCs]
  [./uo]
    type = DirichletBC
    boundary = 'left right'
    variable = u
    value = 0
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat'
    prop_values = '1.0 1.0'
  [../]
  [./thermal_conductivity]
    type = ParsedMaterial
    property_name = 'thermal_conductivity'
    coupled_variables = u
    expression = '1 * (1 + 1e-3*u)'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/heat_source_bar/heat_source_bar.i)

# This is a simple 1D test of the volumetric heat source with material properties
# of a representative ceramic material.  A bar is uniformly heated, and a temperature
# boundary condition is applied to the left side of the bar.

# Important properties of problem:
# Length: 0.01 m
# Thermal conductivity = 3.0 W/(mK)
# Specific heat = 300.0 J/K
# density = 10431.0 kg/m^3
# Prescribed temperature on left side: 600 K

# When it has reached steady state, the temperature as a function of position is:
#  T = -q/(2*k) (x^2 - 2*x*length) + 600
#  or
#  T = -6.3333e+7 * (x^2 - 0.02*x) + 600
#  on left side: T=600, on right side, T=6933.3

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmax = 0.01
  nx = 20
[]

[Variables]
  [./temp]
    initial_condition = 300.0
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./heatsource]
    type = HeatSource
    function = volumetric_heat
    variable = temp
  [../]
[]

[BCs]
  [./lefttemp]
    type = DirichletBC
    boundary = left
    variable = temp
    value = 600
  [../]
[]

[Materials]
  [./density]
    type = GenericConstantMaterial
    prop_names = 'density  thermal_conductivity'
    prop_values = '10431.0 3.0'
  [../]
[]

[Functions]
  [./volumetric_heat]
     type = ParsedFunction
     expression = 3.8e+8
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./right]
    type = SideAverageValue
    variable = temp
    boundary = right
  [../]
  [./error]
    type = NodalL2Error
    function = '-3.8e+8/(2*3) * (x^2 - 2*x*0.01) + 600'
    variable = temp
  [../]
[]

[Outputs]
  execute_on = FINAL
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/gap_heat_transfer_mortar.i)

[Mesh]
  [file]
    type = FileMeshGenerator
    file = 2blk-gap.e
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '101'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
    input = file
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '100'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
    input = secondary
  []
[]

[Problem]
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    block = '1 2'
  [../]

  [./lm]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  [../]
[]

[Materials]
  [./left]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1000
    specific_heat = 1
  [../]

  [./right]
    type = HeatConductionMaterial
    block = 2
    thermal_conductivity = 500
    specific_heat = 1
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
    use_displaced_mesh = false
    block = '1 2'
  [../]
[]

[Constraints]
  [./ced]
    type = GapConductanceConstraint
    variable = lm
    secondary_variable = temp
    k = 100
    primary_boundary = 100
    primary_subdomain = 10000
    secondary_boundary = 101
    secondary_subdomain = 10001
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temp
    boundary = 'left'
    value = 1
  [../]

  [./right]
    type = DirichletBC
    variable = temp
    boundary = 'right'
    value = 0
  [../]
[]

[Preconditioning]
  [./fmp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  nl_rel_tol = 1e-11
[]

[Outputs]
  exodus = true
[]

(modules/functional_expansion_tools/examples/2D_interface_different_submesh/sub.i)

# Derived from the example '2D_interface' with the following differences:
#
#   1) The number of y divisions in the sub app is not the same as the master app
#   2) The subapp mesh is skewed in y
#   3) The Functional Expansion order for the flux term was increased to 7
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.4
  xmax = 2.4
  nx = 30
  ymin = 0.0
  ymax = 10.0
  ny = 23
  bias_y = 1.2
[]

[Variables]
  [./s]
  [../]
[]

[Kernels]
  [./diff_s]
    type = HeatConduction
    variable = s
  [../]
  [./time_diff_s]
    type = HeatConductionTimeDerivative
    variable = s
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_s]
    type = ConstantIC
    value = 2
    variable = s
  [../]
[]

[BCs]
  [./bottom]
    type = DirichletBC
    variable = s
    boundary = bottom
    value = 0.1
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = left
    variable = s
    function = FX_Basis_Flux_Sub
  [../]
[]

[Functions]
  [./FX_Basis_Value_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '7'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Sub]
    type = FXBoundaryValueUserObject
    function = FX_Basis_Value_Sub
    variable = s
    boundary = left
  [../]
  [./FX_Flux_UserObject_Sub]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Sub
    variable = s
    boundary = left
    diffusivity = thermal_conductivity
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

(modules/heat_transfer/test/tests/meshed_gap_thermal_contact/meshed_gap_thermal_contact_constant_conductance.i)

[Mesh]
  [fmesh]
    type = FileMeshGenerator
    file = meshed_gap.e
  []
  [block0]
    type = SubdomainBoundingBoxGenerator
    input = fmesh
    bottom_left = '.5 -.5 0'
    top_right = '.7 .5 0'
    block_id = 4
  []
[]

[Variables]
  [./temp]
    block = '1 3'
    initial_condition = 1.0
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
    block = '1 3'
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temp
    boundary = 1
    value = 1
  [../]
  [./right]
    type = DirichletBC
    variable = temp
    boundary = 4
    value = 2
  [../]
[]

[ThermalContact]
  [./gap_conductance]
    type = GapHeatTransfer
    variable = temp
    primary = 2
    secondary = 3
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductance = 2.5
  [../]
[]

[Materials]
  [./hcm]
    type = HeatConductionMaterial
    block = '1 3'
    temp = temp
    thermal_conductivity = 1
  [../]
[]

[Problem]
  type = FEProblem
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  [./out]
    type = Exodus
  [../]
[]

(modules/combined/test/tests/fdp_geometric_coupling/fdp_geometric_coupling.i)

[Mesh]
  file = twoBlocksContactDiceSecondary2OffsetGap.e
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
  [./temp]
    initial_condition = 100.0
  [../]
[]

[Functions]
  [./pressure]
    type = PiecewiseLinear
    x = '0 1 2'
    y = '0 1 1'
    scale_factor = 10.0
  [../]

  [./tempFunc]
    type = PiecewiseLinear
    x = '0. 3.'
    y = '100.0 440.0'
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  [./block1]
    block = 1
    volumetric_locking_correction = true
    incremental = true
    strain = FINITE
    eigenstrain_names = 'thermal_expansion1'
    decomposition_method = EigenSolution
    temperature = temp
  [../]
  [./block2]
    block = 2
    volumetric_locking_correction = true
    incremental = true
    strain = FINITE
    eigenstrain_names = 'thermal_expansion2'
    decomposition_method = EigenSolution
    temperature = temp
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./left_right_x]
    type = DirichletBC
    variable = disp_x
    boundary = '1 4'
    value = 0.0
  [../]

  [./left_right_y]
    type = DirichletBC
    variable = disp_y
    boundary = '1 4'
    value = 0.0
  [../]

  [./left_right_z]
    type = DirichletBC
    variable = disp_z
    boundary = '1 4'
    value = 0.0
  [../]

  [./temp]
    type = FunctionDirichletBC
    variable = temp
    boundary = '2 3'
    function = tempFunc
  [../]
[]

[Contact]
  [./dummy_name]
    primary = 2
    secondary = 3
    penalty = 1e8
  [../]
[]

[Materials]

  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2'
    youngs_modulus = 1e6
    poissons_ratio = 0.0
  [../]

  [./stress1]
    type = ComputeFiniteStrainElasticStress
    block = '1 2'
  [../]

  [./thermal_expansion1]
    type = ComputeThermalExpansionEigenstrain
    block = 1
    thermal_expansion_coeff = 1e-4
    stress_free_temperature = 100.0
    temperature = temp
    eigenstrain_name = thermal_expansion1
  [../]

  [./thermal_expansion2]
    type = ComputeThermalExpansionEigenstrain
    block = 2
    thermal_expansion_coeff = 1e-5
    stress_free_temperature = 100.0
    temperature = temp
    eigenstrain_name = thermal_expansion2
  [../]

  [./heat]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./density]
    type = Density
    block = '1 2'
    density = 1.0
  [../]
[]

[Preconditioning]
  [./FDP]
    type = FDP
    full = true
    implicit_geometric_coupling = true
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -mat_fd_coloring_err -mat_fd_type'
  petsc_options_value = 'lu       1e-8                 ds'

  nl_rel_tol = 1e-10

  l_max_its = 5
  nl_max_its = 3
  dt = 5.0e-1
  num_steps = 2
[]

[Outputs]
  file_base = fdp_geometric_coupling_out
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_balance/large_gap_heat_transfer_test_sphere.i)

sphere_outer_htc = 10 # W/m^2/K
sphere_outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = cyl2D.e
  []
  coord_type = RZ
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
[]

[AuxVariables]
  [gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  []
  [power_density]
    block = 'fuel'
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = 'fuel'
    v = power_density
  []
[]

[AuxKernels]
  [gap_cond]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_conductance
    boundary = 2
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0.8
    emissivity_secondary = 0.8
    gap_conductivity = 0.1
    quadrature = true
    gap_geometry_type = SPHERE
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = '4' # outer RPV
    coefficient = ${sphere_outer_htc}
    T_infinity = ${sphere_outer_Tinf}
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

  [Quadrature]
    order = fifth
    side_order = seventh
  []
[]

[Outputs]
  exodus = false
  csv = true
  [Console]
    type = Console
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  []

  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 'fuel'
  []
  [sphere_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = '4' # outer RVP
    T_fluid = ${sphere_outer_Tinf}
    htc = ${sphere_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(sphere_convective_out - ptot) / ptot'
    pp_names = 'sphere_convective_out ptot'
  []
[]

(modules/heat_transfer/tutorials/introduction/therm_step02.i)

#
# Single block thermal input with boundary conditions
# https://mooseframework.inl.gov/modules/heat_transfer/tutorials/introduction/therm_step02.html
#

[Mesh]
  [generated]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 2
    ymax = 1
  []
[]

[Variables]
  [T]
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 45.0
  []
[]

[BCs]
  [t_left]
    type = DirichletBC
    variable = T
    value = 300
    boundary = 'left'
  []
  [t_right]
    type = FunctionDirichletBC
    variable = T
    function = '300+5*t'
    boundary = 'right'
  []
[]

[Executioner]
  type = Transient
  end_time = 5
  dt = 1
[]

[Outputs]
  exodus = true
[]

(modules/combined/tutorials/introduction/thermal_mechanical_contact/thermomech_cont_step01.i)

#
# A first attempt at thermo mechanical contact
# https://mooseframework.inl.gov/modules/combined/tutorials/introduction/step01.html
#

[GlobalParams]
  displacements = 'disp_x disp_y'
  block = 0
[]

[Mesh]
  [generated1]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 15
    xmin = -0.6
    xmax = -0.1
    ymax = 5
    bias_y = 0.9
    boundary_name_prefix = pillar1
  []
  [generated2]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 6
    ny = 15
    xmin = 0.1
    xmax = 0.6
    ymax = 4.999
    bias_y = 0.9
    boundary_name_prefix = pillar2
    boundary_id_offset = 4
  []
  [collect_meshes]
    type = MeshCollectionGenerator
    inputs = 'generated1 generated2'
  []

  patch_update_strategy = iteration
[]

[Variables]
  # temperature field variable
  [T]
    # initialize to an average temperature
    initial_condition = 50
    order = FIRST
    family = LAGRANGE
  []
  # temperature lagrange multiplier
  [Tlm]
    block = 'pillars_secondary_subdomain'
    order = FIRST
    family = LAGRANGE
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
  [dTdt]
    type = HeatConductionTimeDerivative
    variable = T
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    strain = FINITE
    generate_output = 'vonmises_stress'
  []
[]

[Contact]
  [pillars]
    primary = pillar1_right
    secondary = pillar2_left
    model = frictionless
    formulation = mortar
  []
[]

[Constraints]
  # thermal contact constraint
  [Tlm]
    type = GapConductanceConstraint
    variable = Tlm
    secondary_variable = T
    use_displaced_mesh = true
    k = 1e-1
    primary_boundary = pillar1_right
    primary_subdomain = pillars_primary_subdomain
    secondary_boundary = pillar2_left
    secondary_subdomain = pillars_secondary_subdomain
  []
[]

[BCs]
  [bottom_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'pillar1_bottom pillar2_bottom'
    value = 0
  []
  [bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'pillar1_bottom pillar2_bottom'
    value = 0
  []
  [Pressure]
    [sides]
      boundary = 'pillar1_left pillar2_right'
      function = 1e4*t^2
    []
  []

  # thermal boundary conditions (pillars are heated/cooled from the bottom)
  [heat_left]
    type = DirichletBC
    variable = T
    boundary = pillar1_bottom
    value = 100
  []
  [cool_right]
    type = DirichletBC
    variable = T
    boundary = pillar2_bottom
    value = 0
  []
[]

[Materials]
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
  []

  # thermal properties
  [thermal_conductivity]
    type = HeatConductionMaterial
    thermal_conductivity = 100
    specific_heat = 1
  []
  [density]
    type = Density
    density = 1
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  line_search = none
  # we deal with the saddle point structure of the system by adding a small shift
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       nonzero'
  end_time = 5
  dt = 0.1
  [Predictor]
    type = SimplePredictor
    scale = 1
  []
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
  perf_graph = true
[]

(modules/combined/test/tests/adaptive_timestepping/adapt_tstep_function_change_restart1.i)

# This is a test designed to evaluate the cabability of the
# IterationAdaptiveDT TimeStepper to adjust time step size according to
# a function.  For example, if the power input function for a BISON
# simulation rapidly increases or decreases, the IterationAdaptiveDT
# TimeStepper should take time steps small enough to capture the
# oscillation.

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  file = 1hex8_10mm_cube.e
[]

[Functions]
  [./Fiss_Function]
    type = PiecewiseLinear
    x = '0 1e6  2e6  2.001e6 2.002e6'
    y = '0 3e8  3e8  12e8    0'
  [../]
[]

[Variables]
  [./disp_x]
  [../]

  [./disp_y]
  [../]

  [./disp_z]
  [../]

  [./temp]
    initial_condition = 300.0
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  [./all]
    strain = FINITE
    incremental = true
    volumetric_locking_correction = true
    eigenstrain_names = thermal_expansion
    decomposition_method = EigenSolution
    add_variables  = true
    generate_output = 'vonmises_stress'
    temperature = temp
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]

  [./heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]

  [./heat_source]
     type = HeatSource
     variable = temp
     value = 1.0
     function = Fiss_Function
  [../]
[]

[BCs]
 [./bottom_temp]
   type = DirichletBC
   variable = temp
   boundary = 1
   value = 300
 [../]
 [./top_bottom_disp_x]
   type = DirichletBC
   variable = disp_x
   boundary = '1'
   value = 0
 [../]
 [./top_bottom_disp_y]
   type = DirichletBC
   variable = disp_y
   boundary = '1'
   value = 0
 [../]
 [./top_bottom_disp_z]
   type = DirichletBC
   variable = disp_z
   boundary = '1'
   value = 0
 [../]
[]

[Materials]
 [./thermal]
    type = HeatConductionMaterial
    temp = temp
    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 300e6
    poissons_ratio = .3
  [../]

  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]

  [./thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 5e-6
    stress_free_temperature = 300.0
    temperature = temp
    eigenstrain_name = thermal_expansion
  [../]

  [./density]
    type = Density
    density = 10963.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  verbose = true
  nl_abs_tol = 1e-10
  start_time = 0.0

  num_steps = 65
  end_time = 2.002e6
  [./TimeStepper]
    type = IterationAdaptiveDT
    timestep_limiting_function = Fiss_Function
    max_function_change = 3e7
    dt = 1e6
  [../]
[]

[Postprocessors]
  [./Temperature_of_Block]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./vonMises]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  [./out]
    type = Exodus
    elemental_as_nodal = true
  [../]
  [./console]
    type = Console
    max_rows = 10
  [../]
  [./checkpoint]
    type = Checkpoint
    num_files = 1
  [../]
[]

(modules/subchannel/test/tests/problems/coupling/sub.i)

pin_diameter = 0.012065
heated_length = 1.0

[Mesh]
  second_order = true
  [myMesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 0.0060325 # pin diameter / 2.0
    bias_x = 1.0
    nx = 20
    ymax = 1.0 # heated length
    ny = 10 # number of axial cells
  []
  coord_type = RZ
  rz_coord_axis = Y
  beta_rotation = 90
[]

[Functions]
  [volumetric_heat_rate] # Defined such as to be consistent with the IC in SCM
      type = ParsedFunction
      expression = '(4.0 * 1000 / (pi * D * D * L)) * (pi/2)*sin(pi*y/L)'
      symbol_names = 'L D'
      symbol_values = '${heated_length} ${pin_diameter}'
  []
[]

[Variables]
  [temperature]
    order = SECOND
    family = LAGRANGE
  []
[]

[AuxVariables]
  [Pin_surface_temperature]
  []
  [q_prime]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [QPrime]
    type = SCMRZPinQPrimeAux
    diffusivity = 'thermal_conductivity'
    variable = q_prime
    diffusion_variable = temperature
    component = normal
    boundary = 'right'
    execute_on = 'timestep_end'
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temperature
  []
  [heat_source]
    type = HeatSource
    variable = temperature
    function = volumetric_heat_rate
  []
[]

[Materials]
  [heat_conductor]
    type = HeatConductionMaterial
    thermal_conductivity = 1.0
    block = 0
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = temperature
    boundary = 'left'
  []
  [right]
    type = MatchedValueBC
    variable = temperature
    boundary = 'right'
    v = Pin_surface_temperature
  []
[]

[VectorPostprocessors]
  # These samplers are used for testing purposes.
  [sample_center_line]
    type = LineValueSampler
    variable = 'temperature'
    sort_by = 'y'
    num_points = 11
    start_point = '0 0 0'
    end_point = '0 1.0 0'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/gap_heat_transfer_htonly_rspherical.i)

#
# 1-D spherical Gap Heat Transfer Test
#
# This test exercises 1-D gap heat transfer for a constant conductivity gap.
#
# The mesh consists of two "blocks" with a mesh biased toward the gap
#   between them.  Each block is unit length.  The gap between them is one
#   unit in length.
#
# The conductivity of both blocks is set very large to achieve a uniform temperature
#  across each block. The temperature of the far left boundary
#  is ramped from 100 to 200 over one time unit, and then held fixed for an additional
#  time unit.  The temperature of the far right boundary is held fixed at 100.
#
# A simple analytical solution is possible for the heat flux between the blocks, or spheres in the case of RSPHERICAL.:
#
#  Flux = (T_left - T_right) * (gapK/(r^2*((1/r1)-(1/r2))))
#
# For gapK = 1 (default value)
#
# The area is taken as the area of the secondary (inner) surface:
#
# Area = 4 * pi * 1 * 1
#
# The integrated heat flux across the gap at time 2 is then:
#
# 4*pi*k*delta_T/((1/r1)-(1/r2))
# 4*pi*1*100/((1/1) - (1/2)) =  2513.3 watts
#
# For comparison, see results from the flux post processors.
#
#

[Mesh]
  file = gap_heat_transfer_htonly_rspherical.e
  construct_side_list_from_node_list = true
  coord_type = RSPHERICAL
[]

[Functions]
  [./temp]
    type = PiecewiseLinear
    x = '0   1   2'
    y = '100 200 200'
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_geometry_type = sphere
  [../]
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  [../]
[]

[AuxVariables]
  [./gap_cond]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]


[BCs]
  [./temp_far_left]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  [../]

  [./temp_far_right]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
[]

[AuxKernels]
  [./conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 2
  [../]
[]

[Materials]
  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 1e6
  [../]
  [./density]
    type = GenericConstantMaterial
    block = '1 2'
    prop_names = 'density'
    prop_values = '1.0'
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  # I don't know enough about this test to say why it needs such a
  # loose nl_abs_tol... after timestep 10 the residual basically can't
  # be reduced much beyond the initial residual.  The test probably
  # needs to be revisited to determine why.
  nl_abs_tol = 1e-3
  nl_rel_tol = 1e-10
  l_tol = 1e-6
  l_max_its = 100
  line_search = 'none'
  nl_max_its = 10

  dt = 1e-1
  dtmin = 1e-1
  end_time = 2.0
[]

[Postprocessors]

  [./temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  [../]

  [./flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  [../]
[]


[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/NAFEMS/transient/T3/nafems_t3_edge_template.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 5
  xmin = 0.0
  xmax = 0.1
  elem_type = EDGE2
[]

[Variables]
  [./temp]
    initial_condition = 0.0
  [../]
[]

[BCs]
  [./FixedTempLeft]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 0.0
  [../]
  [./FunctionTempRight]
    type = FunctionDirichletBC
    variable = temp
    boundary = right
    function = '100.0 * sin(pi*t/40)'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./HeatTdot]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]
[]

[Materials]
  [./density]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '35.0 440.5 7200.0'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  l_tol = 1e-5
  nl_max_its = 50
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-12

  dt = 1
  end_time = 32.0
[]

[Postprocessors]
  [./target_temp]
    type = NodalVariableValue
    variable = temp
    nodeid = 4
  [../]
[]

[Outputs]
  csv = true
[]

(modules/combined/test/tests/thermal_strain/thermal_strain.i)

# Patch Test

# This test is designed to compute displacements from a thermal strain.

# The cube is displaced by 1e-6 units in x, 2e-6 in y, and 3e-6 in z.
#  The faces are sheared as well (1e-6, 2e-6, and 3e-6 for xy, yz, and
#  zx).  This gives a uniform strain/stress state for all six unique
#  tensor components.

# The temperature moves 100 degrees, and the coefficient of thermal
#  expansion is 1e-6.  Therefore, the strain (and the displacement
#  since this is a unit cube) is 1e-4.
[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  file = thermal_strain_test.e
[]

[Functions]
  [./tempFunc]
    type = PiecewiseLinear
    x = '0. 1.'
    y = '117.56 217.56'
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]

  [./temp]
    initial_condition = 117.56
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  add_variables = true
  strain = SMALL
  incremental = true
  generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_yz stress_zx'
  temperature = temp

  [./block1]
    eigenstrain_names = eigenstrain1
    block = 1
  [../]
  [./block2]
    eigenstrain_names = eigenstrain2
    block = 2
  [../]
  [./block3]
    eigenstrain_names = eigenstrain3
    block = 3
  [../]
  [./block4]
    eigenstrain_names = eigenstrain4
    block = 4
  [../]
  [./block5]
    eigenstrain_names = eigenstrain5
    block = 5
  [../]
  [./block6]
    eigenstrain_names = eigenstrain6
    block = 6
  [../]
  [./block7]
    eigenstrain_names = eigenstrain7
    block = 7
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./no_x]
    type = DirichletBC
    variable = disp_x
    boundary = 10
    value = 0.0
  [../]
  [./no_y]
    type = DirichletBC
    variable = disp_y
    boundary = 9
    value = 0.0
  [../]
  [./no_z]
    type = DirichletBC
    variable = disp_z
    boundary = 14
    value = 0
  [../]

  [./temp]
    type = FunctionDirichletBC
    variable = temp
    boundary = '10 12'
    function = tempFunc
  [../]
[]

[Materials]
  [./elasticity_tensor1]
    type = ComputeIsotropicElasticityTensor
    block = 1
    bulk_modulus = 0.333333333333e6
    poissons_ratio = 0.0
  [../]
  [./thermal_strain1]
    type = ComputeThermalExpansionEigenstrain
    block = 1
    temperature = temp
    stress_free_temperature = 117.56
    thermal_expansion_coeff = 1e-6
    eigenstrain_name = eigenstrain1
  [../]
  [./stress1]
    type = ComputeStrainIncrementBasedStress
    block = 1
  [../]

  [./elasticity_tensor2]
    type = ComputeIsotropicElasticityTensor
    block = 2
    bulk_modulus = 0.333333333333e6
    lambda = 0.0
  [../]
  [./thermal_strain2]
    type = ComputeThermalExpansionEigenstrain
    block = 2
    temperature = temp
    stress_free_temperature = 117.56
    thermal_expansion_coeff = 1e-6
    eigenstrain_name = eigenstrain2
  [../]
  [./stress2]
    type = ComputeStrainIncrementBasedStress
    block = 2
  [../]

  [./elasticity_tensor3]
    type = ComputeIsotropicElasticityTensor
    block = 3
    youngs_modulus = 1e6
    poissons_ratio = 0.0
  [../]
  [./thermal_strain3]
    type = ComputeThermalExpansionEigenstrain
    block = 3
    temperature = temp
    stress_free_temperature = 117.56
    thermal_expansion_coeff = 1e-6
    eigenstrain_name = eigenstrain3
  [../]
  [./stress3]
    type = ComputeStrainIncrementBasedStress
    block = 3
  [../]

  [./elasticity_tensor4]
    type = ComputeIsotropicElasticityTensor
    block = 4
    youngs_modulus = 1e6
    poissons_ratio = 0.0
  [../]
  [./thermal_strain4]
    type = ComputeThermalExpansionEigenstrain
    block = 4
    temperature = temp
    stress_free_temperature = 117.56
    thermal_expansion_coeff = 1e-6
    eigenstrain_name = eigenstrain4
  [../]
  [./stress4]
    type = ComputeStrainIncrementBasedStress
    block = 4
  [../]

  [./elasticity_tensor5]
    type = ComputeIsotropicElasticityTensor
    block = 5
    youngs_modulus = 1e6
    lambda = 0.0
  [../]
  [./thermal_strain5]
    type = ComputeThermalExpansionEigenstrain
    block = 5
    temperature = temp
    stress_free_temperature = 117.56
    thermal_expansion_coeff = 1e-6
    eigenstrain_name = eigenstrain5
  [../]
  [./stress5]
    type = ComputeStrainIncrementBasedStress
    block = 5
  [../]

  [./elasticity_tensor6]
    type = ComputeIsotropicElasticityTensor
    block = 6
    youngs_modulus = 1e6
    shear_modulus = 5e5
  [../]
  [./thermal_strain6]
    type = ComputeThermalExpansionEigenstrain
    block = 6
    temperature = temp
    stress_free_temperature = 117.56
    thermal_expansion_coeff = 1e-6
    eigenstrain_name = eigenstrain6
  [../]
  [./stress6]
    type = ComputeStrainIncrementBasedStress
    block = 6
  [../]

  [./elasticity_tensor7]
    type = ComputeIsotropicElasticityTensor
    block = 7
    shear_modulus = 5e5
    poissons_ratio = 0.0
  [../]
  [./thermal_strain7]
    type = ComputeThermalExpansionEigenstrain
    block = 7
    temperature = temp
    stress_free_temperature = 117.56
    thermal_expansion_coeff = 1e-6
    eigenstrain_name = eigenstrain7
  [../]
  [./stress7]
    type = ComputeStrainIncrementBasedStress
    block = 7
  [../]

  [./heat]
    type = HeatConductionMaterial
    block = '1 2 3 4 5 6 7'
    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./density]
    type = Density
    block = '1 2 3 4 5 6 7'
    density = 1.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  nl_abs_tol = 1e-10

  l_max_its = 20

  start_time = 0.0
  dt = 0.5
  num_steps = 2
  end_time = 1.0
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/multiple_radiation_cavities/multiple_radiation_cavities.i)

[Problem]
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
  [cartesian]
    type = CartesianMeshGenerator
    dim = 2
    dx = '0.5 4 1 4 0.5'
    ix = '2 2 2 2 2'
    dy = '0.3 10 1'
    iy = '2 2 2'
    subdomain_id = '1  2  3  4   5
                    6  7  8  9  10
                    11 12 13 14 15'
  []

  [add_side_left_left]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 6
    paired_block = 7
    new_boundary = left_left
    input = cartesian
  []

  [add_side_left_bottom]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 2
    paired_block = 7
    new_boundary = left_bottom
    input = add_side_left_left
  []

  [add_side_left_right]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 8
    paired_block = 7
    new_boundary = left_right
    input = add_side_left_bottom
  []

  [add_side_left_top]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 12
    paired_block = 7
    new_boundary = left_top
    input = add_side_left_right
  []

  [add_side_right_left]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 8
    paired_block = 9
    new_boundary = right_left
    input = add_side_left_top
  []

  [add_side_right_bottom]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 4
    paired_block = 9
    new_boundary = right_bottom
    input = add_side_right_left
  []

  [add_side_right_right]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 10
    paired_block = 9
    new_boundary = right_right
    input = add_side_right_bottom
  []

  [add_side_right_top]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 14
    paired_block = 9
    new_boundary = right_top
    input = add_side_right_right
  []
[]

[GrayDiffuseRadiation]
  [left]
    boundary = 'left_left left_right left_bottom left_top'
    emissivity = '0.8 0.8 0.9 0.5'
    n_patches = '2 2 2 2'
    temperature = temperature
    ray_tracing_face_order = SECOND
  []

  [right]
    boundary = 'right_left right_right right_bottom right_top'
    emissivity = '0.8 0.8 0.9 0.5'
    n_patches = '2 2 2 2'
    temperature = temperature
    ray_tracing_face_order = SECOND
  []
[]

[Variables]
  [temperature]
    block =  '1  2  3  4  5 6   8  10 11 12 13 14 15'
    initial_condition = 300
  []
[]

[Kernels]
  [conduction]
    type = HeatConduction
    variable = temperature
    diffusion_coefficient = 10
    block =  '1  2  3  4  5 6   8  10 11 12 13 14 15'
  []
[]

[BCs]
  [bottom]
    type = DirichletBC
    variable = temperature
    value = 300
    boundary = bottom
  []

  [top]
    type = DirichletBC
    variable = temperature
    value = 400
    boundary = top
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/functional_expansion_tools/examples/2D_interface/sub.i)

# Basic example coupling a master and sub app at an interface in a 2D model.
# The master app provides a flux term to the sub app via Functional Expansions, which then performs
# its calculations.  The sub app's interface conditions, both value and flux, are transferred back
# to the master app
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.4
  xmax = 2.4
  nx = 30
  ymin = 0.0
  ymax = 10.0
  ny = 20
[]

[Variables]
  [./s]
  [../]
[]

[Kernels]
  [./diff_s]
    type = HeatConduction
    variable = s
  [../]
  [./time_diff_s]
    type = HeatConductionTimeDerivative
    variable = s
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_s]
    type = ConstantIC
    value = 2
    variable = s
  [../]
[]

[BCs]
  [./bottom]
    type = DirichletBC
    variable = s
    boundary = bottom
    value = 0.1
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = left
    variable = s
    function = FX_Basis_Flux_Sub
  [../]
[]

[Functions]
  [./FX_Basis_Value_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '5'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Sub]
    type = FXBoundaryValueUserObject
    function = FX_Basis_Value_Sub
    variable = s
    boundary = left
  [../]
  [./FX_Flux_UserObject_Sub]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Sub
    variable = s
    boundary = left
    diffusivity = thermal_conductivity
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/cyl2D_yz.i)

#
# 2D Cylindrical Gap Heat Transfer Test.
#
# This test exercises 2D gap heat transfer for a constant conductivity gap.
#
# The mesh consists of an inner solid cylinder of radius = 1 unit, and outer
# hollow cylinder with an inner radius of 2 in the y-z plane. In other words,
# the gap between them is 1 radial unit in length.
#
# The calculated results are the same as for the cyl2D.i case in the x-y plane.

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = cyl2D.e
  []
  [./rotate]
    type = TransformGenerator
    transform = ROTATE
    vector_value = '0 90 90'
    input = file
  [../]
[]

[Functions]
  [./temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  [../]
[]

[Variables]
  [./temp]
   initial_condition = 100
  [../]
[]

[AuxVariables]
  [./gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temp
  [../]
[]

[AuxKernels]
  [./gap_cond]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_conductance
    boundary = 2
  [../]
[]

[Materials]
  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 1000000.0
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductivity = 1
    quadrature = true
    gap_geometry_type = CYLINDER
    cylinder_axis_point_1 = '0 0 0'
    cylinder_axis_point_2 = '1 0 0'
  [../]
[]

[BCs]
  [./mid]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  [../]
  [./temp_far_right]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

  [./Quadrature]
     order = fifth
     side_order = seventh
  [../]
[]

[Outputs]
  exodus = true
[]

[Postprocessors]
  [./temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  [../]

  [./temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  [../]

  [./flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  [../]

  [./flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  [../]
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_sphere_mortar_error.i)

sphere_outer_htc = 10 # W/m^2/K
sphere_outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Problem]
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = cyl2D.e
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '2'
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    input = file
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '3'
    new_block_id = 10000
    new_block_name = 'primary_lower'
    input = secondary
  []
  allow_renumbering = false
  coord_type = RZ
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
  [lm]
    order = SECOND
    family = LAGRANGE
    block = 'secondary_lower'
  []
[]

[AuxVariables]
  [power_density]
    block = 'fuel'
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
    block = '1 2'
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = 'fuel'
    v = power_density
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[UserObjects]
  [radiation]
    type = GapFluxModelRadiation
    temperature = temp
    boundary = 2
    primary_emissivity = 0.0
    secondary_emissivity = 0.0
  []
  [conduction]
    type = GapFluxModelConduction
    temperature = temp
    boundary = 2
    gap_conductivity = 5.0
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = temp
    primary_boundary = 3
    primary_subdomain = 10000
    secondary_boundary = 2
    secondary_subdomain = 10001
    gap_flux_models = 'radiation conduction'
    gap_geometry_type = SPHERE
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = '4' # outer RPV
    coefficient = ${sphere_outer_htc}
    T_infinity = ${sphere_outer_Tinf}
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

[]

[Outputs]
  exodus = true
  csv = true
  [Console]
    type = Console
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = '2 3'
    variable = temp
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  []

  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 'fuel'
  []
  [sphere_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = '4' # outer RVP
    T_fluid = ${sphere_outer_Tinf}
    htc = ${sphere_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(sphere_convective_out - ptot) / ptot'
    pp_names = 'sphere_convective_out ptot'
  []
[]

(tutorials/tutorial03_verification/app/test/tests/step04_mms/2d_main.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    ymax = 0
    ymin = -0.2
    nx = 20
    ny = 4
  []
[]

[Variables]
  [T]
  []
[]

[ICs]
  [T_O]
    type = ConstantIC
    variable = T
    value = 263.15
  []
[]

[Functions]
  [source]
    type = ParsedFunction
    symbol_names = 'hours shortwave kappa'
    symbol_values = '9     650      40'
    expression = 'shortwave*sin(0.5*x*pi)*exp(kappa*y)*sin(1/(hours*3600)*pi*t)'
  []
[]

[Kernels]
  [T_time]
    type = HeatConductionTimeDerivative
    variable = T
    density_name = 150
    specific_heat = 2000
  []
  [T_cond]
    type = HeatConduction
    variable = T
    diffusion_coefficient = 0.01
  []
  [T_source]
    type = HeatSource
    variable = T
    function = source
  []
[]

[BCs]
  [top]
    type = NeumannBC
    boundary = top
    variable = T
    value = -5
  []
  [bottom]
    type = DirichletBC
    boundary = bottom
    variable = T
    value = 263.15
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  dt = 600 # 10 min
  end_time = 32400 # 9 hour
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/gap_heat_transfer_htonly_test.i)

#
# 1-D Gap Heat Transfer Test without mechanics
#
# This test exercises 1-D gap heat transfer for a constant conductivity gap.
#
# The mesh consists of two element blocks containing one element each.  Each
#   element is a unit cube.  They sit next to one another with a unit between them.
#
# The conductivity of both blocks is set very large to achieve a uniform temperature
#  across each block. The temperature of the far left boundary
#  is ramped from 100 to 200 over one time unit.  The temperature of the far right
#  boundary is held fixed at 100.
#
# A simple analytical solution is possible for the heat flux between the blocks:
#
#  Flux = (T_left - T_right) * (gapK/gap_width)
#
# The gap conductivity is specified as 1, thus
#
#  gapK(Tavg) = 1.0*Tavg
#
#
# The heat flux across the gap at time = 1 is then:
#
#  Flux(2) = 100 * (1.0/1.0) = 100
#
# For comparison, see results from the flux post processors
#
# This test has been augmented with a second scalar field that solves nearly
#   the same problem.  The conductivity has been changed to 10.  Thus, the
#   flux for the second field is 1000.
#


[Mesh]
  file = gap_heat_transfer_htonly_test.e
[]

[Functions]

  [./temp]
    type = PiecewiseLinear
    x = '0   1   2'
    y = '100 200 200'
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
  [../]
  [./awesomium_contact]
    type = GapHeatTransfer
    variable = awesomium
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductivity = 10
    appended_property_name = _awesomium
  [../]
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  [../]
  [./awesomium]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  [../]
[]

[AuxVariables]
  [./gap_cond]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./gap_cond_awesomium]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./awe]
    type = HeatConduction
    variable = awesomium
  [../]
[]


[BCs]
  [./temp_far_left]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  [../]
  [./temp_far_right]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
  [./awesomium_far_left]
    type = FunctionDirichletBC
    boundary = 1
    variable = awesomium
    function = temp
  [../]
  [./awesomium_far_right]
    type = DirichletBC
    boundary = 4
    variable = awesomium
    value = 100
  [../]
[]

[AuxKernels]
  [./conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 2
  [../]
  [./conductance_awe]
    type = MaterialRealAux
    property = gap_conductance_awesomium
    variable = gap_cond_awesomium
    boundary = 2
  [../]
[]

[Materials]

  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 100000000.0
  [../]
  [./density]
    type = GenericConstantMaterial
    block = '1 2'
    prop_names = 'density'
    prop_values = '1.0'
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'
  nl_rel_tol = 1e-12
  l_tol = 1e-3
  l_max_its = 100

  dt = 1e-1
  end_time = 1.0
[]

[Postprocessors]

  [./temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  [../]

  [./flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  [../]

  [./awe_left]
    type = SideAverageValue
    boundary = 2
    variable = awesomium
    execute_on = 'initial timestep_end'
  [../]

  [./awe_right]
    type = SideAverageValue
    boundary = 3
    variable = awesomium
    execute_on = 'initial timestep_end'
  [../]

  [./awe_flux_left]
    type = SideDiffusiveFluxIntegral
    variable = awesomium
    boundary = 2
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  [../]

  [./awe_flux_right]
    type = SideDiffusiveFluxIntegral
    variable = awesomium
    boundary = 3
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/radiation_transfer_action/radiative_transfer_action_external_boundary.i)

[Problem]
  kernel_coverage_check = false
[]

[Mesh]
  [./cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1.3 1.9'
    ix = '3 3 3'
    dy = '6'
    iy = '9'
    subdomain_id = '0 1 2'
  [../]

    [./inner_left]
      type = SideSetsBetweenSubdomainsGenerator
      input = cmg
      primary_block = 0
      paired_block = 1
      new_boundary = 'inner_left'
    [../]

    [./inner_right]
      type = SideSetsBetweenSubdomainsGenerator
      input = inner_left
      primary_block = 2
      paired_block = 1
      new_boundary = 'inner_right'
    [../]

    [./inner_top]
      type = ParsedGenerateSideset
      combinatorial_geometry = 'abs(y - 6) < 1e-10'
      normal = '0 1 0'
      included_subdomains = 1
      new_sideset_name = 'inner_top'
      input = 'inner_right'
    [../]

    [./inner_bottom]
      type = ParsedGenerateSideset
      combinatorial_geometry = 'abs(y) < 1e-10'
      normal = '0 -1 0'
      included_subdomains = 1
      new_sideset_name = 'inner_bottom'
      input = 'inner_top'
    [../]

    [./rename]
      type = RenameBlockGenerator
      old_block = '2'
      new_block = '0'
      input = inner_bottom
    [../]
[]

[Variables]
  [./temperature]
    block = 0
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temperature
    block = 0
    diffusion_coefficient = 5
  [../]
[]

[GrayDiffuseRadiation]
  [./cavity]
    boundary = '4 5 6 7'
    emissivity = '0.9 0.8 eps_fn 1'
    n_patches = '2 2 2 3'
    partitioners = 'centroid centroid centroid centroid'
    centroid_partitioner_directions = 'x y y x'
    temperature = temperature
    adiabatic_boundary = '7'
    fixed_temperature_boundary = '6'
    fixed_boundary_temperatures = '800'
    view_factor_calculator = analytical
  [../]
[]

[Functions]
  [eps_fn]
    type = ConstantFunction
    value = 0.4
  []
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 1000
  [../]

  [./right]
    type = DirichletBC
    variable = temperature
    boundary = right
    value = 300
  [../]
[]

[Postprocessors]
  [./average_T_inner_right]
    type = SideAverageValue
    variable = temperature
    boundary = inner_right
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/cyl2D.i)

#
# 2D Cylindrical Gap Heat Transfer Test.
#
# This test exercises 2D gap heat transfer for a constant conductivity gap.
#
# The mesh consists of an inner solid cylinder of radius = 1 unit, and outer
# hollow cylinder with an inner radius of 2 in the x-y plane. In other words,
# the gap between them is 1 radial unit in length.
#
# The conductivity of both cylinders is set very large to achieve a uniform
# temperature in each cylinder. The temperature of the center node of the
# inner cylinder is ramped from 100 to 200 over one time unit. The temperature
# of the outside of the outer, hollow cylinder is held fixed at 100.
#
# A simple analytical solution is possible for the integrated heat flux
# between the inner and outer cylinders:
#
#  Integrated Flux = (T_left - T_right) * (gapK/(r*ln(r2/r1))) * Area
#
# For gapK = 1 (default value)
#
# The area is taken as the area of the secondary (inner) surface:
#
# Area = 2 * pi * h * r, where h is the height of the cylinder.
#
# The integrated heat flux across the gap at time 1 is then:
#
# 2*pi*h*k*delta_T/(ln(r2/r1))
# 2*pi*1*1*100/(ln(2/1)) = 906.5 watts
#
# For comparison, see results from the integrated flux post processors.
# This simulation makes use of symmetry, so only 1/4 of the cylinders is meshed
# As such, the integrated flux from the post processors is 1/4 of the total,
# or 226.6 watts.
# The value coming from the post processor is slightly less than this
# but converges as mesh refinement increases.
# Note that the 2D and 3D results are the same.
#
# Simulating contact is challenging. Regression tests that exercise
# contact features can be difficult to solve consistently across multiple
# platforms. While designing these tests, we felt it worth while to note
# some aspects of these tests. The following applies to:
# sphere3D.i, sphere2DRZ.i, cyl2D.i, and cyl3D.i.
# 1. We decided that to perform consistently across multiple platforms we
# would use very small convergence tolerance. In this test we chose an
# nl_rel_tol of 1e-12.
# 2. Due to such a high value for thermal conductivity (used here so that the
# domains come to a uniform temperature) the integrated flux at time = 0
# was relatively large (the value coming from SideIntegralFlux =
#  -_diffusion_coef[_qp]*_grad_u[_qp]*_normals[_qp] where the diffusion coefficient
# here is thermal conductivity).
# Even though _grad_u[_qp] is small, in this case the diffusion coefficient
# is large. The result is a number that isn't exactly zero and tends to
# fail exodiff. For this reason the parameter execute_on = initial should not
# be used. That parameter is left to default settings in these regression tests.
#
[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]


[Mesh]
  file = cyl2D.e
[]

[Functions]
  [./temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  [../]
[]


[Variables]
  [./temp]
   initial_condition = 100
  [../]
[]

[AuxVariables]
  [./gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]


[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temp
  [../]
[]


[AuxKernels]
  [./gap_cond]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_conductance
    boundary = 2
  [../]
[]

[Materials]
  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 1000000.0
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductivity = 1
    quadrature = true
    gap_geometry_type = CYLINDER
    cylinder_axis_point_1 = '0 0 0'
    cylinder_axis_point_2 = '0 0 1'
  [../]
[]

[BCs]
  [./mid]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  [../]
  [./temp_far_right]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

  [./Quadrature]
     order = fifth
     side_order = seventh
  [../]
[]

[Outputs]
  exodus = true
  [./Console]
    type = Console
  [../]
[]

[Postprocessors]
  [./temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  [../]

  [./temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  [../]

  [./flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  [../]

  [./flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  [../]
[]

(modules/heat_transfer/test/tests/truss_heat_conduction/block_w_bar.i)

[Mesh]
  [whole]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 3
    ny = 50
    nz = 1
    xmin = -0.5
    xmax = 0.5
    ymin = -1.25
    ymax = 1.25
    zmin = -0.04
    zmax = 0.04
  []
  [bar]
    type = SubdomainBoundingBoxGenerator
    input = whole
    bottom_left = '-0.6 -0.05 -0.04'
    top_right = '0.6 0.05 0.04'
    block_id = 2
    block_name = 'bar'
    location = INSIDE
  []
  [block]
    type = SubdomainBoundingBoxGenerator
    input = bar
    bottom_left = '-0.6 -0.05 -0.04'
    top_right = '0.6 0.05 0.04'
    block_id = 1
    block_name = 'block'
    location = OUTSIDE
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat_conduction]
    type = HeatConduction
    variable = temperature
  []
[]

[Materials]
  [block]
    type = GenericConstantMaterial
    block = 'block'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
  [line]
    type = GenericConstantMaterial
    block = 'bar'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '10.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
[]

[BCs]
  [right]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'right'
    function = '10*t'
  []
[]

[VectorPostprocessors]
  [x_n0_25]
    type = LineValueSampler
    start_point = '-0.25 0 0'
    end_point = '-0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
  [x_0_25]
    type = LineValueSampler
    start_point = '0.25 0 0'
    end_point = '0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1
  end_time = 1
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'csv/block_w_bar'
    time_data = true
  []
[]

(modules/heat_transfer/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/perfectQ9.i)

[GlobalParams]
  order = SECOND
[]

[Mesh]
  file = perfectQ9.e
[]

[Variables]
  [./temp]
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temp
    boundary = leftleft
    value = 300
  [../]
  [./right]
    type = DirichletBC
    variable = temp
    boundary = rightright
    value = 400
  [../]
[]

[ThermalContact]
  [./left_to_right]
    secondary = leftright
    quadrature = true
    primary = rightleft
    emissivity_primary = 0
    emissivity_secondary = 0
    variable = temp
    type = GapHeatTransfer
  [../]
[]

[Materials]
  [./hcm]
    type = HeatConductionMaterial
    block = 'left right'
    specific_heat = 1
    thermal_conductivity = 1
  [../]
[]

[Executioner]
  type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'


  [./Quadrature]
    order = THIRD
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/generalized_plane_strain_tm_contact/generalized_plane_strain_tm_contact.i)

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  scalar_out_of_plane_strain = scalar_strain_zz
  temperature = temp
[]

[Mesh]
  file = 2squares.e
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./temp]
  [../]
  [./scalar_strain_zz]
    order = FIRST
    family = SCALAR
  [../]
[]

[AuxVariables]
  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Postprocessors]
  [./react_z]
    type = MaterialTensorIntegral
    rank_two_tensor = stress
    index_i = 2
    index_j = 2
  [../]
[]

[Kernels]
  [./TensorMechanics]
    use_displaced_mesh = true
  [../]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]

[Physics]
  [./SolidMechanics]
    [./GeneralizedPlaneStrain]
      [./gps]
        use_displaced_mesh = true
      [../]
    [../]
  [../]
[]

[AuxKernels]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  [../]
  [./stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
  [../]

  [./strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xx
    index_i = 0
    index_j = 0
  [../]
  [./strain_xy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xy
    index_i = 0
    index_j = 1
  [../]
  [./strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_yy
    index_i = 1
    index_j = 1
  [../]
  [./strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zz
    index_i = 2
    index_j = 2
  [../]
[]

[Functions]
  [./tempramp]
    type = ParsedFunction
    expression = 't'
  [../]
[]

[BCs]
  [./x]
    type = DirichletBC
    boundary = '4 6'
    variable = disp_x
    value = 0.0
  [../]
  [./y]
    type = DirichletBC
    boundary = '4 6'
    variable = disp_y
    value = 0.0
  [../]
  [./t]
    type = DirichletBC
    boundary = '4'
    variable = temp
    value = 0.0
  [../]
  [./tramp]
    type = FunctionDirichletBC
    variable = temp
    boundary = '6'
    function = tempramp
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    off_diag_row =    'disp_x disp_y'
    off_diag_column = 'disp_y disp_x'
  [../]
[]

[Contact]
  [./mech]
    primary = 8
    secondary = 2
    penalty = 1e+10
    normalize_penalty = true
    tangential_tolerance = .1
    normal_smoothing_distance = .1
    model = frictionless
    formulation = kinematic
  [../]
[]

[ThermalContact]
  [./thermal]
    type = GapHeatTransfer
    primary = 8
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
    variable = temp
    tangential_tolerance = .1
    normal_smoothing_distance = .1
    gap_conductivity = 0.01
    min_gap = 0.001
    quadrature = true
  [../]
[]

[Materials]
  [./elastic_tensor]
    type = ComputeIsotropicElasticityTensor
    poissons_ratio = 0.3
    youngs_modulus = 1e6
    block = '1 2'
  [../]
  [./strain]
    type = ComputePlaneSmallStrain
    eigenstrain_names = eigenstrain
    block = '1 2'
  [../]
  [./thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    temperature = temp
    thermal_expansion_coeff = 0.02
    stress_free_temperature = 0.0
    eigenstrain_name = eigenstrain
    block = '1 2'
  [../]
  [./stress]
    type = ComputeLinearElasticStress
    block = '1 2'
  [../]

  [./heatcond]
    type = HeatConductionMaterial
    thermal_conductivity = 3.0
    specific_heat = 300.0
    block = '1 2'
  [../]

  [./density]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = '1'
  [../]
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  line_search = none

  petsc_options_iname = '-pc_type -ps_sub_type -pc_factor_mat_solver_package'
  petsc_options_value = 'asm      lu           superlu_dist'

# controls for linear iterations
  l_max_its = 100
  l_tol = 1e-4

# controls for nonlinear iterations
  nl_max_its = 20
  nl_rel_tol = 1e-9
  nl_abs_tol = 1e-10

# time control
  start_time = 0.0
  dt = 0.2
  dtmin = 0.2
  end_time = 2.0
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/postprocessors/convective_ht_side_integral.i)

[Mesh]
  type = MeshGeneratorMesh

  [./cartesian]
    type = CartesianMeshGenerator
    dim = 2
    dx = '0.45 0.1 0.45'
    ix = '5 1 5'
    dy = '0.45 0.1 0.45'
    iy = '5 1 5'
    subdomain_id = '1 1 1
                    1 2 1
                    1 1 1'
  [../]

  [./add_iss_1]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 1
    paired_block = 2
    new_boundary = 'interface'
    input = cartesian
  [../]

  [./block_deleter]
    type = BlockDeletionGenerator
    block = 2
    input = add_iss_1
  [../]
[]

[Variables]
  [./temperature]
    initial_condition = 300
  [../]
[]

[AuxVariables]
  [./channel_T]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = 400
  [../]

  [./channel_Hw]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = 1000
  [../]
[]

[Kernels]
  [./graphite_diffusion]
    type = HeatConduction
    variable = temperature
    diffusion_coefficient = 'k_s'
  [../]
[]

[BCs]
  ## boundary conditions for the thm channels in the reflector
  [./channel_heat_transfer]
    type = CoupledConvectiveHeatFluxBC
    variable = temperature
    htc = channel_Hw
    T_infinity = channel_T
    boundary = 'interface'
  [../]

  # hot boundary on the left
  [./left]
    type = DirichletBC
    variable = temperature
    value = 1000
    boundary = 'left'
  [../]

  # cool boundary on the right
  [./right]
    type = DirichletBC
    variable = temperature
    value = 300
    boundary = 'right'
  [../]
[]

[Materials]
  [./thermal]
    type = GenericConstantMaterial
    prop_names = 'k_s'
    prop_values = '12'
  [../]

  [./htc_material]
    type = GenericConstantMaterial
    prop_names = 'alpha_wall'
    prop_values = '1000'
  [../]

  [./tfluid_mat]
    type = PiecewiseLinearInterpolationMaterial
    property = tfluid_mat
    variable = channel_T
    x = '400 500'
    y = '400 500'
  [../]
[]

[Postprocessors]
  [./Qw1]
    type = ConvectiveHeatTransferSideIntegral
    T_fluid_var = channel_T
    htc_var = channel_Hw
    T_solid = temperature
    boundary = interface
  [../]

  [./Qw2]
    type = ConvectiveHeatTransferSideIntegral
    T_fluid_var = channel_T
    htc = alpha_wall
    T_solid = temperature
    boundary = interface
  [../]

  [./Qw3]
    type = ConvectiveHeatTransferSideIntegral
    T_fluid = tfluid_mat
    htc = alpha_wall
    T_solid = temperature
    boundary = interface
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/code_verification/cartesian_test_no3.i)

# Problem I.3
#
# The thermal conductivity of an infinite plate varies linearly with
# temperature: k = ko(1+beta*u). It has a constant internal heat generation q,
# and has the boundary conditions du/dx = 0 at x= L and u(L) = uo.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    nx = 4
  [../]
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./exact]
    type = ParsedFunction
    symbol_names = 'q L beta uo ko'
    symbol_values = '1200 1 1e-3 0 1'
    expression = 'uo+(1/beta)*( ( 1 + (1-(x/L)^2) * (beta*q*L^2) / ko )^0.5  - 1)'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
  [./heatsource]
    type = HeatSource
    function = 1200
    variable = u
  [../]
[]

[BCs]
  [./ui]
    type = NeumannBC
    boundary = left
    variable = u
    value = 0
  [../]
  [./uo]
    type = DirichletBC
    boundary = right
    variable = u
    value = 0
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat'
    prop_values = '1.0 1.0'
  [../]
  [./thermal_conductivity]
    type = ParsedMaterial
    property_name = 'thermal_conductivity'
    coupled_variables = u
    expression = '1 * (1 + 1e-3*u)'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/verify_against_analytical/2d_steady_state.i)

# This test solves a 2D steady state heat equation
# The error is found by comparing to the analytical solution

# Note that the thermal conductivity, specific heat, and density in this problem
# Are set to 1, and need to be changed to the constants of the material being
# Analyzed

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 30
  ny = 30
  xmax = 2
  ymax = 2
[]

[Variables]
  [./T]
  [../]
[]

[Kernels]
  [./HeatDiff]
    type = HeatConduction
    variable = T
  [../]
[]

[BCs]
  [./zero]
    type = DirichletBC
    variable = T
    boundary = 'left right bottom'
    value = 0
  [../]
  [./top]
    type = FunctionDirichletBC
    variable = T
    boundary = top
    function = '10*sin(pi*x*0.5)'
  [../]
[]

[Materials]
  [./properties]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '1 1 1'
  [../]
[]

[Postprocessors]
  [./nodal_error]
    type = NodalL2Error
    function = '10/(sinh(pi))*sin(pi*x*0.5)*sinh(pi*y*0.5)'
    variable = T
  [../]
  [./elemental_error]
    type = ElementL2Error
    function = '10/(sinh(pi))*sin(pi*x*0.5)*sinh(pi*y*0.5)'
    variable = T
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/heat_conduction_patch/heat_conduction_patch_rz.i)

#
# This problem is taken from the Abaqus verification manual:
#   "1.5.8 Patch test for heat transfer elements"
#
# The temperature on the exterior nodes is -2e5+200x+100y.
#
# This gives a constant flux at all Gauss points.
#
# In addition, the temperature at all nodes follows the same formula.
#
# Node x         y          Temperature
#    1 1e3       0          0
#    2 1.00024e3 0          48
#    3 1.00018e3 3e-2       39
#    4 1.00004e3 2e-2       10
#    5 1.00008e3 8e-2       24
#    6 1e3       1.2e-1     12
#    7 1.00016e3 8e-2       40
#    8 1.00024e3 1.2e-1     60

[Mesh]#Comment
  file = heat_conduction_patch_rz.e
  coord_type = RZ
[] # Mesh

[Functions]
  [./temps]
    type = ParsedFunction
    expression ='-2e5+200*x+100*y'
  [../]
[] # Functions

[Variables]

  [./temp]
    order = FIRST
    family = LAGRANGE
  [../]

[] # Variables

[Kernels]

  [./heat_r]
    type = HeatConduction
    variable = temp
  [../]

[] # Kernels

[BCs]

  [./temps]
    type = FunctionDirichletBC
    variable = temp
    boundary = 10
    function = temps
  [../]

[] # BCs

[Materials]

  [./heat]
    type = HeatConductionMaterial
    block = 1

    specific_heat = 0.116
    thermal_conductivity = 4.85e-4
  [../]

[] # Materials

[Executioner]

  type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'



  petsc_options_iname = '-pc_type -ksp_gmres_restart'
  petsc_options_value = 'lu       101'


  line_search = 'none'


  nl_abs_tol = 1e-11
  nl_rel_tol = 1e-10


  l_max_its = 20

[] # Executioner

[Outputs]
  exodus = true
[] # Outputs

(modules/combined/test/tests/restart-transient-from-ss-with-stateful/parent_tr.i)

[Problem]
  restart_file_base = parent_ss_checkpoint_cp/LATEST
  force_restart = true

  # The auxiliary field has an initial condition
  allow_initial_conditions_with_restart = true
[]

[Mesh]
  file = parent_ss_checkpoint_cp/LATEST
[]

[Variables]
  [temp]
    # no initial condition for restart.
  []
[]

[AuxVariables]
  [power]
    order = FIRST
    family = L2_LAGRANGE
    initial_condition = 350
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
  [heat_source_fuel]
    type = CoupledForce
    variable = temp
    v = 'power'
  []
[]

[BCs]
  [all]
    type = DirichletBC
    variable = temp
    boundary = 'bottom top left right'
    value = 300
  []
[]

[Materials]
  [heat_material]
    type = HeatConductionMaterial
    temp = temp
    specific_heat = 1000
    thermal_conductivity = 500
  []
  [density]
    type = Density
    density = 2000
  []
[]

[Postprocessors]
  [avg_temp]
    type = ElementAverageValue
    variable = temp
    execute_on = 'timestep_end'
  []
  [avg_power]
    type = ElementAverageValue
    variable = power
    execute_on = 'timestep_end'
  []
[]

[Executioner]
  type = Transient
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre boomeramg 300'
  line_search = 'none'

  l_tol = 1e-02
  nl_rel_tol = 5e-05
  nl_abs_tol = 5e-05

  l_max_its = 50
  nl_max_its = 25

  start_time = 0
  end_time = 40
  dt = 10
[]

[Outputs]
  print_linear_residuals = false
  perf_graph = true
  color = true
  exodus = true
[]

[MultiApps]
  [bison]
    type = TransientMultiApp
    positions = '0 0 0'
    input_files = 'sub_tr.i'
    execute_on = 'timestep_end'
  []
[]

[Transfers]
  [to_bison_mechanics]
    type = MultiAppProjectionTransfer
    to_multi_app = bison
    variable = temp
    source_variable = temp
    execute_on = 'timestep_end'
  []
[]

(modules/combined/test/tests/reference_residual/reference_residual.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 4
  ny = 4
  nz = 4
[]

[Problem]
  type = ReferenceResidualProblem
  extra_tag_vectors = 'ref'
  reference_vector = 'ref'
[]

[Variables]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]

  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]

  [./disp_z]
    order = FIRST
    family = LAGRANGE
  [../]

  [./temp]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./saved_x]
  [../]
  [./saved_y]
  [../]
  [./saved_z]
  [../]
  [./saved_t]
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  [./all]
    volumetric_locking_correction = true
    incremental = true
    save_in = 'saved_x saved_y saved_z'
    eigenstrain_names = thermal_expansion
    strain = FINITE
    decomposition_method = EigenSolution
    extra_vector_tags = 'ref'
    temperature = temp
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
    save_in = saved_t
    extra_vector_tags = 'ref'
  [../]
[]

[Functions]
  [./pull]
    type = PiecewiseLinear
    x = '0 1 2'
    y = '0 1 1'
    scale_factor = 0.1
  [../]
[]

[BCs]
  [./bottom_x]
    type = DirichletBC
    variable = disp_x
    boundary = bottom
    value = 0.0
  [../]

  [./bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]

  [./bottom_z]
    type = DirichletBC
    variable = disp_z
    boundary = bottom
    value = 0.0
  [../]

  [./top_x]
    type = DirichletBC
    variable = disp_x
    boundary = top
    value = 0.0
  [../]

  [./top_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = top
    function = pull
  [../]

  [./top_z]
    type = DirichletBC
    variable = disp_z
    boundary = top
    value = 0.0
  [../]

  [./bottom_temp]
    type = DirichletBC
    variable = temp
    boundary = bottom
    value = 10.0
  [../]

  [./top_temp]
    type = DirichletBC
    variable = temp
    boundary = top
    value = 20.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 0
    youngs_modulus = 1.0
    poissons_ratio = 0.3
  [../]
  [./stress]
    type = ComputeFiniteStrainElasticStress
    block = 0
  [../]

  [./thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = 0
    eigenstrain_name = thermal_expansion
    temperature = temp
    thermal_expansion_coeff = 1e-5
    stress_free_temperature = 0.0
  [../]

  [./heat1]
    type = HeatConductionMaterial
    block = 0
    specific_heat = 1.0
    thermal_conductivity = 1e-3 #Tuned to give temperature reference resid close to that of solidmech
  [../]

  [./density]
    type = Density
    block = 0
    density = 1.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  nl_rel_tol = 1e-10

  l_tol = 1e-3
  l_max_its = 100

  dt = 1.0
  end_time = 2.0
[]

[Postprocessors]
  [./ref_resid_x]
    type = NodalL2Norm
    execute_on = timestep_end
    variable = saved_x
  [../]
  [./ref_resid_y]
    type = NodalL2Norm
    execute_on = timestep_end
    variable = saved_y
  [../]
  [./ref_resid_z]
    type = NodalL2Norm
    execute_on = timestep_end
    variable = saved_z
  [../]
  [./ref_resid_t]
    type = NodalL2Norm
    execute_on = timestep_end
    variable = saved_t
  [../]
  [./nonlinear_its]
    type = NumNonlinearIterations
  []
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/radiation_transfer_symmetry/cavity_with_pillars.i)

#
# inner_left: 8
# inner_right: 9
# inner_top: 12
# inner_bottom: 11
# inner_front: 10
# back_2: 7
# obstruction: 6
#

[Mesh]
  [cartesian]
    type = CartesianMeshGenerator
    dim = 3
    dx = '0.4 0.5 0.5 0.5 0.5 0.5 0.5 0.4'
    dy = '0.5 0.75 0.5'
    dz = '1.5 0.5'
    subdomain_id = '
                    3 1 1 1 1 1 1 4
                    3 1 2 1 1 2 1 4
                    3 1 1 1 1 1 1 4

                    3 1 1 1 1 1 1 4
                    3 1 1 1 1 1 1 4
                    3 1 1 1 1 1 1 4
                    '
  []

  [add_obstruction]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 2
    paired_block = 1
    new_boundary = obstruction
    input = cartesian
  []

  [add_new_back]
    type = ParsedGenerateSideset
    combinatorial_geometry = 'abs(z) < 1e-10'
    included_subdomains = '1'
    normal = '0 0 -1'
    new_sideset_name = back_2
    input = add_obstruction
  []

  [add_inner_left]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 3
    paired_block = 1
    new_boundary = inner_left
    input = add_new_back
  []

  [add_inner_right]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 4
    paired_block = 1
    new_boundary = inner_right
    input = add_inner_left
  []

  [add_inner_front]
    type = ParsedGenerateSideset
    combinatorial_geometry = 'abs(z - 2) < 1e-10'
    included_subdomains = '1'
    normal = '0 0 1'
    new_sideset_name = inner_front
    input = add_inner_right
  []

  [add_inner_bottom]
    type = ParsedGenerateSideset
    combinatorial_geometry = 'abs(y) < 1e-10'
    included_subdomains = '1'
    normal = '0 -1 0'
    new_sideset_name = inner_bottom
    input = add_inner_front
  []

  [add_inner_top]
    type = ParsedGenerateSideset
    combinatorial_geometry = 'abs(y - 1.75) < 1e-10'
    included_subdomains = '1'
    normal = '0 1 0'
    new_sideset_name = inner_top
    input = add_inner_bottom
  []
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [temperature]
    block = '2 3 4'
    initial_condition = 300
  []
[]

[Kernels]
  [conduction]
    type = HeatConduction
    variable = temperature
    block = '2 3 4'
    diffusion_coefficient = 1
  []

  [source]
    type = BodyForce
    variable = temperature
    value = 1000
    block = '2'
  []
[]

[BCs]
  [convective]
    type = CoupledConvectiveHeatFluxBC
    variable = temperature
    T_infinity = 300
    htc = 50
    boundary = 'left right'
  []
[]

[GrayDiffuseRadiation]
  [cavity]
    boundary = '6 7 8 9 10 11 12'
    emissivity = '1 1 1 1 1 1 1'
    n_patches = '1 1 1 1 1 1 1'
    adiabatic_boundary = '7 10 11 12'
    partitioners = 'metis metis metis metis metis metis metis'
    temperature = temperature
    ray_tracing_face_order = SECOND
    normalize_view_factor = false
  []
[]

[Postprocessors]
  [Tpv]
    type = PointValue
    variable = temperature
    point = '0.3 0.5 0.5'
  []

  [volume]
    type = VolumePostprocessor
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/tutorials/introduction/therm_step03a.i)

#
# Single block thermal input with time derivative and volumetric heat source terms
# https://mooseframework.inl.gov/modules/heat_transfer/tutorials/introduction/therm_step03.html
#

[Mesh]
  [generated]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 2
    ymax = 1
  []
[]

[Variables]
  [T]
    initial_condition = 300.0
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = T
  []
  [heat_source]
    type = HeatSource
    variable = T
    value = 1e4
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 45.0
    specific_heat = 0.5
  []
  [density]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = 8000.0
  []
[]

[BCs]
  [t_left]
    type = DirichletBC
    variable = T
    value = 300
    boundary = 'left'
  []
  [t_right]
    type = FunctionDirichletBC
    variable = T
    function = '300+5*t'
    boundary = 'right'
  []
[]

[Executioner]
  type = Transient
  end_time = 5
  dt = 1
[]

[VectorPostprocessors]
  [t_sampler]
    type = LineValueSampler
    variable = T
    start_point = '0 0.5 0'
    end_point = '2 0.5 0'
    num_points = 20
    sort_by = x
  []
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = therm_step03a_out
    execute_on = final
  []
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_cylinder.i)

rpv_core_gap_size = 0.15

core_outer_radius = 2
rpv_inner_radius = '${fparse 2 + rpv_core_gap_size}'
rpv_outer_radius = '${fparse 2.5 + rpv_core_gap_size}'

rpv_outer_htc = 10 # W/m^2/K
rpv_outer_Tinf = 300 # K

core_blocks = '1'
rpv_blocks = '3'

[Mesh]
  [core_gap_rpv]
    type = ConcentricCircleMeshGenerator
    num_sectors = 10
    radii = '${core_outer_radius} ${rpv_inner_radius} ${rpv_outer_radius}'
    rings = '2 1 2'
    has_outer_square = false
    preserve_volumes = true
    portion = full
  []
  [rename_core_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = core_gap_rpv
    primary_block = 1
    paired_block = 2
    new_boundary = 'core_outer'
  []
  [rename_inner_rpv_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = rename_core_bdy
    primary_block = 3
    paired_block = 2
    new_boundary = 'rpv_inner'
  []
  [2d_mesh]
    type = BlockDeletionGenerator
    input = rename_inner_rpv_bdy
    block = 2
  []
  allow_renumbering = false
[]

[Variables]
  [Tsolid]
    initial_condition = 500
  []
[]

[Kernels]
  [heat_source]
    type = CoupledForce
    variable = Tsolid
    block = '${core_blocks}'
    v = power_density
  []
  [heat_conduction]
    type = HeatConduction
    variable = Tsolid
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = Tsolid
    boundary = 'outer' # outer RPV
    coefficient = ${rpv_outer_htc}
    T_infinity = ${rpv_outer_Tinf}
  []
[]

[ThermalContact]
  [RPV_gap]
    type = GapHeatTransfer
    gap_geometry_type = 'CYLINDER'
    emissivity_primary = 0.8
    emissivity_secondary = 0.8
    variable = Tsolid
    primary = 'core_outer'
    secondary = 'rpv_inner'
    gap_conductivity = 0.1
    quadrature = true
    cylinder_axis_point_1 = '0 0 0'
    cylinder_axis_point_2 = '0 0 5'
  []
[]

[AuxVariables]
  [power_density]
    block = '${core_blocks}'
    initial_condition = 50e3
  []
[]

[Materials]
  [simple_mat]
    type = HeatConductionMaterial
    thermal_conductivity = 34.6 # W/m/K
  []
[]

[Postprocessors]
  [Tcore_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Trpv_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = '${core_blocks}'
  []
  [rpv_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = Tsolid
    boundary = 'outer' # outer RVP
    T_fluid = ${rpv_outer_Tinf}
    htc = ${rpv_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(rpv_convective_out - ptot) / ptot'
    pp_names = 'rpv_convective_out ptot'
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = 'rpv_inner core_outer'
    variable = Tsolid
  []
[]

[Executioner]
  type = Steady
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_max_its = 100

  [Quadrature]
    side_order = seventh
  []
  line_search = none
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/functional_expansion_tools/examples/3D_volumetric_cylindrical_subapp_mesh_refine/main.i)

# Derived from the example '3D_volumetric_cylindrical' with the following differences:
#
#   1) The model mesh is refined in the MasterApp by 1
#   2) Mesh adaptivity is enabled for the SubApp
#   3) Output from the SubApp is enabled so that the mesh changes can be visualized
[Mesh]
  type = FileMesh
  file = cyl-tet.e
  uniform_refine = 1
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./s_in] # Add in the contribution from the SubApp
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'top bottom outside'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = CylindricalDuo
    orders = '5   3' # Axial first, then (r, t) FX
    physical_bounds = '-2.5 2.5   0 0 1' # z_min z_max   x_center y_center radius
    z = Legendre # Axial in z
    disc = Zernike # (r, t) default to unit disc in x-y plane
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
    output_sub_cycles = true
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(modules/heat_transfer/test/tests/radiation_transfer_action/radiative_transfer_action_external_boundary_ray_tracing.i)

[Problem]
  kernel_coverage_check = false
[]

[Mesh]
  [cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1.3 1.9'
    ix = '3 3 3'
    dy = '6'
    iy = '9'
    subdomain_id = '0 1 2'
  []

  [inner_left]
    type = SideSetsBetweenSubdomainsGenerator
    input = cmg
    primary_block = 0
    paired_block = 1
    new_boundary = 'inner_left'
  []

  [inner_right]
    type = SideSetsBetweenSubdomainsGenerator
    input = inner_left
    primary_block = 2
    paired_block = 1
    new_boundary = 'inner_right'
  []

  [inner_top]
    type = ParsedGenerateSideset
    combinatorial_geometry = 'abs(y - 6) < 1e-10'
    normal = '0 1 0'
    included_subdomains = 1
    new_sideset_name = 'inner_top'
    input = 'inner_right'
  []

  [inner_bottom]
    type = ParsedGenerateSideset
    combinatorial_geometry = 'abs(y) < 1e-10'
    normal = '0 -1 0'
    included_subdomains = 1
    new_sideset_name = 'inner_bottom'
    input = 'inner_top'
  []

  [rename]
    type = RenameBlockGenerator
    old_block = '2'
    new_block = '0'
    input = inner_bottom
  []
[]

[Variables]
  [temperature]
    block = 0
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temperature
    block = 0
    diffusion_coefficient = 5
  []
[]

[GrayDiffuseRadiation]
  [cavity]
    boundary = '4 5 6 7'
    emissivity = '0.9 0.8 0.4 1'
    n_patches = '2 2 2 3'
    partitioners = 'centroid centroid centroid centroid'
    centroid_partitioner_directions = 'x y y x'
    temperature = temperature
    adiabatic_boundary = '7'
    fixed_temperature_boundary = '6'
    fixed_boundary_temperatures = '800'
    view_factor_calculator = ray_tracing
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 1000
  []

  [right]
    type = DirichletBC
    variable = temperature
    boundary = right
    value = 300
  []
[]

[Postprocessors]
  [average_T_inner_right]
    type = SideAverageValue
    variable = temperature
    boundary = inner_right
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/meshed_gap_thermal_contact/meshed_gap_thermal_contact.i)

[Mesh]
  [fmesh]
    type = FileMeshGenerator
    file = meshed_gap.e
  []
  [block0]
    type = SubdomainBoundingBoxGenerator
    input = fmesh
    bottom_left = '.5 -.5 0'
    top_right = '.7 .5 0'
    block_id = 4
  []
[]

[Variables]
  [./temp]
    block = '1 3'
    initial_condition = 1.0
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
    block = '1 3'
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temp
    boundary = 1
    value = 1
  [../]
  [./right]
    type = DirichletBC
    variable = temp
    boundary = 4
    value = 2
  [../]
[]

[ThermalContact]
  [./gap_conductivity]
    type = GapHeatTransfer
    variable = temp
    primary = 2
    secondary = 3
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductivity = 0.5
  [../]
[]

[Materials]
  [./hcm]
    type = HeatConductionMaterial
    block = '1 3'
    temp = temp
    thermal_conductivity = 1
  [../]
[]

[Problem]
  type = FEProblem
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  [./out]
    type = Exodus
  [../]
[]

(modules/heat_transfer/test/tests/code_verification/cartesian_test_no5.i)

# Problem I.5
#
# The volumetric heat generation in an infinite plate varies linearly
# with spatial location. It has constant thermal conductivity.
# It is insulated on the left boundary and exposed to a
# constant temperature on the right.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    nx = 1
  [../]
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./volumetric_heat]
    type = ParsedFunction
    symbol_names = 'q L beta'
    symbol_values = '1200 1 0.1'
    expression = 'q * (1-beta*x/L)'
  [../]
  [./exact]
    type = ParsedFunction
    symbol_names = 'uo q k L beta'
    symbol_values = '300 1200 1 1 0.1'
    expression = 'uo + (0.5*q*L^2/k) * ( (1-(x/L)^2) - (1-(x/L)^3) * beta/3 )'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
  [./heatsource]
    type = HeatSource
    function = volumetric_heat
    variable = u
  [../]
[]

[BCs]
  [./uo]
    type = DirichletBC
    boundary = right
    variable = u
    value = 300
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat thermal_conductivity'
    prop_values = '1.0 1.0 1.0'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/code_verification/cylindrical_test_no4.i)

# Problem II.4
#
# An infinitely long hollow cylinder has thermal conductivity k and internal
# heat generation q. Its inner radius is ri and outer radius is ro.
# A constant heat flux is applied to the inside surface qin and
# the outside surface is exposed to a fluid temperature T and heat transfer
# coefficient h, which results in the convective boundary condition.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    xmin = 0.2
    nx = 4
  [../]
  coord_type = RZ
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./exact]
    type = ParsedFunction
    symbol_names = 'qin q k ri ro uf h'
    symbol_values = '100 1200 1.0 0.2 1 100 10'
    expression = 'uf+ (0.25*q/k) * ( 2*k*(ro^2-ri^2)/(h*ro) + ro^2-x^2 + 2*ri^2*log(x/ro)) + (k/(h*ro) - log(x/ro)) * qin * ri / k'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
  [./heatsource]
    type = HeatSource
    function = 1200
    variable = u
  [../]
[]

[BCs]
  [./ui]
    type = NeumannBC
    boundary = left
    variable = u
    value = 100
  [../]
  [./uo]
    type = CoupledConvectiveHeatFluxBC
    boundary = right
    variable = u
    htc = 10.0
    T_infinity = 100
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat thermal_conductivity'
    prop_values = '1.0 1.0 1.0'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/cyl2D_xz.i)

#
# 2D Cylindrical Gap Heat Transfer Test.
#
# This test exercises 2D gap heat transfer for a constant conductivity gap.
#
# The mesh consists of an inner solid cylinder of radius = 1 unit, and outer
# hollow cylinder with an inner radius of 2 in the x-z plane. In other words,
# the gap between them is 1 radial unit in length.
#
# The calculated results are the same as for the cyl2D.i case in the x-y plane.

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = cyl2D.e
  []
  [./rotate]
    type = TransformGenerator
    transform = ROTATE
    vector_value = '0 90 0'
    input = file
  [../]
[]

[Functions]
  [./temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  [../]
[]

[Variables]
  [./temp]
   initial_condition = 100
  [../]
[]

[AuxVariables]
  [./gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temp
  [../]
[]

[AuxKernels]
  [./gap_cond]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_conductance
    boundary = 2
  [../]
[]

[Materials]
  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 1000000.0
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductivity = 1
    quadrature = true
    gap_geometry_type = CYLINDER
    cylinder_axis_point_1 = '0 0 0'
    cylinder_axis_point_2 = '0 1 0'
  [../]
[]

[BCs]
  [./mid]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  [../]
  [./temp_far_right]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

  [./Quadrature]
     order = fifth
     side_order = seventh
  [../]
[]

[Outputs]
  exodus = true
[]

[Postprocessors]
  [./temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  [../]

  [./temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  [../]

  [./flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  [../]

  [./flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  [../]
[]

(modules/heat_transfer/test/tests/NAFEMS/transient/T3/nafems_t3_hex_template.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 5
  ny = 1
  nz = 1
  xmin = 0.0
  xmax = 0.1
  ymin = 0.0
  ymax = 0.01
  zmin = 0.0
  zmax = 0.01
  elem_type = HEX8
[]

[Variables]
  [./temp]
    initial_condition = 0.0
  [../]
[]

[BCs]
  [./FixedTempLeft]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 0.0
  [../]
  [./FunctionTempRight]
    type = FunctionDirichletBC
    variable = temp
    boundary = right
    function = '100.0 * sin(pi*t/40)'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./HeatTdot]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]
[]

[Materials]
  [./density]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '35.0 440.5 7200.0'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  l_tol = 1e-5
  nl_max_its = 50
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-12

  dt = 1
  end_time = 32.0
[]

[Postprocessors]
  [./target_temp]
    type = NodalVariableValue
    variable = temp
    nodeid = 19
  [../]
[]

[Outputs]
  csv = true
[]

(modules/combined/test/tests/axisymmetric_2d3d_solution_function/2d.i)

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
[]

[Mesh]
  file = 2d.e
  coord_type = RZ
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 400
  []
[]

[AuxVariables]
  [hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temp_inner_func]
    type = PiecewiseLinear
    xy_data = '0 400
               1 350'
  []
  [temp_outer_func]
    type = PiecewiseLinear
    xy_data = '0 400
               1 400'
  []
  [press_func]
    type = PiecewiseLinear
    xy_data = '0 15
               1 15'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    volumetric_locking_correction = true
    add_variables = true
    incremental = true
    strain = FINITE
    eigenstrain_names = thermal_expansion
    generate_output = 'stress_xx stress_yy stress_zz vonmises_stress hydrostatic_stress'
    temperature = temp
  []
[]

[AuxKernels]
  [hoop_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = hoop_stress
    scalar_type = HoopStress
    execute_on = timestep_end
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = '1'
    value = 0.0
  []

  [Pressure]
    [internal_pressure]
      boundary = '4'
      factor = 1.e6
      function = press_func
    []
  []

  [t_in]
    type = FunctionDirichletBC
    variable = temp
    boundary = '4'
    function = temp_inner_func
  []

  [t_out]
    type = FunctionDirichletBC
    variable = temp
    boundary = '2'
    function = temp_outer_func
  []
[]

[Constraints]
  [disp_y]
    type = EqualValueBoundaryConstraint
    variable = disp_y
    primary = '65'
    secondary = '3'
    penalty = 1e18
  []
[]

[Materials]
  [thermal1]
    type = HeatConductionMaterial
    block = '1'
    thermal_conductivity = 25.0
    specific_heat = 490.0
    temp = temp
  []

  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 193.05e9
    poissons_ratio = 0.3
  []

  [stress]
    type = ComputeFiniteStrainElasticStress
  []

  [thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 13e-6
    stress_free_temperature = 295.00
    temperature = temp
    eigenstrain_name = thermal_expansion
  []

  [density]
    type = Density
    block = '1'
    density = 8000.0
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-ksp_snes_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = ' 201                hypre    boomeramg      4'
  line_search = 'none'
  l_max_its = 25
  nl_max_its = 20
  nl_rel_tol = 1e-9
  l_tol = 1e-2

  start_time = 0.0
  dt = 1
  end_time = 1
  dtmin = 1
[]

[Outputs]
  file_base = 2d_out
  exodus = true
  [console]
    type = Console
    max_rows = 25
  []
[]

(modules/heat_transfer/test/tests/code_verification/spherical_test_no2.i)

# Problem III.2
#
# A spherical shell has a thermal conductivity that varies linearly
# with temperature. The inside and outside surfaces of the shell are
# exposed to constant temperatures.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    xmin = 0.2
    nx = 4
  [../]
  coord_type = RSPHERICAL
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./exact]
    type = ParsedFunction
    symbol_names = 'ri ro beta ki ko ui uo'
    symbol_values = '0.2 1.0 1e-3 5.3 5 300 0'
    expression = 'uo+(ko/beta)* ( ( 1 + beta*(ki+ko)*(ui-uo)*( (1/x-1/ro) / (1/ri-1/ro) )/(ko^2))^0.5 -1 )'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
[]

[BCs]
  [./ui]
    type = DirichletBC
    boundary = left
    variable = u
    value = 300
  [../]
  [./uo]
    type = DirichletBC
    boundary = right
    variable = u
    value = 0
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat'
    prop_values = '1.0 1.0'
  [../]
  [./thermal_conductivity]
    type = ParsedMaterial
    property_name = 'thermal_conductivity'
    coupled_variables = u
    expression = '5 + 1e-3 * (u-0)'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/code_verification/spherical_test_no5.i)

# Problem III.5
#
# A solid sphere has a spatially dependent internal heating. It has a constant thermal
# conductivity. It is exposed to a constant temperature on its boundary.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    nx = 4
  [../]
  coord_type = RSPHERICAL
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./volumetric_heat]
    type = ParsedFunction
    symbol_names = 'q ro beta'
    symbol_values = '1200 1 0.1'
    expression = 'q * (1-beta*(x/ro)^2)'
  [../]
  [./exact]
    type = ParsedFunction
    symbol_names = 'uf q k ro beta'
    symbol_values = '300 1200 1 1 0.1'
    expression = 'uf + (q*ro^2/(6*k)) * ( (1-(x/ro)^2) - 0.3*beta*(1-(x/ro)^4) )'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
  [./heatsource]
    type = HeatSource
    function = volumetric_heat
    variable = u
  [../]
[]

[BCs]
  [./uo]
    type = DirichletBC
    boundary = 'right'
    variable = u
    value = 300
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat thermal_conductivity'
    prop_values = '1.0 1.0 1.0'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/transient_heat/transient_heat.i)

[Mesh]
  file = cube.e
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]

  [./ie]
    type = SpecificHeatConductionTimeDerivative
    variable = u
  [../]
[]

[BCs]
  [./bottom]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 0.0
  [../]

  [./top]
    type = DirichletBC
    variable = u
    boundary = 2
    value = 1.0
  [../]
[]

[Materials]
  [./constant]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1
    specific_heat = 1
  [../]
  [./density]
    type = GenericConstantMaterial
    block = 1
    prop_names = density
    prop_values = 1
  [../]
[]

[Executioner]
  type = Transient

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'



  start_time = 0.0
  num_steps = 5
  dt = .1
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/laser_bc_flux/test.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    nx = 20
    ny = 10
    ymax = 0.5
    dim = 2
  []
[]

[Variables]
  [temperature]
    initial_condition = 1
  []
[]

[Kernels]
  [conduction]
    type = HeatConduction
    variable = temperature
    diffusion_coefficient = 1
  []
[]

[BCs]
  [radiation_flux]
    type = FunctionRadiativeBC
    variable = temperature
    boundary = 'top'
    emissivity_function = '1'
    Tinfinity = 0
    stefan_boltzmann_constant = 1
  []
  [weld_flux]
    type = GaussianEnergyFluxBC
    variable = temperature
    boundary = 'top'
    P0 = 0.06283185307179587
    R = 0.18257418583505539
    x_beam_coord = 0.5
    y_beam_coord = 0.5
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre    boomeramg'
[]

[Postprocessors]
  [average]
    type = ElementAverageValue
    variable = temperature
  []
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/homogenization/homogenize_tc_hex.i)

[Mesh]
  [fmg]
    type = FileMeshGenerator
    file = homogenize_tc_hex.e
  []
[]

[Variables]
  [chi_x]
  []

  [chi_y]
  []

  [chi_z]
  []
[]

[Kernels]
  [conduction_x]
    type = HeatConduction
    variable = chi_x
  []

  [conduction_y]
    type = HeatConduction
    variable = chi_y
  []

  [conduction_z]
    type = HeatConduction
    variable = chi_z
  []

  [rhs_hom_x]
    type = HomogenizedHeatConduction
    variable = chi_x
    component = 0
  []

  [rhs_hom_y]
    type = HomogenizedHeatConduction
    variable = chi_y
    component = 1
  []

  [rhs_hom_z]
    type = HomogenizedHeatConduction
    variable = chi_z
    component = 2
  []
[]

[Materials]
  [thermal_conductivity1]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '20'
    block = 'mat1'
  []

  [thermal_conductivity2]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '10'
    block = 'mat2'
  []

  [thermal_conductivity3]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '4'
    block = 'mat3 mat4 mat5'
  []

  [thermal_conductivity4]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '100'
    block = 'mat6 mat7'
  []

  [thermal_conductivity5]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '0.001'
    block = 'mat8'
  []

  [thermal_conductivity6]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '12'
    block = 'mat9'
  []
[]

[BCs]
  [fix_chi_x]
    type = DirichletBC
    variable = chi_x
    value = 0
    boundary = fix_chi
  []

  [fix_chi_y]
    type = DirichletBC
    variable = chi_y
    value = 0
    boundary = fix_chi
  []

  [fix_chi_z]
    type = DirichletBC
    variable = chi_z
    value = 0
    boundary = fix_chi
  []

  [Periodic]
    [pair_1]
      primary = pb_1a
      secondary = pb_1b
      translation = '0 7 0'
    []

    F2F = 7
    dx = ${fparse 3 * F2F / 2 / sqrt(3)}
    [pair_2]
      primary = pb_2a
      secondary = pb_2b
      translation = '${fparse -dx} ${fparse F2F / 2} 0'
    []

    [pair_3]
      primary = pb_3a
      secondary = pb_3b
      translation = '${fparse dx} ${fparse F2F / 2} 0'
    []

    [pair_4]
      primary = pb_4a
      secondary = pb_4b
      translation = '0 0 -2'
    []
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type -pc_hypre_boomeramg_strong_threshold -ksp_gmres_restart -pc_hypre_boomeramg_max_iter -pc_hypre_boomeramg_tol'
  petsc_options_value = 'hypre boomeramg 0.7 100 30 1e-5'
[]

[Postprocessors]
  [k_xx]
    type = HomogenizedThermalConductivity
    chi = 'chi_x chi_y chi_z'
    row = 0
    col = 0
    execute_on = 'initial timestep_end'
  []
  [k_xy]
    type = HomogenizedThermalConductivity
    chi = 'chi_x chi_y chi_z'
    row = 0
    col = 1
    execute_on = 'initial timestep_end'
  []
  [k_xz]
    type = HomogenizedThermalConductivity
    chi = 'chi_x chi_y chi_z'
    row = 0
    col = 2
    execute_on = 'initial timestep_end'
  []
  [k_yx]
    type = HomogenizedThermalConductivity
    chi = 'chi_x chi_y chi_z'
    row = 1
    col = 0
    execute_on = 'initial timestep_end'
  []
  [k_yy]
    type = HomogenizedThermalConductivity
    chi = 'chi_x chi_y chi_z'
    row = 1
    col = 1
    execute_on = 'initial timestep_end'
  []
  [k_yz]
    type = HomogenizedThermalConductivity
    chi = 'chi_x chi_y chi_z'
    row = 1
    col = 2
    execute_on = 'initial timestep_end'
  []
  [k_zx]
    type = HomogenizedThermalConductivity
    chi = 'chi_x chi_y chi_z'
    row = 2
    col = 0
    execute_on = 'initial timestep_end'
  []
  [k_zy]
    type = HomogenizedThermalConductivity
    chi = 'chi_x chi_y chi_z'
    row = 2
    col = 1
    execute_on = 'initial timestep_end'
  []
  [k_zz]
    type = HomogenizedThermalConductivity
    chi = 'chi_x chi_y chi_z'
    row = 2
    col = 2
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  [outp_csv]
    type = CSV
    # these are too small and will cause issues
    hide = 'k_xz k_yz k_zx k_zy'
  []
[]

(modules/combined/test/tests/heat_conduction_xfem/heat.i)

[GlobalParams]
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 6
  xmin = 0.0
  xmax = 1.0
  ymin = 0.0
  ymax = 1.0
  elem_type = QUAD4
[]

[XFEM]
  geometric_cut_userobjects = 'line_seg_cut_uo'
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [./line_seg_cut_uo]
    type = LineSegmentCutUserObject
    cut_data = '0.5  1.0  0.5  0.5'
    time_start_cut = 0.0
    time_end_cut = 0.0
  [../]
[]

[Variables]
  [./temp]
    initial_condition = 300.0     # set initial temp to ambient
  [../]
[]

[Functions]
  [./temp_left]
    type = PiecewiseLinear
    x = '0   2'
    y = '0  0.1'
  [../]
[]

[Kernels]
  [./heat]         # gradient term in heat conduction equation
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
# Define boundary conditions
  [./left_temp]
    type = FunctionDirichletBC
    variable = temp
    boundary = 3
    function = temp_left
  [../]

  [./right_temp]
    type = DirichletBC
    variable = temp
    boundary = 1
    value = 0
  [../]
[]

[Materials]
  [./fuel_thermal]
    type = HeatConductionMaterial
    block = 0
    temp = temp
    thermal_conductivity = 5.0
    specific_heat = 1.0
  [../]
[]

[Executioner]

  type = Transient

  solve_type = 'PJFNK'

  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      8'

  line_search = 'none'

  l_max_its = 100
  l_tol = 8e-3

  nl_max_its = 15
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10

  start_time = 0.0
  dt = 1.0
  end_time = 2.0
  num_steps = 2
[]

[Outputs]
  # Define output file(s)

  file_base = heat_out
  time_step_interval = 1
  execute_on = timestep_end
  exodus = true
  [./console]
    type = Console
    output_linear = true
  [../]
[]

(modules/heat_transfer/test/tests/code_verification/cylindrical_test_no5.i)

# Problem II.5
#
# The volumetric heat generation in an infinitely long solid cylinder
# varies with spatial location. It has a constant thermal conductivity.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    nx = 1
  [../]
  coord_type = RZ
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./volumetric_heat]
    type = ParsedFunction
    symbol_names = 'q ro beta'
    symbol_values = '1200 1 0.1'
    expression = 'q * (1-beta*x/ro)'
  [../]
  [./exact]
    type = ParsedFunction
    symbol_names = 'uo q k ro beta'
    symbol_values = '300 1200 1 1 0.1'
    expression = 'uo + (0.25*q*ro^2/k) * ( (1-(x/ro)^2) - (1-(x/ro)^3) * beta * 4/9 )'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
  [./heatsource]
    type = HeatSource
    function = volumetric_heat
    variable = u
  [../]
[]

[BCs]
  [./uo]
    type = DirichletBC
    boundary = right
    variable = u
    value = 300
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat thermal_conductivity'
    prop_values = '1.0 1.0 1.0'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/corner_wrap.i)

[Mesh]
  file = corner_wrap.e
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
    check_boundary_restricted = false
    quadrature = true
  []
[]

[Variables]
  [temp]
    initial_condition = 100
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
[]

[BCs]
  [temp_bot_right]
    type = DirichletBC
    boundary = 1
    variable = temp
    value = 50
  []
  [temp_top_left]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 1.0
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  line_search = 'none'
  nl_rel_tol = 1e-14
  l_tol = 1e-3
  l_max_its = 100
#  dt = 1e-1
#  end_time = 1.0
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/gap_heat_transfer_3D.i)

outer_htc = 10 # W/m^2/K
outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 3
    ny = 6
    nz = 6
    xmin = -1
    xmax = -0.5
    ymin = -0.5
    ymax = 0.5
    zmin = -0.5
    zmax = 0.5
    elem_type = HEX27
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3 4 5'
    new_boundary = 'left_bottom left_back left_right left_front left_left left_top'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []

  [right_block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 4
    ny = 8
    nz = 8
    xmin = 0.5
    xmax = 1
    ymin = -0.5
    ymax = 0.5
    zmin = -0.5
    zmax = 0.5
    elem_type = HEX27
  []
  [right_block_sidesets]
    type = RenameBoundaryGenerator
    input = right_block
    old_boundary = '0 1 2 3 4 5'
    # new_boundary = 'right_bottom right_back right_right right_front right_left right_top'
    new_boundary = '100 101 102 103 104 105'
  []
  [right_block_sidesets_rename]
    type = RenameBoundaryGenerator
    input = right_block_sidesets
    old_boundary = '100 101 102 103 104 105'
    new_boundary = 'right_bottom right_back right_right right_front right_left right_top'
  []
  [right_block_id]
    type = SubdomainIDGenerator
    input = right_block_sidesets_rename
    subdomain_id = 2
  []

  [combined_mesh]
    type = MeshCollectionGenerator
    inputs = 'left_block_id right_block_id'
  []
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
[]

[AuxVariables]
  [gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  []
  [power_density]
    block = 1
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = 1
    v = power_density
  []
[]

[AuxKernels]
  [gap_cond]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_conductance
    boundary = 'left_right'
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 'right_left'
    secondary = 'left_right'
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductivity = 5
    gap_geometry_type = PLATE
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = 'right_right' # outer RPV
    coefficient = ${outer_htc}
    T_infinity = ${outer_Tinf}
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-8

  [Quadrature]
    order = fifth
    side_order = seventh
  []
[]

[Outputs]
  exodus = true
  csv = true
  [Console]
    type = Console
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 'left_right'
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 'right_left'
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 'left_right'
    diffusivity = thermal_conductivity
  []
  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 'right_left'
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 1
  []
  [convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = 'right_right' # outer RVP
    T_fluid = ${outer_Tinf}
    htc = ${outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(convective_out - ptot) / ptot'
    pp_names = 'convective_out ptot'
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = 'left_right right_left'
    variable = temp
  []
[]

(modules/combined/examples/stochastic/thermomech/graphite_ring_thermomechanics.i)

# Generate 1/4 of a 2-ring disk and extrude it by half to obtain
# 1/8 of a 3D tube.  Mirror boundary conditions will exist on the
# cut portions.

[Mesh]
  [disk]
    type = ConcentricCircleMeshGenerator
    num_sectors = 10
    radii = '1.0 1.1 1.2'
    rings = '1 1 1'
    has_outer_square = false
    preserve_volumes = false
    portion = top_right
  []
  [ring]
    type = BlockDeletionGenerator
    input = disk
    block = 1
    new_boundary = 'inner'
  []
  [cylinder]
    type = MeshExtruderGenerator
    input = ring
    extrusion_vector = '0 0 1.5'
    num_layers = 15
    bottom_sideset = 'back'
    top_sideset = 'front'
  []
[]

[Variables]
  [T]
    initial_condition = 300
  []
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[Kernels]
  [hc]
    type = HeatConduction
    variable = T
  []
  [TensorMechanics]
    displacements = 'disp_x disp_y disp_z'
  []
[]

[BCs]
  [temp_inner]
    type = FunctionNeumannBC
    variable = T
    boundary = 'inner'
    function = surface_source
  []
  [temp_front]
    type = ConvectiveHeatFluxBC
    variable = T
    boundary = 'front'
    T_infinity = 300
    heat_transfer_coefficient = 10
  []
  [temp_outer]
    type = ConvectiveHeatFluxBC
    variable = T
    boundary = 'outer'
    T_infinity = 300
    heat_transfer_coefficient = 10
  []
  # mirror boundary conditions.
  [disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0.0
  []
  [disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0.0
  []
  [disp_z]
    type = DirichletBC
    variable = disp_z
    boundary = 'back'
    value = 0.0
  []
[]

[Materials]
  [cond_inner]
    type = GenericConstantMaterial
    block = 2
    prop_names = thermal_conductivity
    prop_values = 25
  []
  [cond_outer]
    type = GenericConstantMaterial
    block = 3
    prop_names = thermal_conductivity
    prop_values = 100
  []
  [elasticity_tensor_inner]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 2.1e5
    poissons_ratio = 0.3
    block = 2
  []
  [elasticity_tensor_outer]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 3.1e5
    poissons_ratio = 0.2
    block = 3
  []
  [thermal_strain_inner]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 2e-6
    temperature = T
    stress_free_temperature = 300
    eigenstrain_name = eigenstrain_inner
    block = 2
  []
  [thermal_strain_outer]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 1e-6
    temperature = T
    stress_free_temperature = 300
    eigenstrain_name = eigenstrain_outer
    block = 3
  []
  [strain_inner] #We use small deformation mechanics
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y disp_z'
    eigenstrain_names = 'eigenstrain_inner'
    block = 2
  []
  [strain_outer] #We use small deformation mechanics
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y disp_z'
    eigenstrain_names = 'eigenstrain_outer'
    block = 3
  []
  [stress] #We use linear elasticity
    type = ComputeLinearElasticStress
  []
[]

[Functions]
  [surface_source]
    type = ParsedFunction
    expression = 'Q_t*pi/2.0/3.0 * cos(pi/3.0*z)'
    symbol_names = 'Q_t'
    symbol_values = heat_source
  []
[]

[Executioner]
  type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre boomeramg 101'

  l_max_its = 30
  nl_max_its = 100
  nl_abs_tol = 1e-9
  l_tol = 1e-04
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
  []
[]

[Controls]
  [stochastic]
    type = SamplerReceiver
  []
[]

[VectorPostprocessors]
  [temp_center]
    type = LineValueSampler
    variable = T
    start_point = '1 0 0'
    end_point = '1.2 0 0'
    num_points = 11
    sort_by = 'x'
  []
  [temp_end]
    type = LineValueSampler
    variable = T
    start_point = '1 0 1.5'
    end_point = '1.2 0 1.5'
    num_points = 11
    sort_by = 'x'
  []
  [dispx_center]
    type = LineValueSampler
    variable = disp_x
    start_point = '1 0 0'
    end_point = '1.2 0 0'
    num_points = 11
    sort_by = 'x'
  []
  [dispx_end]
    type = LineValueSampler
    variable = disp_x
    start_point = '1 0 1.5'
    end_point = '1.2 0 1.5'
    num_points = 11
    sort_by = 'x'
  []
  [dispz_end]
    type = LineValueSampler
    variable = disp_z
    start_point = '1 0 1.5'
    end_point = '1.2 0 1.5'
    num_points = 11
    sort_by = 'x'
  []
[]

[Postprocessors]
  [heat_source]
    type = FunctionValuePostprocessor
    function = 1
    scale_factor = 10000
    execute_on = linear
  []
  [temp_center_inner]
    type = PointValue
    variable = T
    point = '1 0 0'
  []
  [temp_center_outer]
    type = PointValue
    variable = T
    point = '1.2 0 0'
  []
  [temp_end_inner]
    type = PointValue
    variable = T
    point = '1 0 1.5'
  []
  [temp_end_outer]
    type = PointValue
    variable = T
    point = '1.2 0 1.5'
  []
  [dispx_center_inner]
    type = PointValue
    variable = disp_x
    point = '1 0 0'
  []
  [dispx_center_outer]
    type = PointValue
    variable = disp_x
    point = '1.2 0 0'
  []
  [dispx_end_inner]
    type = PointValue
    variable = disp_x
    point = '1 0 1.5'
  []
  [dispx_end_outer]
    type = PointValue
    variable = disp_x
    point = '1.2 0 1.5'
  []
  [dispz_inner]
    type = PointValue
    variable = disp_z
    point = '1 0 1.5'
  []
  [dispz_outer]
    type = PointValue
    variable = disp_z
    point = '1.2 0 1.5'
  []
[]

[Outputs]
  exodus = false
  csv = false
[]

(modules/heat_transfer/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/gap_conductivity_property.i)

[Mesh]
  file = perfect.e
[]

[Variables]
  [./temp]
  [../]
[]

[AuxVariables]
  [./gap_conductivity]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
  [../]
[]

[AuxKernels]
  [./gap_conductivity]
    type = MaterialRealAux
    boundary = leftright
    property = gap_conductivity
    variable = gap_conductivity
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temp
    boundary = leftleft
    value = 300
  [../]
  [./right]
    type = DirichletBC
    variable = temp
    boundary = rightright
    value = 400
  [../]
[]

[ThermalContact]
  [./left_to_right]
    secondary = leftright
    quadrature = true
    primary = rightleft
    emissivity_primary = 0
    emissivity_secondary = 0
    variable = temp
    type = GapHeatTransfer
    gap_conductivity = 3.0
  [../]
[]

[Materials]
  [./hcm]
    type = HeatConductionMaterial
    block = 'left right'
    specific_heat = 1
    thermal_conductivity = 1
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/heat_conduction/min_gap/min_gap.i)

[Mesh]
  type = MeshGeneratorMesh
  displacements = 'disp_x disp_y'
  [./left_gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 3
    xmin = -3
    xmax = 0
    ymin = -5
    ymax = 5
  [../]
  [./right_gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 3
    xmin = 3
    xmax = 6
    ymin = -5
    ymax = 5
  [../]

  [./left_and_right]
    type = MeshCollectionGenerator
    inputs = 'left_gen right_gen'
  [../]
  [./leftleft]
    type = SideSetsAroundSubdomainGenerator
    block = 0
    new_boundary = leftleft
    normal = '-1 0 0'
    input = left_and_right
  [../]
  [./leftright]
    type = SideSetsAroundSubdomainGenerator
    block = 0
    new_boundary = leftright
    normal = '1 0 0'
    input = leftleft
  [../]

  [./right]
    type = SubdomainBoundingBoxGenerator
    top_right = '6 5 0'
    bottom_left = '3 -5 0'
    block_id = 1
    input = leftright
  [../]

  [./rightleft]
    type = SideSetsAroundSubdomainGenerator
    block = 1
    new_boundary = rightleft
    normal = '-1 0 0'
    input = right
  [../]
  [./rightright]
    type = SideSetsAroundSubdomainGenerator
    block = 1
    new_boundary = rightright
    normal = '1 0 0'
    input = rightleft
  [../]
[]

[Variables]
  [./temp]
  [../]
[]

[AuxVariables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Functions]
  [./disp_x]
    type = ParsedFunction
    expression = -3+t
  [../]
  [./left_temp]
    type = ParsedFunction
    expression = 1000+t
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
  [../]
[]

[AuxKernels]
  [./disp_x]
    type = FunctionAux
    block = 1
    variable = disp_x
    function = disp_x
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./gap_conductivity]
    type = MaterialRealAux
    boundary = leftright
    property = gap_conductance
    variable = gap_conductance
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

[BCs]
  [./left]
    type = FunctionDirichletBC
    variable = temp
    boundary = leftleft
    function = left_temp
  [../]
  [./right]
    type = DirichletBC
    variable = temp
    boundary = rightright
    value = 400
  [../]
[]

[ThermalContact]
  [./left_to_right]
    secondary = leftright
    quadrature = true
    primary = rightleft
    variable = temp
    min_gap = 1
    min_gap_order = 1
    emissivity_primary = 0
    emissivity_secondary = 0
    type = GapHeatTransfer
  [../]
[]

[Materials]
  [./hcm]
    type = HeatConductionMaterial
    block = '0 1'
    specific_heat = 1
    thermal_conductivity = 1
    use_displaced_mesh = true
  [../]
[]

[Postprocessors]
  [./gap_conductance]
    type = PointValue
    point = '0 0 0'
    variable = gap_conductance
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.25
  end_time = 3.0
  solve_type = 'PJFNK'
[]

[Outputs]
  csv = true
  execute_on = 'TIMESTEP_END'
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/gap_heat_transfer_sphere3D.i)

sphere_outer_htc = 10 # W/m^2/K
sphere_outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  file = sphere3D.e
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
[]

[AuxVariables]
  [gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  []
  [power_density]
    block = 'fuel'
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = 'fuel'
    v = power_density
  []
[]

[AuxKernels]
  [gap_cond]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_conductance
    boundary = 2
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductivity = 5
    gap_geometry_type = SPHERE
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = '4' # outer RPV
    coefficient = ${sphere_outer_htc}
    T_infinity = ${sphere_outer_Tinf}
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

  [Quadrature]
    order = fifth
    side_order = seventh
  []
[]

[Outputs]
  exodus = true
  csv = true
  [Console]
    type = Console
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  []
  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 'fuel'
  []
  [sphere_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = '4' # outer RVP
    T_fluid = ${sphere_outer_Tinf}
    htc = ${sphere_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(sphere_convective_out - ptot) / ptot'
    pp_names = 'sphere_convective_out ptot'
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = '2 3'
    variable = temp
  []
[]

(modules/functional_expansion_tools/examples/2D_interface/main.i)

# Basic example coupling a master and sub app at an interface in a 2D model.
# The master app provides a flux term to the sub app via Functional Expansions, which then performs
# its calculations.  The sub app's interface conditions, both value and flux, are transferred back
# to the master app
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.0
  xmax = 0.4
  nx = 6
  ymin = 0.0
  ymax = 10.0
  ny = 20
[]

[Variables]
  [./m]
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./source_m]
    type = BodyForce
    variable = m
    value = 100
  [../]
[]

[Materials]
  [./Impervium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '0.00001              50.0          100.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    value = 2
    variable = m
  [../]
[]

[BCs]
  [./interface_value]
    type = FXValueBC
    variable = m
    boundary = right
    function = FX_Basis_Value_Main
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = right
    variable = m
    function = FX_Basis_Flux_Main
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '5'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Flux_UserObject_Main]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Main
    variable = m
    boundary = right
    diffusivity = thermal_conductivity
  [../]
[]

[Postprocessors]
  [./average_interface_value]
    type = SideAverageValue
    variable = m
    boundary = right
  [../]
  [./total_flux]
    type = SideDiffusiveFluxIntegral
    variable = m
    boundary = right
    diffusivity = thermal_conductivity
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
    sub_cycling = true
  [../]
[]

[Transfers]
  [./FluxToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Flux_UserObject_Main
    multi_app_object_name = FX_Basis_Flux_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
  [./FluxToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Flux_Main
    multi_app_object_name = FX_Flux_UserObject_Sub
  [../]
[]

(modules/combined/tutorials/introduction/thermal_mechanical/thermomech_step01.i)

#
# Single block coupled thermal/mechanical
# https://mooseframework.inl.gov/modules/combined/tutorials/introduction/thermoech_step01.html
#

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [generated]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 2
    ymax = 1
  []
  [pin]
    type = ExtraNodesetGenerator
    input = generated
    new_boundary = pin
    coord = '0 0 0'
  []
[]

[Variables]
  [T]
    initial_condition = 300.0
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = T
  []
  [heat_source]
    type = HeatSource
    variable = T
    value = 5e4
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    strain = FINITE
    automatic_eigenstrain_names = true
    generate_output = 'vonmises_stress'
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 45.0
    specific_heat = 0.5
  []
  [density]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = 8000.0
  []
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []
  [expansion1]
    type = ComputeThermalExpansionEigenstrain
    temperature = T
    thermal_expansion_coeff = 0.001
    stress_free_temperature = 300
    eigenstrain_name = thermal_expansion
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
  []
[]

[BCs]
  [t_left]
    type = DirichletBC
    variable = T
    value = 300
    boundary = 'left'
  []
  [t_right]
    type = FunctionDirichletBC
    variable = T
    function = '300+5*t'
    boundary = 'right'
  []
  [pin_x]
    type = DirichletBC
    variable = disp_x
    boundary = pin
    value = 0
  []
  [bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  end_time = 5
  dt = 1
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/thermo_mech/thermo_mech.i)

#Run with 4 procs
[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  temperature = temp
  volumetric_locking_correction = true
[]

[Mesh]
  file = cube.e
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]

  [./temp]
  [../]
[]

[Kernels]
  [./TensorMechanics]
  [../]

  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./bottom_x]
    type = DirichletBC
    variable = disp_x
    boundary = 1
    value = 0.0
  [../]
  [./bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = 1
    value = 0.0
  [../]
  [./bottom_z]
    type = DirichletBC
    variable = disp_z
    boundary = 1
    value = 0.0
  [../]

  [./bottom_temp]
    type = DirichletBC
    variable = temp
    boundary = 1
    value = 10.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1.0
    poissons_ratio = 0.3
  [../]
  [./strain]
    type = ComputeSmallStrain
    eigenstrain_names = eigenstrain
  [../]
  [./thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    stress_free_temperature = 0.0
    thermal_expansion_coeff = 1e-5
    eigenstrain_name = eigenstrain
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]

  [./heat]
    type = HeatConductionMaterial
    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./density]
    type = Density
    density = 1.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  nl_rel_tol = 1e-14
  l_tol = 1e-3

  l_max_its = 100

  dt = 1.0
  end_time = 1.0
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/thin_layer_heat_transfer/transient_2d.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    nx = 10
    ny = 10
    dim = 2
  []
  [block1]
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '0 0 0'
    top_right = '0.5 1 0'
    input = gen
  []
  [block2]
    type = SubdomainBoundingBoxGenerator
    block_id = 2
    bottom_left = '0.5 0 0'
    top_right = '1 1 0'
    input = block1
  []
  [breakmesh]
    input = block2
    type = BreakMeshByBlockGenerator
    block_pairs = '1 2'
    split_interface = true
    add_interface_on_two_sides = true
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [thermal_cond]
    type = HeatConduction
    variable = temperature
  []
[]

[InterfaceKernels]
  [thin_layer]
    type = ThinLayerHeatTransfer
    thermal_conductivity = thermal_conductivity_layer
    specific_heat = specific_heat_layer
    density = density_layer
    heat_source = heat_source_layer
    thickness = 0.01
    variable = temperature
    neighbor_var = temperature
    boundary = Block1_Block2
  []
[]

[BCs]
  [left_temp]
    type = DirichletBC
    value = 0
    variable = temperature
    boundary = left
  []
  [right_temp]
    type = DirichletBC
    value = 0
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [thermal_cond]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '1 1 1'
  []
  [thermal_cond_layer]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity_layer specific_heat_layer heat_source_layer density_layer'
    prop_values = '0.05 1 10000 1'
    boundary = Block1_Block2
  []
[]
[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10

  dt = 0.05
  num_steps = 2
[]

[Outputs]
  print_linear_residuals = false
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/gap_heat_transfer_htonly_syntax.i)

#
# 1-D Gap Heat Transfer Test without mechanics
#
# This test exercises 1-D gap heat transfer for a constant conductivity gap.
#
# The mesh consists of two element blocks containing one element each.  Each
#   element is a unit cube.  They sit next to one another with a unit between them.
#
# The conductivity of both blocks is set very large to achieve a uniform temperature
#  across each block. The temperature of the far left boundary
#  is ramped from 100 to 200 over one time unit.  The temperature of the far right
#  boundary is held fixed at 100.
#
# A simple analytical solution is possible for the heat flux between the blocks:
#
#  Flux = (T_left - T_right) * (gapK/gap_width)
#
# The gap conductivity is specified as 1, thus
#
#  gapK(Tavg) = 1.0*Tavg
#
#
# The heat flux across the gap at time = 1 is then:
#
#  Flux(2) = 100 * (1.0/1.0) = 100
#
# For comparison, see results from the flux post processors
#
# This test has been augmented with a second scalar field that solves nearly
#   the same problem.  The conductivity has been changed to 10.  Thus, the
#   flux for the second field is 1000.
#


[Mesh]
  file = gap_heat_transfer_htonly_test.e
[]

[Functions]

  [./temp]
    type = PiecewiseLinear
    x = '0   1   2'
    y = '100 200 200'
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
  [../]
  [./awesomium_contact]
    type = GapHeatTransfer
    variable = awesomium
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductivity = 10
    appended_property_name = _awesomium
  [../]
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  [../]
  [./awesomium]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  [../]
[]

[AuxVariables]
  [./gap_cond]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./gap_cond_awesomium]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./awe]
    type = HeatConduction
    variable = awesomium
  [../]
[]


[BCs]
  [./temp_far_left]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  [../]
  [./temp_far_right]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
  [./awesomium_far_left]
    type = FunctionDirichletBC
    boundary = 1
    variable = awesomium
    function = temp
  [../]
  [./awesomium_far_right]
    type = DirichletBC
    boundary = 4
    variable = awesomium
    value = 100
  [../]
[]

[AuxKernels]
  [./conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 2
  [../]
  [./conductance_awe]
    type = MaterialRealAux
    property = gap_conductance_awesomium
    variable = gap_cond_awesomium
    boundary = 2
  [../]
[]

[Materials]

  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 100000000.0
  [../]
  [./density]
    type = GenericConstantMaterial
    block = '1 2'
    prop_names = 'density'
    prop_values = '1.0'
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'
  nl_rel_tol = 1e-12
  l_tol = 1e-3
  l_max_its = 100

  dt = 1e-1
  end_time = 1.0
[]

[Postprocessors]

  [./temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  [../]

  [./flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  [../]

  [./awe_left]
    type = SideAverageValue
    boundary = 2
    variable = awesomium
    execute_on = 'initial timestep_end'
  [../]

  [./awe_right]
    type = SideAverageValue
    boundary = 3
    variable = awesomium
    execute_on = 'initial timestep_end'
  [../]

  [./awe_flux_left]
    type = SideDiffusiveFluxIntegral
    variable = awesomium
    boundary = 2
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  [../]

  [./awe_flux_right]
    type = SideDiffusiveFluxIntegral
    variable = awesomium
    boundary = 3
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_perfect_transfer/perfect_transfer_gap.i)

#
# 1-D Gap Perfect Heat Transfer
#
# The mesh consists of two element blocks containing one element each.  Each
#   element is a unit line.  They sit next to one another with a unit between
#   them.
#
# The temperature of the far left boundary is ramped from 100 to 200 over one
#   second and then held fixed.  The temperature of the far right boundary
#   follows due to the perfect heat transfer.
#

[Mesh]
  [left]
    type = GeneratedMeshGenerator
    dim = 1
    boundary_name_prefix = left
  []
  [right]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 2
    xmax = 3
    boundary_name_prefix = right
    boundary_id_offset = 2
  []
  [right_block]
    type = SubdomainIDGenerator
    input = right
    subdomain_id = 1
  []
  [collect]
    type = CombinerGenerator
    inputs = 'left right_block'
  []
[]

[Functions]
  [temperature]
    type = PiecewiseLinear
    x = '0   1   2'
    y = '100 200 200'
  []
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
[]

[BCs]
  [temp_far_left]
    type = FunctionDirichletBC
    boundary = 0
    variable = temperature
    function = temperature
  []
[]

[ThermalContact]
  [thermal_contact_1]
    type = GapPerfectConductance
    penalty = 1e3
    variable = temperature
    primary = 1
    secondary = 2
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = 0
    specific_heat = 1.0
    thermal_conductivity = 1.0
  []
  [heat2]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 1.0
    thermal_conductivity = 10.0
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu superlu_dist'

  line_search = 'none'

  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-14

  l_tol = 1e-3
  l_max_its = 100

  start_time = 0.0
  dt = 1e-1
  end_time = 2.0
  num_steps = 50
[]

[Postprocessors]
  [aveTempLeft]
    type = SideAverageValue
    boundary = 0
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [aveTempRight]
    type = SideAverageValue
    boundary = 3
    variable = temperature
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
[]

(modules/subchannel/examples/duct/wrapper.i)

# a wrapper mesh for coupling to subchannel

# sqrt(3) / 2 is by how much flat to flat is smaller than corer to corner
f = '${fparse sqrt(3) / 2}'

# units are meters
height = 1.0
duct_inside = 0.085
wrapper_thickness = 0.002
duct_outside = '${fparse duct_inside + 2 * wrapper_thickness}'

# number of radial elements in the wrapper
n_radial = 4

# number of azimuthal elements per side
n_az = 4

# number of axial elements
n_ax = 10

# System variables
T_in = 660
[DefaultElementQuality]
  failure_type = warning
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [bisonMesh]
    type = PolygonConcentricCircleMeshGenerator
    num_sides = 6
    num_sectors_per_side = '${n_az} ${n_az} ${n_az} ${n_az} ${n_az} ${n_az}'
    background_intervals = 1
    background_block_ids = '1'
    # note that polygon_size is "like radius"
    polygon_size = '${fparse duct_outside / 2}'
    duct_sizes = '${fparse duct_inside / 2 / f}'
    duct_intervals = '${n_radial}'
    duct_block_ids = '2'
    # interface_boundary_names = 'inside'
    external_boundary_name = 'outside'
  []

  [extrude]
    type = AdvancedExtruderGenerator
    # type = FancyExtruderGenerator
    direction = '0 0 1'
    input = bisonMesh
    heights = '${height}'
    num_layers = '${n_ax}'
  []

  [inlet_boundary]
    type = ParsedGenerateSideset
    input = extrude
    combinatorial_geometry = 'z < 1e-6'
    normal = '0 0 -1'
    new_sideset_name = 'inlet'
  []

  [outlet_boundary]
    type = ParsedGenerateSideset
    input = inlet_boundary
    combinatorial_geometry = 'z > ${fparse height - 1e-6}'
    normal = '0 0 1'
    new_sideset_name = 'outlet'
  []

  [inside_boundary]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 2
    paired_block = 1
    new_boundary = 'inside'
    input = outlet_boundary
  []

  [remove]
    type = BlockDeletionGenerator
    block = 1
    input = inside_boundary
  []

  [rename]
    type = RenameBlockGenerator
    input = remove
    old_block = '2'
    new_block = 'wrapper'
  []

  [rotate]
    type = TransformGenerator
    input = rename
    transform = ROTATE
    vector_value = '30 0 0'
  []

  coord_type = XYZ
[]

[Functions]
  [volumetric_heat_rate]
    type = ParsedFunction
    expression = '1.0*H'
    symbol_names = 'H'
    symbol_values = '${height}'
  []
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
  []
[]

[Modules]

  [TensorMechanics]

    [Master]
      add_variables = true
      strain = SMALL
      incremental = true
      generate_output = 'stress_xx stress_yy stress_xy'
      temperature = temperature

      [block0]
        eigenstrain_names = eigenstrain
        block = wrapper
      []
    []
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temperature
  []
  [heat_source]
    type = HeatSource
    variable = temperature
    function = volumetric_heat_rate
  []
[]

[AuxVariables]
  [q_prime]
    order = CONSTANT
    family = MONOMIAL
  []
  [duct_surface_temperature]
  []
  [disp_magnitude]
  []
[]

[AuxKernels]
  [QPrime]
    type = SCMTriDuctQPrimeAux
    diffusivity = 'thermal_conductivity'
    flat_to_flat = '${fparse duct_inside}'
    variable = q_prime
    diffusion_variable = temperature
    component = normal
    boundary = 'inside'
    execute_on = 'timestep_end'
  []
  [Deformation]
    type = ParsedAux
    variable = disp_magnitude
    coupled_variables = 'disp_x disp_y disp_z'
    expression = 'sqrt(disp_x^2 + disp_y^2 + disp_z^2)'
    execute_on = 'timestep_end'
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = wrapper
    bulk_modulus = 0.333333333333e6
    poissons_ratio = 0.0
  []
  [thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = wrapper
    temperature = temperature
    stress_free_temperature = ${T_in}
    thermal_expansion_coeff = 1e-5
    eigenstrain_name = eigenstrain
  []
  [stress]
    type = ComputeStrainIncrementBasedStress
    block = wrapper
  []
  [heat_conductor]
    type = HeatConductionMaterial
    thermal_conductivity = 1.0
    block = wrapper
  []
  [density]
    type = Density
    block = wrapper
    density = 1.0
  []
[]

[BCs]
  [isolated_bc]
    type = NeumannBC
    variable = temperature
    boundary = 'inlet outlet'
  []
  [inside_bc]
    type = MatchedValueBC
    variable = temperature
    boundary = 'inside'
    v = duct_surface_temperature
  []
  [outside_bc]
    type = DirichletBC
    variable = temperature
    boundary = 'outside'
    value = '${fparse T_in+10}'
  []

  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'inlet outlet'
    value = 0.0
  []

  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'inlet outlet'
    value = 0.0
  []

  [no_z]
    type = DirichletBC
    variable = disp_z
    boundary = 'inlet'
    value = 0.0
  []
[]

[ICs]
  [temperature_ic]
    type = ConstantIC
    variable = temperature
    value = ${T_in}
  []
  [q_prime_ic]
    type = ConstantIC
    variable = q_prime
    value = 0.0
  []
[]

[UserObjects]
  [q_prime_uo]
    type = LayeredSideAverage
    boundary = 'inside'
    variable = q_prime
    num_layers = 1000
    direction = z
    execute_on = 'TIMESTEP_END'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'

  [Quadrature]
    order = THIRD
    side_order = FOURTH
  []
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/joule_heating/transient_jouleheating.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 5
  ymax = 5
[]

[Variables]
  [./T]
    initial_condition = 293.0 #in K
  [../]
  [./elec]
  [../]
[]

[Kernels]
  [./HeatDiff]
    type = HeatConduction
    variable = T
  [../]
  [./HeatTdot]
    type = HeatConductionTimeDerivative
    variable = T
  [../]
  [./HeatSrc]
    type = JouleHeatingSource
    variable = T
    elec = elec
  [../]
  [./electric]
    type = HeatConduction
    variable = elec
    diffusion_coefficient = electrical_conductivity
  [../]
[]

[BCs]
  [./lefttemp]
    type = DirichletBC
    boundary = left
    variable = T
    value = 293 #in K
  [../]
  [./elec_left]
    type = DirichletBC
    variable = elec
    boundary = left
    value = 1 #in V
  [../]
  [./elec_right]
    type = DirichletBC
    variable = elec
    boundary = right
    value = 0
  [../]
[]

[Materials]
  [./k]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '397.48' #copper in W/(m K)
    block = 0
  [../]
  [./cp]
    type = GenericConstantMaterial
    prop_names = 'specific_heat'
    prop_values = '385.0' #copper in J/(kg K)
    block = 0
  [../]
  [./rho]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = '8920.0' #copper in kg/(m^3)
    block = 0
  [../]
  [./sigma] #copper is default material
    type = ElectricalConductivity
    temperature = T
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -ksp_grmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         101   preonly   ilu      1'
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-4
  dt = 1
  end_time = 5
  automatic_scaling = true
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/heat_transfer/test/tests/homogenization/heatConduction2D.i)

#
# Homogenization of thermal conductivity according to
#   Homogenization of Temperature-Dependent Thermal Conductivity in Composite
#   Materials, Journal of Thermophysics and Heat Transfer, Vol. 15, No. 1,
#   January-March 2001.
#
# The problem solved here is a simple square with two blocks.  The square is
#   divided vertically between the blocks.  One block has a thermal conductivity
#   of 10.  The other block's thermal conductivity is 100.
#
# The analytic solution for the homogenized thermal conductivity in the
#   horizontal direction is found by summing the thermal resistance, recognizing
#   that the blocks are in series:
#
#   R = L/A/k = R1 + R2 = L1/A1/k1 + L2/A2/k2 = .5/1/10 + .5/1/100
#   Since L = A = 1, k_xx = 18.1818.
#
# The analytic solution for the homogenized thermal conductivity in the vertical
#   direction is found by summing reciprocals of resistance, recognizing that
#   the blocks are in parallel:
#
#   1/R = k*A/L = 1/R1 + 1/R2 = 10*.5/1 + 100*.5/1
#   Since L = A = 1, k_yy = 55.0.
#

[Mesh]
  file = heatConduction2D.e
[]

[Variables]
  [temp_x]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  []
  [temp_y]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  []
[]

[Kernels]
  [heat_x]
    type = HeatConduction
    variable = temp_x
  []
  [heat_y]
    type = HeatConduction
    variable = temp_y
  []
  [heat_rhs_x]
    type = HomogenizedHeatConduction
    variable = temp_x
    component = 0
  []
  [heat_rhs_y]
    type = HomogenizedHeatConduction
    variable = temp_y
    component = 1
  []
[]

[BCs]
 [Periodic]
   [left_right]
     primary = 10
     secondary = 20
     translation = '1 0 0'
   []
   [bottom_top]
     primary = 30
     secondary = 40
     translation = '0 1 0'
   []
 []
 [fix_center_x]
   type = DirichletBC
   variable = temp_x
   value = 100
   boundary = 1
 []
 [fix_center_y]
   type = DirichletBC
   variable = temp_y
   value = 100
   boundary = 1
 []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 0.116
    thermal_conductivity = 10
  []
  [heat2]
    type = HeatConductionMaterial
    block = 2
    specific_heat = 0.116
    thermal_conductivity = 100
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -ksp_gmres_restart'
  petsc_options_value = 'lu       101'
  line_search = 'none'
  nl_abs_tol = 1e-11
  nl_rel_tol = 1e-10
  l_max_its = 20
[]

[Outputs]
  exodus = true
[]

[Postprocessors]
  [k_xx]
    type = HomogenizedThermalConductivity
    chi = 'temp_x temp_y'
    row = 0
    col = 0
    execute_on = 'initial timestep_end'
  []

  [k_yy]
    type = HomogenizedThermalConductivity
    chi = 'temp_x temp_y'
    row = 1
    col = 1
    execute_on = 'initial timestep_end'
  []
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_cylinder_mortar_error.i)

rpv_core_gap_size = 0.15

core_outer_radius = 2
rpv_inner_radius = ${fparse 2 + rpv_core_gap_size}
rpv_outer_radius = ${fparse 2.5 + rpv_core_gap_size}

rpv_outer_htc = 10 # W/m^2/K
rpv_outer_Tinf = 300 # K

core_blocks = '1'
rpv_blocks = '3'

[Mesh]
  [core_gap_rpv]
    type = ConcentricCircleMeshGenerator
    num_sectors = 10
    radii = '${core_outer_radius} ${rpv_inner_radius} ${rpv_outer_radius}'
    rings = '2 1 2'
    has_outer_square = false
    preserve_volumes = true
    portion = full
  []
  [rename_core_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = core_gap_rpv
    primary_block = 1
    paired_block = 2
    new_boundary = 'core_outer'
  []
  [rename_inner_rpv_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = rename_core_bdy
    primary_block = 3
    paired_block = 2
    new_boundary = 'rpv_inner'
  []
  [2d_mesh]
    type = BlockDeletionGenerator
    input = rename_inner_rpv_bdy
    block = 2
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'rpv_inner'
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    input = 2d_mesh
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'core_outer'
    new_block_id = 10000
    new_block_name = 'primary_lower'
    input = secondary
  []
  allow_renumbering = false
[]

[Variables]
  [Tsolid]
    initial_condition = 500
  []
  [lm]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  []
[]

[Kernels]
  [heat_source]
    type = CoupledForce
    variable = Tsolid
    block = '${core_blocks}'
    v = power_density
  []
  [heat_conduction]
    type = HeatConduction
    variable = Tsolid
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = Tsolid
    boundary = 'outer' # outer RPV
    coefficient = ${rpv_outer_htc}
    T_infinity = ${rpv_outer_Tinf}
  []
[]

[UserObjects]
  [radiation]
    type = GapFluxModelRadiation
    temperature = Tsolid
    boundary = 'rpv_inner'
    primary_emissivity = 0.8
    secondary_emissivity = 0.8
  []
  [conduction]
    type = GapFluxModelConduction
    temperature = Tsolid
    boundary = 'rpv_inner'
    gap_conductivity = 0.1
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = Tsolid
    primary_boundary = 'core_outer'
    primary_subdomain = 10000
    secondary_boundary = 'rpv_inner'
    secondary_subdomain = 10001
    gap_flux_models = 'radiation conduction'
    gap_geometry_type = 'CYLINDER'
    cylinder_axis_point_2 = '0 0 5'
  []
[]

[AuxVariables]
  [power_density]
    block = '${core_blocks}'
    initial_condition = 50e3
  []
[]

[Materials]
  [simple_mat]
    type = HeatConductionMaterial
    thermal_conductivity = 34.6 # W/m/K
  []
[]

[Postprocessors]
  [Tcore_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Trpv_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = '${core_blocks}'
  []
  [rpv_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = Tsolid
    boundary = 'outer' # outer RVP
    T_fluid = ${rpv_outer_Tinf}
    htc = ${rpv_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(rpv_convective_out - ptot) / ptot'
    pp_names = 'rpv_convective_out ptot'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = 'rpv_inner core_outer'
    variable = 'Tsolid'
  []
[]

[Executioner]
  type = Steady

  petsc_options = '-snes_converged_reason -pc_svd_monitor'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err -pc_factor_shift_type '
                        '-pc_factor_shift_amount'
  petsc_options_value = ' lu       superlu_dist                  1e-5          NONZERO               '
                        '1e-15'
  snesmf_reuse_base = false

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_max_its = 100

  line_search = none
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/ref-displaced.i)

[Mesh]
  file = 3blk.e
  displacements = 'disp_x disp_y'
[]

[AuxVariables]
  [./disp_x]
    block = 1
  [../]
  [./disp_y]
    block = 1
  [../]
[]

[AuxKernels]
  [./disp_x_kernel]
    type = ConstantAux
    variable = disp_x
    value = 0.1
  [../]

  [./disp_y_kernel]
    type = ConstantAux
    variable = disp_y
    value = 0
  [../]
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    block = '1 2 3'
  [../]
[]

[Materials]
  [./left]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1000
    specific_heat = 1
  [../]

  [./right]
    type = HeatConductionMaterial
    block = 2
    thermal_conductivity = 500
    specific_heat = 1
  [../]

  [./middle]
    type = HeatConductionMaterial
    block = 3
    thermal_conductivity = 100
    specific_heat = 1
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
    use_displaced_mesh = true
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temp
    boundary = 'left'
    value = 1
  [../]

  [./right]
    type = DirichletBC
    variable = temp
    boundary = 'right'
    value = 0
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  nl_rel_tol = 1e-11
  l_tol = 1e-11
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/code_verification/spherical_test_no3.i)

# Problem III.3
#
# The thermal conductivity of a spherical shell varies linearly with
# temperature: k = k0(1+beta* u). The inside radius is ri and the outside radius
# is ro. It has a constant internal heat generation q and is exposed to
# the same constant temperature on both surfaces: u(ri) = u(ro) = uo.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    nx = 4
    xmin = 0.2
  [../]
  coord_type = RSPHERICAL
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./exact]
    type = ParsedFunction
    symbol_names = 'q k0 ri ro beta u0'
    symbol_values = '1200 1 0.2 1.0 1e-3 0'
    expression = 'u0+(1/beta)*( ( 1 + (1/3)*beta*((ro^2-x^2)-(ro^2-ri^2) * (1/x-1/ro)/(1/ri-1/ro))*q/k0 )^0.5  - 1)'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
  [./heatsource]
    type = HeatSource
    function = 1200
    variable = u
  [../]
[]

[BCs]
  [./uo]
    type = DirichletBC
    boundary = 'left right'
    variable = u
    value = 0
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat'
    prop_values = '1.0 1.0'
  [../]
  [./thermal_conductivity]
    type = ParsedMaterial
    property_name = 'thermal_conductivity'
    coupled_variables = u
    expression = '1 * (1 + 1e-3*u)'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_radiation/gap_heat_transfer_radiation_test.i)

#
# 1-D Gap Heat Transfer Test without mechanics
#
# This test exercises 1-D gap heat transfer for a helium-filled gap including radiation.
#
# The mesh consists of two element blocks containing one element each.  Each
#   element is a unit cube.  They sit next to one another with a unit between them.
#
# The conductivity of both blocks is set very large to achieve a uniform temperature
#  across each block. The temperature of the far left boundary
#  is ramped from 100 to 200 over one time unit, and then held fixed for an additional
#  time unit.  The temperature of the far right boundary is held fixed at 100.
#
# A simple analytical solution is possible for the heat flux between the blocks:
#
#  Flux = (T_left - T_right) * h_gap
#
#    where  h_gap = h_gas + h_cont + h_rad
#
# By setting the contact pressure, roughnesses, and jump distances to zero, the gap
#   conductance simplifies to:
#
#    h_gap = gapK/d_gap + sigma*Fe*(T_left^2 + T_right^2)*(T_left + T_right)
#
#      where Fe = 1/(1/eps_left + 1/eps_right - 1)
#            eps = emissivity
#
# For pure helium, BISON computes the gas conductivity as:
#
#  gapK(Tavg) = 2.639e-3*Tavg^0.7085
#
# For the test, the final (t=2) average gas temperature is (200 +100)/2 = 150,
#  giving gapK(150) = 0.09187557
#
# Assuming ems_left = ems_right = 0.5, Fe = 1/3
#
# The heat flux across the gap at that time is then:
#
#  Flux(2) = 100 * ((0.09187557/1.0) + (5.669e-8/3)*(200^2 + 100^2)*(200 + 100))
#          = 37.532557
#
# The flux post processors give 37.53255
#

[Mesh]
  file = gap_heat_transfer_radiation_test.e
[]

[Functions]
  [./temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '200 200'
  [../]
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]


[BCs]
  [./temp_far_left]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  [../]

  [./temp_far_right]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
[]

[ThermalContact]
  [./gap]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    gap_conductivity = 0.09187557
    emissivity_primary = 0.5
    emissivity_secondary = 0.5
  [../]
[]

[Materials]
  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 10000000.0
  [../]
  [./density]
    type = GenericConstantMaterial
    block = '1 2'
    prop_names = 'density'
    prop_values = '1.0'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  nl_abs_tol = 1e-6
  nl_rel_tol = 1e-10

  l_tol = 1e-3
  l_max_its = 100

  start_time = 0.0
  dt = 1
  end_time = 1.0
[]

[Postprocessors]
  [./temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  [../]

  [./flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/heat_conduction_patch/heat_conduction_patch_hex20.i)

#
# This problem is taken from the Abaqus verification manual:
#   "1.5.8 Patch test for heat transfer elements"
#
# The temperature on the exterior nodes is 200x+100y+200z.
#
# This gives a constant flux at all Gauss points.
#
# In addition, the temperature at all nodes follows the same formula.
#
# Node x          y          z          Temperature
#   1  1.000E+00  0.000E+00  1.000E+00  4.0000E+02
#   2  6.770E-01  3.050E-01  6.830E-01  3.0250E+02
#   3  3.200E-01  1.860E-01  6.430E-01  2.1120E+02
#   4  0.000E+00  0.000E+00  1.000E+00  2.0000E+02
#   5  1.000E+00  1.000E+00  1.000E+00  5.0000E+02
#   6  7.880E-01  6.930E-01  6.440E-01  3.5570E+02
#   7  1.650E-01  7.450E-01  7.020E-01  2.4790E+02
#   8  0.000E+00  1.000E+00  1.000E+00  3.0000E+02
#   9  8.385E-01  1.525E-01  8.415E-01  3.5125E+02
#  10  4.985E-01  2.455E-01  6.630E-01  2.5685E+02
#  11  1.600E-01  9.300E-02  8.215E-01  2.0560E+02
#  12  5.000E-01  0.000E+00  1.000E+00  3.0000E+02
#  13  1.000E+00  5.000E-01  1.000E+00  4.5000E+02
#  14  7.325E-01  4.990E-01  6.635E-01  3.2910E+02
#  15  2.425E-01  4.655E-01  6.725E-01  2.2955E+02
#  16  0.000E+00  5.000E-01  1.000E+00  2.5000E+02
#  17  8.940E-01  8.465E-01  8.220E-01  4.2785E+02
#  18  4.765E-01  7.190E-01  6.730E-01  3.0180E+02
#  19  8.250E-02  8.725E-01  8.510E-01  2.7395E+02
#  20  5.000E-01  1.000E+00  1.000E+00  4.0000E+02
#  21  1.000E+00  0.000E+00  0.000E+00  2.0000E+02
#  22  0.000E+00  0.000E+00  0.000E+00  0.0000E+00
#  23  8.260E-01  2.880E-01  2.880E-01  2.5160E+02
#  24  2.490E-01  3.420E-01  1.920E-01  1.2240E+02
#  25  1.000E+00  0.000E+00  5.000E-01  3.0000E+02
#  26  5.000E-01  0.000E+00  0.000E+00  1.0000E+02
#  27  0.000E+00  0.000E+00  5.000E-01  1.0000E+02
#  28  9.130E-01  1.440E-01  1.440E-01  2.2580E+02
#  29  1.245E-01  1.710E-01  9.600E-02  6.1200E+01
#  30  7.515E-01  2.965E-01  4.855E-01  2.7705E+02
#  31  5.375E-01  3.150E-01  2.400E-01  1.8700E+02
#  32  2.845E-01  2.640E-01  4.175E-01  1.6680E+02
#  33  2.730E-01  7.500E-01  2.300E-01  1.7560E+02
#  34  0.000E+00  1.000E+00  0.000E+00  1.0000E+02
#  35  2.610E-01  5.460E-01  2.110E-01  1.4900E+02
#  36  0.000E+00  5.000E-01  0.000E+00  5.0000E+01
#  37  2.190E-01  7.475E-01  4.660E-01  2.1175E+02
#  38  1.365E-01  8.750E-01  1.150E-01  1.3780E+02
#  39  0.000E+00  1.000E+00  5.000E-01  2.0000E+02
#  40  8.500E-01  6.490E-01  2.630E-01  2.8750E+02
#  41  8.380E-01  4.685E-01  2.755E-01  2.6955E+02
#  42  8.190E-01  6.710E-01  4.535E-01  3.2160E+02
#  43  5.615E-01  6.995E-01  2.465E-01  2.3155E+02
#  44  1.000E+00  1.000E+00  0.000E+00  3.0000E+02
#  45  1.000E+00  5.000E-01  0.000E+00  2.5000E+02
#  46  1.000E+00  1.000E+00  5.000E-01  4.0000E+02
#  47  9.250E-01  8.245E-01  1.315E-01  2.9375E+02
#  48  5.000E-01  1.000E+00  0.000E+00  2.0000E+02


[Mesh]#Comment
  file = heat_conduction_patch_hex20.e
[] # Mesh

[Functions]
  [./temps]
    type = ParsedFunction
    expression ='200*x+100*y+200*z'
  [../]
[] # Functions

[Variables]

  [./temp]
    order = SECOND
    family = LAGRANGE
  [../]

[] # Variables

[Kernels]

  [./heat_r]
    type = HeatConduction
    variable = temp
  [../]

[] # Kernels

[BCs]

  [./temps]
    type = FunctionDirichletBC
    variable = temp
    boundary = 10
    function = temps
  [../]

[] # BCs

[Materials]

  [./heat]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 0.116
    thermal_conductivity = 4.85e-4
  [../]

[] # Materials

[Executioner]

  type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -ksp_gmres_restart'
  petsc_options_value = 'lu       101'

  line_search = 'none'

  nl_abs_tol = 1e-11
  nl_rel_tol = 1e-10


  l_max_its = 20

  [./Quadrature]
    order = THIRD
  [../]

[] # Executioner

[Outputs]
  exodus = true
[] # Output

(modules/combined/test/tests/elastic_thermal_patch/elastic_thermal_weak_plane_stress_jacobian.i)

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  temperature = temp
  out_of_plane_strain = strain_zz
[]

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]

  [./strain_zz]
  [../]

  [./temp]
  [../]
[]

[Kernels]
  [./disp_x]
    type = StressDivergenceTensors
    variable = disp_x
    eigenstrain_names = thermal_eigenstrain
    component = 0
  [../]
  [./disp_y]
    type = StressDivergenceTensors
    variable = disp_y
    eigenstrain_names = thermal_eigenstrain
    component = 1
  [../]

  [./solid_z]
    type = WeakPlaneStress
    variable = strain_zz
    eigenstrain_names = thermal_eigenstrain
  [../]

  [./heat]
    type = HeatConduction
    variable = temp
    use_displaced_mesh = false
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    poissons_ratio = 0.0
    youngs_modulus = 1
  [../]
  [./strain]
    type = ComputePlaneSmallStrain
    eigenstrain_names = thermal_eigenstrain
  [../]
  [./thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 1e-5
    stress_free_temperature = 0
    eigenstrain_name = thermal_eigenstrain
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]

  [./conductivity]
    type = HeatConductionMaterial
    thermal_conductivity = 1
    use_displaced_mesh = false
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON

  petsc_options_iname = '-ksp_type -pc_type -snes_type'
  petsc_options_value = 'bcgs bjacobi test'

  end_time = 1.0
[]

(modules/combined/examples/thermomechanics/circle_thermal_expansion_stress.i)

# This example problem demonstrates coupling heat conduction with mechanics.
# A circular domain has as uniform heat source that increases with time
# and a fixed temperature on the outer boundary, resulting in a temperature gradient.
# This results in heterogeneous thermal expansion, where it is pinned in the center.
# Looking at the hoop stress demonstrates why fuel pellets have radial cracks
# that extend from the outer boundary to about halfway through the radius.
# The problem is run with length units of microns.

[Mesh]
  #Circle mesh has a radius of 1000 units
  type = FileMesh
  file = circle.e
  uniform_refine = 1
[]

[Variables]
  # We solve for the temperature and the displacements
  [./T]
    initial_condition = 800
    scaling = 1e7
  [../]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[AuxVariables]
  [./radial_stress]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  active = 'TensorMechanics htcond Q_function'
  [./htcond] #Heat conduction equation
    type = HeatConduction
    variable = T
  [../]
  [./TensorMechanics] #Action that creates equations for disp_x and disp_y
    displacements = 'disp_x disp_y'
  [../]
  [./Q_function] #Heat generation term
    type = BodyForce
    variable = T
    value = 1
    function = 0.8e-9*t
  [../]
[]

[AuxKernels]
  [./radial_stress] #Calculates radial stress from cartesian
    type = CylindricalRankTwoAux
    variable = radial_stress
    rank_two_tensor = stress
    index_j = 0
    index_i = 0
    center_point = '0 0 0'
  [../]
  [./hoop_stress] #Calculates hoop stress from cartesian
    type = CylindricalRankTwoAux
    variable = hoop_stress
    rank_two_tensor = stress
    index_j = 1
    index_i = 1
    center_point = '0 0 0'
  [../]
[]

[BCs]
  [./outer_T] #Temperature on outer edge is fixed at 800K
    type = DirichletBC
    variable = T
    boundary = 1
    value = 800
  [../]
  [./outer_x] #Displacements in the x-direction are fixed in the center
    type = DirichletBC
    variable = disp_x
    boundary = 2
    value = 0
  [../]
  [./outer_y] #Displacements in the y-direction are fixed in the center
    type = DirichletBC
    variable = disp_y
    boundary = 2
    value = 0
  [../]
[]

[Materials]
  [./thcond] #Thermal conductivity is set to 5 W/mK
    type = GenericConstantMaterial
    block = 1
    prop_names = 'thermal_conductivity'
    prop_values = '5e-6'
  [../]
  [./iso_C] #Sets isotropic elastic constants
    type = ComputeElasticityTensor
    fill_method = symmetric_isotropic
    C_ijkl = '2.15e5 0.74e5'
    block = 1
  [../]
  [./strain] #We use small deformation mechanics
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y'
    block = 1
    eigenstrain_names = eigenstrain
  [../]
  [./stress] #We use linear elasticity
    type = ComputeLinearElasticStress
    block = 1
  [../]
  [./thermal_strain]
    type= ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 1e-6
    temperature = T
    stress_free_temperature = 273
    block = 1
    eigenstrain_name = eigenstrain
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  num_steps = 10
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre boomeramg 101'
  l_max_its = 30
  nl_max_its = 10
  nl_abs_tol = 1e-9
  l_tol = 1e-04
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/heat_transfer/test/tests/semiconductor_linear_conductivity/steinhart-hart_linear.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 1.0
  ymax = 1.0
[]

[Variables]
  [./T]
      initial_condition = 400.0   # unit in Kelvin only!!
  [../]
[]

[AuxVariables]
  [./elec_conduct]
      order = FIRST
      family = MONOMIAL
  [../]
[]

[Kernels]
  [./diff]
    type = HeatConduction
    variable = T
  [../]
[]

[AuxKernels]
  [./elec_conduct]
    type = MaterialRealAux
    variable = elec_conduct
    property = electrical_conductivity
    execute_on = timestep_end
  [../]
[]

[BCs]
  [./inlet]
    type = DirichletBC
    variable = T
    boundary = left
    value = 1000 # K
  [../]
  [./outlet]
    type = DirichletBC
    variable = T
    boundary = right
    value = 400 # K
  [../]
[]

[Materials]
  [./k]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '10' # in W/mK
  [../]
  [./sigma]
    type = SemiconductorLinearConductivity
    temp = T
    sh_coeff_A = 0.002
    sh_coeff_B = 0.001
  [../]
[]

[VectorPostprocessors]
  [./line_sample]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    variable = 'T elec_conduct'
    start_point = '0 0. 0'
    end_point = '1.0 0. 0'
    num_points = 11
    sort_by = id
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_rel_tol = 1e-12
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
  execute_on = 'initial timestep_end'
[]

(modules/functional_expansion_tools/examples/3D_volumetric_Cartesian_direct/main.i)

# Derived from the example '3D_volumetric_Cartesian' with the following differences:
#
#   1) The coupling is performed via BodyForce instead of the
#      FunctionSeriesToAux+CoupledForce approach
[Mesh]
  type = GeneratedMesh
  dim = 3

  xmin = 0.0
  xmax = 10.0
  nx = 15

  ymin = 1.0
  ymax = 11.0
  ny = 25

  zmin = 2.0
  zmax = 12.0
  nz = 35
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./s_in] # Add in the contribution from the SubApp
    type = BodyForce
    variable = m
    function = FX_Basis_Value_Main
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'top bottom left right front back'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3   4   5'
    physical_bounds = '0.0  10.0    1.0 11.0    2.0 12.0'
    x = Legendre
    y = Legendre
    z = Legendre
    enable_cache = true
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(modules/heat_transfer/test/tests/gray_lambert_radiator/coupled_heat_conduction.i)

[Problem]
  kernel_coverage_check = false
[]

[Mesh]
  type = MeshGeneratorMesh

  [./cartesian]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1 1'
    ix = '2 2 2'
    dy = '5'
    iy = '10'
    subdomain_id = '1 2 3'
  [../]

  [./break_sides]
    type = BreakBoundaryOnSubdomainGenerator
    boundaries = 'bottom top'
    input = cartesian
  [../]

  [./left_interior]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 1
    paired_block = 2
    new_boundary = left_interior
    input = break_sides
  [../]

  [./right_interior]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 3
    paired_block = 2
    new_boundary = right_interior
    input = left_interior
  [../]
  [./rename]
    type = RenameBlockGenerator
    input = right_interior
    old_block = '1 2 3'
    new_block = '1 4 3'
  [../]
[]


[Variables]
  [./temperature]
    initial_condition = 300
    block = '1 3'
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temperature
    diffusion_coefficient = 1
    block = '1 3'
  [../]
[]

[UserObjects]
  [./cavity_radiation]
    type = ConstantViewFactorSurfaceRadiation
    boundary = 'left_interior right_interior bottom_to_2 top_to_2'
    temperature = temperature
    emissivity = '0.8 0.8 0.8 0.8'
    adiabatic_boundary = 'bottom_to_2 top_to_2'
    # these view factors are made up to exactly balance energy
    # transfer through the cavity
    view_factors = '0    0.8 0.1 0.1;
                    0.8  0   0.1 0.1;
                    0.45 0.45  0 0.1;
                    0.45 0.45 0.1  0'
    execute_on = 'INITIAL LINEAR TIMESTEP_END'
  [../]
[]

[BCs]
  [./bottom_left]
    type = DirichletBC
    preset = false
    variable = temperature
    boundary = bottom_to_1
    value = 1500
  [../]

  [./top_right]
    type = DirichletBC
    preset = false
    variable = temperature
    boundary = top_to_3
    value = 300
  [../]

  [./radiation]
    type = GrayLambertNeumannBC
    variable = temperature
    reconstruct_emission = false
    surface_radiation_object_name = cavity_radiation
    boundary = 'left_interior right_interior'
  [../]
[]

[Postprocessors]
  [./qdot_left]
    type = GrayLambertSurfaceRadiationPP
    boundary = left_interior
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_right]
    type = GrayLambertSurfaceRadiationPP
    boundary = right_interior
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_top]
    type = GrayLambertSurfaceRadiationPP
    boundary = top_to_2
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_bottom]
    type = GrayLambertSurfaceRadiationPP
    boundary = bottom_to_2
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/code_verification/cartesian_test_no2.i)

# Problem I.2
#
# An infinite plate with a thermal conductivity that varies linearly with
# temperature. Each boundary is exposed to a constant temperature.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    nx = 1
  [../]
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./exact]
    type = ParsedFunction
    symbol_names = 'L beta ki ko ui uo'
    symbol_values = '1 1e-3 5.3 5 300 0'
    expression = 'uo+(ko/beta)* ( (1 + L*beta*(ki+ko)*(ui-uo)*((L-x)/(ko*L)^2) )^0.5  - 1)'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
[]

[BCs]
  [./ui]
    type = DirichletBC
    boundary = left
    variable = u
    value = 300
  [../]
  [./uo]
    type = DirichletBC
    boundary = right
    variable = u
    value = 0
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat'
    prop_values = '1.0 1.0'
  [../]
  [./thermal_conductivity]
    type = ParsedMaterial
    property_name = 'thermal_conductivity'
    coupled_variables = u
    expression = '5 + 1e-3 * (u-0)'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/radiation_transfer_symmetry/cavity_with_pillars_symmetry_bc.i)

#
# inner_left: 8
# inner_top: 11
# inner_bottom: 10
# inner_front: 9
# back_2: 7
# obstruction: 6
#

[Mesh]
  [cartesian]
    type = CartesianMeshGenerator
    dim = 3
    dx = '0.4 0.5 0.5 0.5'
    dy = '0.5 0.75 0.5'
    dz = '1.5 0.5'
    subdomain_id = '
                    3 1 1 1
                    3 1 2 1
                    3 1 1 1

                    3 1 1 1
                    3 1 1 1
                    3 1 1 1
                    '
  []

  [add_obstruction]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 2
    paired_block = 1
    new_boundary = obstruction
    input = cartesian
  []

  [add_new_back]
    type = ParsedGenerateSideset
    combinatorial_geometry = 'abs(z) < 1e-10'
    included_subdomains = '1'
    normal = '0 0 -1'
    new_sideset_name = back_2
    input = add_obstruction
  []

  [add_inner_left]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 3
    paired_block = 1
    new_boundary = inner_left
    input = add_new_back
  []

  [add_inner_front]
    type = ParsedGenerateSideset
    combinatorial_geometry = 'abs(z - 2) < 1e-10'
    included_subdomains = '1'
    normal = '0 0 1'
    new_sideset_name = inner_front
    input = add_inner_left
  []

  [add_inner_bottom]
    type = ParsedGenerateSideset
    combinatorial_geometry = 'abs(y) < 1e-10'
    included_subdomains = '1'
    normal = '0 -1 0'
    new_sideset_name = inner_bottom
    input = add_inner_front
  []

  [add_inner_top]
    type = ParsedGenerateSideset
    combinatorial_geometry = 'abs(y - 1.75) < 1e-10'
    included_subdomains = '1'
    normal = '0 1 0'
    new_sideset_name = inner_top
    input = add_inner_bottom
  []
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [temperature]
    block = '2 3'
    initial_condition = 300
  []
[]

[Kernels]
  [conduction]
    type = HeatConduction
    variable = temperature
    block = '2 3'
    diffusion_coefficient = 1
  []

  [source]
    type = BodyForce
    variable = temperature
    value = 1000
    block = '2'
  []
[]

[BCs]
  [convective]
    type = CoupledConvectiveHeatFluxBC
    variable = temperature
    T_infinity = 300
    htc = 50
    boundary = 'left'
  []
[]

[GrayDiffuseRadiation]
  [./cavity]
    boundary = '6 7 8 9 10 11'
    emissivity = '1 1 1 1 1 1'
    n_patches = '1 1 1 1 1 1'
    adiabatic_boundary = '7 9 10 11'
    symmetry_boundary = '2'
    partitioners = 'metis metis metis metis metis metis'
    temperature = temperature
    ray_tracing_face_order = SECOND
    normalize_view_factor = false
  [../]
[]

[Postprocessors]
  [Tpv]
    type = PointValue
    variable = temperature
    point = '0.3 0.5 0.5'
  []

  [volume]
    type = VolumePostprocessor
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/transient_heat/transient_heat_derivatives.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
  []
[]

[Variables]
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 2
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []

  [ie]
    type = HeatConductionTimeDerivative
    variable = temp
    specific_heat_dT = specific_heat_dT
    density_name_dT = density_dT
  []
[]

[Functions]
  [spheat]
    type = ParsedFunction
    expression = 't^4'
  []
  [thcond]
    type = ParsedFunction
    expression = 'exp(t)'
  []
[]

[BCs]
  [bottom]
    type = DirichletBC
    variable = temp
    boundary = 1
    value = 4
  []

  [top]
    type = DirichletBC
    variable = temp
    boundary = 2
    value = 1
  []
[]

[Materials]
  [constant]
    type = HeatConductionMaterial
    thermal_conductivity_temperature_function = thcond
    specific_heat_temperature_function = spheat
    temp = temp
  []
  [density]
    type = ParsedMaterial
    property_name = density
    coupled_variables = temp
    expression = 'temp^3 + 2/temp'
  []
  [density_dT]
    type = ParsedMaterial
    property_name = density_dT
    coupled_variables = temp
    expression = '3 * temp^2 - 2/temp/temp'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  num_steps = 1
  dt = .1
  nl_max_its = 10
  dtmin = .1
[]

[Postprocessors]
  [avg]
    type = ElementAverageValue
    variable = temp
  []
[]

[Outputs]
  csv = true
[]

(modules/combined/test/tests/elastic_thermal_patch/elastic_thermal_patch.i)

# Patch Test

# This test is designed to compute constant xx, yy, zz, xy, yz, and zx
#  stress on a set of irregular hexes.  The mesh is composed of one
#  block with seven elements.  The elements form a unit cube with one
#  internal element.  There is a nodeset for each exterior node.

# The cube is displaced by 1e-6 units in x, 2e-6 in y, and 3e-6 in z.
#  The faces are sheared as well (1e-6, 2e-6, and 3e-6 for xy, yz, and
#  zx).  This gives a uniform strain/stress state for all six unique
#  tensor components.

# With Young's modulus at 1e6 and Poisson's ratio at 0, the shear
#  modulus is 5e5 (G=E/2/(1+nu)).  Therefore, for the mechanical strain,
#
#  stress xx = 1e6 * 1e-6 = 1
#  stress yy = 1e6 * 2e-6 = 2
#  stress zz = 1e6 * 3e-6 = 3
#  stress xy = 2 * 5e5 * 1e-6 / 2 = 0.5
#             (2 * G   * gamma_xy / 2 = 2 * G * epsilon_xy)
#  stress yz = 2 * 5e5 * 2e-6 / 2 = 1
#  stress zx = 2 * 5e5 * 3e-6 / 2 = 1.5

# However, we must also consider the thermal strain.
# The temperature moves 100 degrees, and the coefficient of thermal
#  expansion is 1e-8.  Therefore, the thermal strain (and the displacement
#  since this is a unit cube) is 1e-6.

# Therefore, the overall effect is (at time 1, with a 50 degree delta):
#
#  stress xx = 1e6 * (1e-6-0.5e-6) = 0.5
#  stress yy = 1e6 * (2e-6-0.5e-6) = 1.5
#  stress zz = 1e6 * (3e-6-0.5e-6) = 2.5
#  stress xy = 2 * 5e5 * 1e-6 / 2 = 0.5
#             (2 * G   * gamma_xy / 2 = 2 * G * epsilon_xy)
#  stress yz = 2 * 5e5 * 2e-6 / 2 = 1
#  stress zx = 2 * 5e5 * 3e-6 / 2 = 1.5
#
# At time 2:
#
#  stress xx = 1e6 * (1e-6-1e-6) = 0
#  stress yy = 1e6 * (2e-6-1e-6) = 1
#  stress zz = 1e6 * (3e-6-1e-6) = 2
#  stress xy = 2 * 5e5 * 1e-6 / 2 = 0.5
#             (2 * G   * gamma_xy / 2 = 2 * G * epsilon_xy)
#  stress yz = 2 * 5e5 * 2e-6 / 2 = 1
#  stress zx = 2 * 5e5 * 3e-6 / 2 = 1.5

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  temperature = temp
[]

[Mesh]
  file = elastic_thermal_patch_test.e
[]

[Functions]
  [./rampConstant1]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 1e-6
  [../]
  [./rampConstant2]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 2e-6
  [../]
  [./rampConstant3]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 3e-6
  [../]
  [./rampConstant4]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 4e-6
  [../]
  [./rampConstant6]
    type = PiecewiseLinear
    x = '0. 1. 2.'
    y = '0. 1. 1.'
    scale_factor = 6e-6
  [../]
  [./tempFunc]
    type = PiecewiseLinear
    x = '0. 2.'
    y = '117.56 217.56'
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]

  [./temp]
    initial_condition = 117.56
  [../]
[]

[Physics/SolidMechanics/QuasiStatic/All]
  add_variables = true
  strain = FINITE
  eigenstrain_names = eigenstrain
  generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_yz stress_zx'
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./node1_x]
    type = DirichletBC
    variable = disp_x
    boundary = 1
    value = 0.0
  [../]
  [./node1_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 1
    function = rampConstant2
  [../]
  [./node1_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 1
    function = rampConstant3
  [../]

  [./node2_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 2
    function = rampConstant1
  [../]
  [./node2_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 2
    function = rampConstant2
  [../]
  [./node2_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 2
    function = rampConstant6
  [../]

  [./node3_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 3
    function = rampConstant1
  [../]
  [./node3_y]
    type = DirichletBC
    variable = disp_y
    boundary = 3
    value = 0.0
  [../]
  [./node3_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 3
    function = rampConstant3
  [../]

  [./node4_x]
    type = DirichletBC
    variable = disp_x
    boundary = 4
    value = 0.0
  [../]
  [./node4_y]
    type = DirichletBC
    variable = disp_y
    boundary = 4
    value = 0.0
  [../]
  [./node4_z]
    type = DirichletBC
    variable = disp_z
    boundary = 4
    value = 0.0
  [../]

  [./node5_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 5
    function = rampConstant1
  [../]
  [./node5_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 5
    function = rampConstant4
  [../]
  [./node5_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 5
    function = rampConstant3
  [../]

  [./node6_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 6
    function = rampConstant2
  [../]
  [./node6_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 6
    function = rampConstant4
  [../]
  [./node6_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 6
    function = rampConstant6
  [../]

  [./node7_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 7
    function = rampConstant2
  [../]
  [./node7_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 7
    function = rampConstant2
  [../]
  [./node7_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 7
    function = rampConstant3
  [../]

  [./node8_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 8
    function = rampConstant1
  [../]
  [./node8_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 8
    function = rampConstant2
  [../]
  [./node8_z]
    type = DirichletBC
    variable = disp_z
    boundary = 8
    value = 0.0
  [../]

  [./temp]
    type = FunctionDirichletBC
    variable = temp
    boundary = '10 12'
    function = tempFunc
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    bulk_modulus = 0.333333333333333e6
    shear_modulus = 0.5e6
  [../]
  [./thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    stress_free_temperature = 117.56
    thermal_expansion_coeff = 1e-8
    eigenstrain_name = eigenstrain
  [../]
  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]

  [./heat]
    type = HeatConductionMaterial
    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./density]
    type = Density
    density = 1.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  nl_rel_tol = 1e-12

  l_max_its = 20

  start_time = 0.0
  dt = 1.0
  num_steps = 2
  end_time = 2.0
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/adaptive_timestepping/adapt_tstep_function_change_restart2.i)

# This is a test designed to evaluate the cabability of the
# IterationAdaptiveDT TimeStepper to adjust time step size according to
# a function.  For example, if the power input function for a BISON
# simulation rapidly increases or decreases, the IterationAdaptiveDT
# TimeStepper should take time steps small enough to capture the
# oscillation.

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  file = 1hex8_10mm_cube.e
[]

[Functions]
  [./Fiss_Function]
    type = PiecewiseLinear
    x = '0 1e6  2e6  2.001e6 2.002e6'
    y = '0 3e8  3e8  12e8    0'
  [../]
[]

[Variables]
  [./disp_x]
  [../]

  [./disp_y]
  [../]

  [./disp_z]
  [../]

  [./temp]
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  [./all]
    strain = FINITE
    volumetric_locking_correction = true
    incremental = true
    eigenstrain_names = thermal_expansion
    decomposition_method = EigenSolution
    add_variables  = true
    generate_output = 'vonmises_stress'
    temperature = temp
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]

  [./heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]

  [./heat_source]
     type = HeatSource
     variable = temp
     value = 1.0
     function = Fiss_Function
  [../]
[]

[BCs]
 [./bottom_temp]
   type = DirichletBC
   variable = temp
   boundary = 1
   value = 300
 [../]
 [./top_bottom_disp_x]
   type = DirichletBC
   variable = disp_x
   boundary = '1'
   value = 0
 [../]
 [./top_bottom_disp_y]
   type = DirichletBC
   variable = disp_y
   boundary = '1'
   value = 0
 [../]
 [./top_bottom_disp_z]
   type = DirichletBC
   variable = disp_z
   boundary = '1'
   value = 0
 [../]
[]

[Materials]
 [./thermal]
    type = HeatConductionMaterial
    temp = temp
    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 300e6
    poissons_ratio = .3
  [../]

  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]

  [./thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 5e-6
    stress_free_temperature = 300.0
    temperature = temp
    eigenstrain_name = thermal_expansion
  [../]

  [./density]
    type = Density
    density = 10963.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  verbose = true
  nl_abs_tol = 1e-10
  num_steps = 50000
  end_time = 2.002e6
  [./TimeStepper]
    type = IterationAdaptiveDT
    timestep_limiting_function = Fiss_Function
    max_function_change = 3e7
    dt = 1e6
  [../]
[]

[Postprocessors]
  [./Temperature_of_Block]
    type = ElementAverageValue
    variable = temp
    execute_on = 'timestep_end'
  [../]

  [./vonMises]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  [./out]
    type = Exodus
    elemental_as_nodal = true
  [../]
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

[Problem]
  restart_file_base = adapt_tstep_function_change_restart1_checkpoint_cp/0065
[]

(modules/heat_transfer/test/tests/thin_layer_heat_transfer/steady_3d.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    nx = 10
    ny = 10
    nz = 2
    zmax = 0.2
    dim = 3
  []
  [block1]
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '0 0 0'
    top_right = '0.5 1 0.2'
    input = gen
  []
  [block2]
    type = SubdomainBoundingBoxGenerator
    block_id = 2
    bottom_left = '0.5 0 0'
    top_right = '1 1 0.2'
    input = block1
  []
  [breakmesh]
    input = block2
    type = BreakMeshByBlockGenerator
    block_pairs = '1 2'
    split_interface = true
    add_interface_on_two_sides = true
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [thermal_cond]
    type = HeatConduction
    variable = temperature
  []
[]

[InterfaceKernels]
  [thin_layer]
    type = ThinLayerHeatTransfer
    thermal_conductivity = thermal_conductivity_layer
    thickness = 0.01
    variable = temperature
    neighbor_var = temperature
    boundary = Block1_Block2
  []
[]

[BCs]
  [left_temp]
    type = DirichletBC
    value = 100
    variable = temperature
    boundary = left
  []
  [right_temp]
    type = DirichletBC
    value = 0
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [thermal_cond]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '1'
  []
  [thermal_cond_layer]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity_layer'
    prop_values = '0.05'
    boundary = Block1_Block2
  []
[]
[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10

  dt = 0.05
  num_steps = 1
[]


[Outputs]
  print_linear_residuals = false
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_rz_cylinder_mortar.i)

rpv_core_gap_size = 0.2

core_outer_radius = 2
rpv_inner_radius = '${fparse 2 + rpv_core_gap_size}'
rpv_outer_radius = '${fparse 2.5 + rpv_core_gap_size}'
rpv_width = '${fparse rpv_outer_radius - rpv_inner_radius}'

rpv_outer_htc = 10 # W/m^2/K
rpv_outer_Tinf = 300 # K

core_blocks = '1'
rpv_blocks = '3'

[Mesh]
  [gmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '${core_outer_radius} ${rpv_core_gap_size} ${rpv_width}'
    ix = '400 1 100'
    dy = 1
    iy = '5'
  []
  [set_block_id1]
    type = SubdomainBoundingBoxGenerator
    input = gmg
    bottom_left = '0 0 0'
    top_right = '${core_outer_radius} 1 0'
    block_id = 1
    location = INSIDE
  []
  [rename_core_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = set_block_id1
    primary_block = 1
    paired_block = 0
    new_boundary = 'core_outer'
  []
  [set_block_id3]
    type = SubdomainBoundingBoxGenerator
    input = rename_core_bdy
    bottom_left = '${rpv_inner_radius} 0 0'
    top_right = '${rpv_outer_radius} 1 0'
    block_id = 3
    location = INSIDE
  []
  [rename_inner_rpv_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = set_block_id3
    primary_block = 3
    paired_block = 0
    new_boundary = 'rpv_inner'
  []
  # comment out for test without gap
  [2d_mesh]
    type = BlockDeletionGenerator
    input = rename_inner_rpv_bdy
    block = 0
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'rpv_inner'
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    input = 2d_mesh
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'core_outer'
    new_block_id = 10000
    new_block_name = 'primary_lower'
    input = secondary
  []
  allow_renumbering = false
  coord_type = RZ
[]

[Variables]
  [Tsolid]
    initial_condition = 500
  []
    [lm]
      order = FIRST
      family = LAGRANGE
      block = 'secondary_lower'
    []
[]

[Kernels]
  [heat_source]
    type = CoupledForce
    variable = Tsolid
    block = '${core_blocks}'
    v = power_density
  []
  [heat_conduction]
    type = HeatConduction
    variable = Tsolid
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = Tsolid
    boundary = 'right' # outer RPV
    coefficient = ${rpv_outer_htc}
    T_infinity = ${rpv_outer_Tinf}
  []
[]

[UserObjects]
  [radiation]
    type = GapFluxModelRadiation
    temperature = Tsolid
    boundary = 'rpv_inner'
    primary_emissivity = 0.8
    secondary_emissivity = 0.8
  []
  [conduction]
    type = GapFluxModelConduction
    temperature = Tsolid
    boundary = 'rpv_inner'
    gap_conductivity = 0.1
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = Tsolid
    primary_boundary = 'core_outer'
    primary_subdomain = 10000
    secondary_boundary = 'rpv_inner'
    secondary_subdomain = 10001
    gap_flux_models = 'radiation conduction'
    gap_geometry_type = 'CYLINDER'
  []
[]

[AuxVariables]
  [power_density]
    block = '${core_blocks}'
    initial_condition = 50e3
  []
[]

[Materials]
  [simple_mat]
    type = HeatConductionMaterial
    thermal_conductivity = 34.6 # W/m/K
  []
[]

[Postprocessors]
  [Tcore_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Trpv_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = '${core_blocks}'
  []
  [rpv_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = Tsolid
    boundary = 'right' # outer RVP
    T_fluid = ${rpv_outer_Tinf}
    htc = ${rpv_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(rpv_convective_out - ptot) / ptot'
    pp_names = 'rpv_convective_out ptot'
  []
  [flux_from_core] # converges to ptot as the mesh is refined
    type = SideDiffusiveFluxIntegral
    variable = Tsolid
    boundary = core_outer
    diffusivity = thermal_conductivity
  []
  [flux_into_rpv] # converges to rpv_convective_out as the mesh is refined
    type = SideDiffusiveFluxIntegral
    variable = Tsolid
    boundary = rpv_inner
    diffusivity = thermal_conductivity
  []

[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = 'rpv_inner core_outer'
    variable = Tsolid
  []
[]

[Executioner]
  type = Steady

  petsc_options = '-snes_converged_reason -pc_svd_monitor'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err -pc_factor_shift_type '
                        '-pc_factor_shift_amount'
  petsc_options_value = ' lu       superlu_dist                  1e-5          NONZERO               '
                        '1e-15'
  snesmf_reuse_base = false
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_max_its = 100

  line_search = none
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/heat_transfer/tutorials/introduction/therm_step02a.i)

#
# Single block thermal input with a line value sampler
# https://mooseframework.inl.gov/modules/heat_transfer/tutorials/introduction/therm_step02.html
#

[Mesh]
  [generated]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 2
    ymax = 1
  []
[]

[Variables]
  [T]
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 45.0
  []
[]

[BCs]
  [t_left]
    type = DirichletBC
    variable = T
    value = 300
    boundary = 'left'
  []
  [t_right]
    type = FunctionDirichletBC
    variable = T
    function = '300+5*t'
    boundary = 'right'
  []
[]

[Executioner]
  type = Transient
  end_time = 5
  dt = 1
[]

[VectorPostprocessors]
  [t_sampler]
    type = LineValueSampler
    variable = T
    start_point = '0 0.5 0'
    end_point = '2 0.5 0'
    num_points = 20
    sort_by = x
  []
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = therm_step02a_out
    execute_on = final
  []
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/sphere2DRZ.i)

#
# 2DRZ Spherical Gap Heat Transfer Test.
#
# This test exercises 2D gap heat transfer for a constant conductivity gap.
#
# The mesh consists of an inner solid sphere of radius = 1 unit, and outer
# hollow sphere with an inner radius of 2. In other words, the gap between
# them is 1 radial unit in length.
#
# The conductivity of both spheres is set very large to achieve a uniform
# temperature in each sphere. The temperature of the center node of the
# inner sphere is ramped from 100 to 200 over one time unit. The
# temperature of the outside of the outer, hollow sphere is held fixed
# at 100.
#
# A simple analytical solution is possible for the integrated heat flux
# between the inner and outer spheres:
#
#  Integrated Flux = (T_left - T_right) * (gapK/(r^2*((1/r1)-(1/r2)))) * Area
#
# For gapK = 1 (default value)
#
# The area is taken as the area of the secondary (inner) surface:
#
# Area = 4 * pi * 1^2 (4*pi*r^2)
#
# The integrated heat flux across the gap at time 1 is then:
#
# 4*pi*k*delta_T/((1/r1)-(1/r2))
# 4*pi*1*100/((1/1) - (1/2)) =  2513.3 watts
#
# For comparison, see results from the integrated flux post processors.
# This simulation makes use of symmetry, so only 1/2 of the spheres is meshed
# As such, the integrated flux from the post processors is 1/2 of the total,
# or 1256.6 watts... i.e. 400*pi.
# The value coming from the post processor is slightly less than this
# but converges as mesh refinement increases.
#
# Simulating contact is challenging. Regression tests that exercise
# contact features can be difficult to solve consistently across multiple
# platforms. While designing these tests, we felt it worth while to note
# some aspects of these tests. The following applies to:
# sphere3D.i, sphere2DRZ.i, cyl2D.i, and cyl3D.i.
# 1. We decided that to perform consistently across multiple platforms we
# would use very small convergence tolerance. In this test we chose an
# nl_rel_tol of 1e-12.
# 2. Due to such a high value for thermal conductivity (used here so that the
# domains come to a uniform temperature) the integrated flux at time = 0
# was relatively large (the value coming from SideIntegralFlux =
#  -_diffusion_coef[_qp]*_grad_u[_qp]*_normals[_qp] where the diffusion coefficient
# here is thermal conductivity).
# Even though _grad_u[_qp] is small, in this case the diffusion coefficient
# is large. The result is a number that isn't exactly zero and tends to
# fail exodiff. For this reason the parameter execute_on = initial should not
# be used. That parameter is left to default settings in these regression tests.
#
[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  file = cyl2D.e
  coord_type = RZ
[]

[Functions]
  [./temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  [../]
[]


[Variables]
  [./temp]
    initial_condition = 100
  [../]
[]

[AuxVariables]
  [./gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]


[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temp
  [../]
[]


[AuxKernels]
  [./gap_cond]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_conductance
    boundary = 2
  [../]
[]

[Materials]
  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 1000000.0
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductivity = 1
    quadrature = true
    gap_geometry_type = SPHERE
    sphere_origin = '0 0 0'
  [../]
[]

[BCs]
  [./mid]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  [../]
  [./temp_far_right]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

  [./Quadrature]
    order = fifth
    side_order = seventh
  [../]
[]

[Outputs]
  exodus = true
  [./Console]
    type = Console
  [../]
[]

[Postprocessors]
  [./temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  [../]

  [./temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  [../]

  [./flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  [../]

  [./flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  [../]
[]

(modules/combined/test/tests/restart-transient-from-ss-with-stateful/parent_ss.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    nx = 8
    ny = 8
    xmin = -82.627
    xmax = 82.627
    ymin = -82.627
    ymax = 82.627
    dim = 2
  []
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 500
  [../]
[]

[AuxVariables]
  [./power]
    order = FIRST
    family = L2_LAGRANGE
    initial_condition = 350
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./heat_source_fuel]
    type = CoupledForce
    variable = temp
    v = 'power'
  [../]
[]

[BCs]
  [./all]
    type = DirichletBC
    variable = temp
    boundary = 'bottom top left right'
    value = 300
  [../]
[]

[Materials]
  [./heat_material]
    type = HeatConductionMaterial
    temp = temp
    specific_heat = 1000
    thermal_conductivity = 500
  [../]
  [./density]
    type = Density
    density = 2000
  [../]
[]

[Postprocessors]
  [./avg_temp]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  [../]
  [./avg_power]
    type = ElementAverageValue
    variable = power
  [../]
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre boomeramg 300'
  line_search = 'none'

  l_tol = 1e-05
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-9

  l_max_its = 50
  nl_max_its = 25
[]

[Outputs]
  perf_graph = true
  color = true
  exodus = true

  [checkpoint]
    type = Checkpoint
    num_files = 2
    additional_execute_on = 'FINAL' # seems to be a necessary to avoid a Checkpoint bug
  []
[]

[MultiApps]
  [./bison]
    type = FullSolveMultiApp
    positions = '0 0 0'
    input_files = 'sub_ss.i'
    execute_on = 'timestep_end'
  [../]
[]

[Transfers]
  [./to_bison_mechanics]
    type = MultiAppProjectionTransfer
    to_multi_app = bison
    variable = temp
    source_variable = temp
    execute_on = 'timestep_end'
  [../]
[]

(modules/combined/examples/xfem/xfem_thermomechanics_stress_growth.i)

# This is a demonstration of a simple thermomechanics simulation using
# XFEM in which a single crack propagates based on a principal stress
# criterion.
#
# The top and bottom of the plate are fixed in the y direction, and the
# top of the plate is cooled down over time. The thermal contraction
# causes tensile stresses, which lead to crack propagation. The crack
# propagates in a curved path because of the changinging nature of
# the thermal gradient as a result of the crack. There is no heat
# conduction across the crack as soon as it forms.

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 11
  ny = 11
  xmin = 0.0
  xmax = 1.0
  ymin = 0.0
  ymax = 1.0
  elem_type = QUAD4
[]

[Variables]
  # Solve for the temperature and the displacements
  # Displacements are not specified because the TensorMechanics/Master Action sets them up
  [./temp]
    initial_condition = 300
  [../]
[]

[XFEM]
  geometric_cut_userobjects = 'line_seg_cut_uo'
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [./line_seg_cut_uo]
    type = LineSegmentCutUserObject
    cut_data = '1.0  0.5  0.8  0.5'
    time_start_cut = 0.0
    time_end_cut = 0.0
  [../]
  [./xfem_marker_uo]
    type = XFEMRankTwoTensorMarkerUserObject
    execute_on = timestep_end
    tensor = stress
    scalar_type = MaxPrincipal
    threshold = 5e+1
    average = true
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  [./all]
    strain = FINITE
    planar_formulation = plane_strain
    add_variables = true
    eigenstrain_names = eigenstrain
  [../]
[]

[Kernels]
  [./htcond]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./bottomx]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  [../]
  [./bottomy]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  [../]
  [./topx]
    type = DirichletBC
    boundary = top
    variable = disp_x
    value = 0.0
  [../]
  [./topy]
    type = DirichletBC
    boundary = top
    variable = disp_y
    value = 0.0
  [../]
  [./topt]
    type = FunctionDirichletBC
    boundary = top
    variable = temp
    function = 273-t*27.3
  [../]
  [./bott]
    type = FunctionDirichletBC
    boundary = bottom
    variable = temp
    function = 273
#    value = 273.0
  [../]
[]

[Materials]
  [./thcond]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '5e-6'
  [../]

  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e6
    poissons_ratio = 0.3
  [../]

  [./_elastic_strain]
    type = ComputeFiniteStrainElasticStress
  [../]

  [./thermal_strain]
    type= ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 10e-6
    temperature = temp
    stress_free_temperature = 273
    eigenstrain_name = eigenstrain
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      8'

  line_search = 'none'

  [./Predictor]
    type = SimplePredictor
    scale = 1.0
  [../]

# controls for linear iterations
  l_max_its = 100
  l_tol = 1e-2

# controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-9

# time control
  start_time = 0.0
  dt = 1.0
  end_time = 10.0

  max_xfem_update = 5
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
  [./console]
    type = Console
    output_linear = true
  [../]
[]

(modules/heat_transfer/test/tests/multiple_contact_pairs/multiple_contact_pairs.i)

[Mesh]
  file = 3blk.e
[]

[Functions]
  [temperature]
    type = PiecewiseLinear
    x = '0   1   2'
    y = '100 300 300'
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temperature
    primary = '101 201'
    secondary = '100 200'
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductance = 1.0e9
  []
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  []
[]

[AuxVariables]
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
[]

[BCs]
  [temp_far_left]
    type = FunctionDirichletBC
    boundary = '101 201'
    variable = temperature
    function = temperature
  []
  [temp_far_right]
    type = DirichletBC
    boundary = 'left right'
    variable = temperature
    value = 100
  []
[]

[AuxKernels]
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 100
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2 3'
    specific_heat = 1.0
    thermal_conductivity = 100000000.0
  []
  [density]
    type = GenericConstantMaterial
    block = '1 2 3'
    prop_names = 'density'
    prop_values = '1.0'
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'
  nl_rel_tol = 1e-8
  l_tol = 1e-3
  l_max_its = 100

  dt = 1e-1
  end_time = 1.0
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 100
    variable = temperature
    execute_on = 'initial timestep_end'
  []

  [temp_right]
    type = SideAverageValue
    boundary = 200
    variable = temperature
    execute_on = 'initial timestep_end'
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temperature
    boundary = 100
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  []

  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temperature
    boundary = 200
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/heat_transfer/test/tests/NAFEMS/transient/T3/nafems_t3_quad_template.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 1
  xmin = 0.0
  xmax = 0.1
  ymin = 0.0
  ymax = 0.01
  elem_type = QUAD4
[]

[Variables]
  [./temp]
    initial_condition = 0.0
  [../]
[]

[BCs]
  [./FixedTempLeft]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 0.0
  [../]
  [./FunctionTempRight]
    type = FunctionDirichletBC
    variable = temp
    boundary = right
    function = '100.0 * sin(pi*t/40)'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./HeatTdot]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]
[]

[Materials]
  [./density]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '35.0 440.5 7200.0'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  l_tol = 1e-5
  nl_max_its = 50
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-12

  dt = 1
  end_time = 32.0
[]

[Postprocessors]
  [./target_temp]
    type = NodalVariableValue
    variable = temp
    nodeid = 9
  [../]
[]

[Outputs]
  csv = true
[]

(modules/combined/test/tests/heat_convection/heat_convection_function.i)

[Mesh]    # Mesh Start
  file = patch_3d.e
#
[]    # Mesh END

[Functions]
  [./t_infinity]
    type = ParsedFunction
    expression = '300'
  [../]
  [./htc]
    type = ParsedFunction
    expression = 10.0*5.7                 # convective heat transfer coefficient (w/m^2-K)[50 BTU/hr-ft^2-F]
  [../]
[]

[Variables]  # Variables Start
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 294.26
  [../]
[]    # Variables END


[Kernels]  # Kernels Start
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]    # Kernels END


[BCs]    # Boundary Conditions Start
# Heat transfer coefficient on outer parallelpiped radius and ends
  [./convective_clad_surface]    # Convective Start
    type = ConvectiveFluxFunction  # Convective flux, e.g. q'' = h*(Tw - Tf)
    boundary = 12
    variable = temp
    coefficient = htc
    T_infinity = t_infinity
  [../]                                  # Convective End

  [./fixed]
    type = DirichletBC
    variable = temp
    boundary = 10
    value = 100
  [../]
[]    # BCs END

[Materials]    # Materials Start
  [./thermal]
    type = HeatConductionMaterial
    block = '1 2 3 4 5 6 7'
    specific_heat = 826.4
    thermal_conductivity = 57
  [../]

  [./density]
    type = Density
    block = '1 2 3 4 5 6 7'
    density = 2405.28
  [../]
[]      # Materials END

[Executioner]    # Executioner Start
   type = Transient

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'


   petsc_options = '-snes_ksp_ew '
   petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type'
   petsc_options_value = '70 hypre boomeramg'
   l_max_its = 60
   nl_rel_tol = 1e-8
   nl_abs_tol = 1e-10
   l_tol = 1e-5

   start_time = 0.0
   dt = 1
   num_steps = 1
[]      # Executioner END

[Outputs]    # Output Start
  # Output Start
  exodus = true
[]      # Output END
#      # Input file END

(modules/combined/test/tests/gap_heat_transfer_convex/gap_heat_transfer_convex.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  temperature = temp
[]

[Mesh]
  file = gap_heat_transfer_convex.e
[]

[Functions]
  [./disp]
    type = PiecewiseLinear
    x = '0 2.0'
    y = '0 1.0'
  [../]
  [./temp]
    type = PiecewiseLinear
    x = '0     1'
    y = '200 200'
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]

  [./temp]
    initial_condition = 100
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 2
    secondary = 3
    emissivity_primary = 0
    emissivity_secondary = 0
  [../]
[]

[Physics/SolidMechanics/QuasiStatic/All]
  volumetric_locking_correction = true
  strain = FINITE
  eigenstrain_names = eigenstrain
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./move_right]
    type = FunctionDirichletBC
    boundary = '3'
    variable = disp_x
    function = disp
  [../]

  [./fixed_x]
    type = DirichletBC
    boundary = '1'
    variable = disp_x
    value = 0
  [../]
  [./fixed_y]
    type = DirichletBC
    boundary = '1 2 3 4'
    variable = disp_y
    value = 0
  [../]
  [./fixed_z]
    type = DirichletBC
    boundary = '1 2 3 4'
    variable = disp_z
    value = 0
  [../]

  [./temp_bottom]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  [../]
  [./temp_top]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2'
    youngs_modulus = 1e6
    poissons_ratio = 0.3
  [../]
  [./thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    stress_free_temperature = 100
    thermal_expansion_coeff = 0
    eigenstrain_name = eigenstrain
  [../]
  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]

  [./heat1]
    type = HeatConductionMaterial
    block = 1

    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]
  [./heat2]
    type = HeatConductionMaterial
    block = 2

    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./density]
    type = Density
    block = '1 2'
    density = 1.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  start_time = 0.0
  dt = 0.1
  end_time = 2.0
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/perfect_split.i)

[Mesh]
  [fmg]
    type = FileMeshGenerator
    file = 'perfect.cpa.gz'
  []
  parallel_type = distributed
[]

[Variables]
  [temp]
  []
[]

[Kernels]
  [hc]
    type = HeatConduction
    variable = temp
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = temp
    boundary = leftleft
    value = 300
  []
  [right]
    type = DirichletBC
    variable = temp
    boundary = rightright
    value = 400
  []
[]

[ThermalContact]
  [left_to_right]
    secondary = leftright
    quadrature = true
    primary = rightleft
    emissivity_primary = 0
    emissivity_secondary = 0
    variable = temp
    type = GapHeatTransfer
  []
[]

[Materials]
  [hcm]
    type = HeatConductionMaterial
    block = 'left right'
    specific_heat = 1
    thermal_conductivity = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
[]

[Outputs]
  exodus = true
[]

(tutorials/shield_multiphysics/inputs/step11_multiapps/step11_local.i)

[Mesh]
  # We make a 3D sphere, but really this could be done in 1D
  [sphere]
    type = SphereMeshGenerator
    radius = 10
    nr = 3
    n_smooth = 10
  []
  # Dimensions of each layer are not realistic
  [HDPE_inner]
    type = ParsedSubdomainMeshGenerator
    input = 'sphere'
    combinatorial_geometry = 'x*x + y*y + z*z < 2*2'
    block_id = 1
  []
  [boron_inner]
    type = ParsedSubdomainMeshGenerator
    input = 'HDPE_inner'
    combinatorial_geometry = '(x*x + y*y + z*z > 2*2) & (x*x + y*y + z*z < 3*3)'
    block_id = 2
  []
  [HDPE_mid]
    type = ParsedSubdomainMeshGenerator
    input = 'boron_inner'
    combinatorial_geometry = '(x*x + y*y + z*z > 3*3) & (x*x + y*y + z*z < 6*6)'
    block_id = 3
  []
  [boron_mid]
    type = ParsedSubdomainMeshGenerator
    input = 'HDPE_mid'
    combinatorial_geometry = '(x*x + y*y + z*z > 6*6) & (x*x + y*y + z*z < 7*7)'
    block_id = 4
  []
  [HDPE_outer]
    type = ParsedSubdomainMeshGenerator
    input = 'boron_mid'
    combinatorial_geometry = 'x*x + y*y + z*z > 7*7'
    block_id = 5
  []
  [rename]
    type = RenameBlockGenerator
    input = 'HDPE_outer'
    old_block = '1 2 3 4 5'
    new_block = 'HDPE_inner boron_inner HDPE_mid boron_mid HDPE_outer'
  []
  [rename_boundary]
    type = RenameBoundaryGenerator
    input = 'rename'
    old_boundary = '0'
    new_boundary = 'outer'
  []

  # length_unit = 0.01
  [scale]
    type = TransformGenerator
    input = rename_boundary
    transform = SCALE
    vector_value = '0.01 0.01 0.01'
  []
[]

[Variables]
  [T]
    initial_condition = 300
  []
[]

# Solve heat equation, with a source from boron absorption
[Kernels]
  [conduction]
    type = HeatConduction
    variable = T
  []
  [source]
    type = CoupledForce
    variable = T
    block = 'boron_inner boron_mid'
    v = flux
    # 2 is our arbitrary value for the group cross section
    coef = 2
  []
[]

[BCs]
  [outer]
    type = PostprocessorDirichletBC
    boundary = 'outer'
    variable = 'T'
    postprocessor = 'T_boundary'
  []
[]

[AuxVariables]
  # Received from the main solve
  [flux]
    initial_condition = 1e5
  []
[]

[Materials]
  [hdpe]
    type = HeatConductionMaterial
    block = 'HDPE_inner HDPE_mid HDPE_outer'
    # arbitrary
    thermal_conductivity = 10
  []
  [boron]
    type = HeatConductionMaterial
    block = 'boron_inner boron_mid'
    # arbitrary
    thermal_conductivity = 7
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Postprocessors]
  # Used for boundary condition, received from the main solve
  [T_boundary]
    type = Receiver
    default = 320
  []

  # Compute those then send to the main app
  [T_hdpe_out]
    type = ElementAverageValue
    variable = 'T'
    block = 'HDPE_outer'
  []
  [T_boron_mid]
    type = ElementAverageValue
    variable = 'T'
    block = 'boron_mid'
  []
  [T_hdpe_mid]
    type = ElementAverageValue
    variable = 'T'
    block = 'HDPE_mid'
  []
  [T_boron_inner]
    type = ElementAverageValue
    variable = 'T'
    block = 'boron_inner'
  []
  [T_hdpe_inner]
    type = ElementAverageValue
    variable = 'T'
    block = 'HDPE_inner'
  []
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/gap_heat_transfer_3D_mortar.i)

outer_htc = 10 # W/m^2/K
outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Problem]
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 3
    ny = 6
    nz = 6
    xmin = -1
    xmax = -0.5
    ymin = -0.5
    ymax = 0.5
    zmin = -0.5
    zmax = 0.5
    elem_type = HEX27
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3 4 5'
    new_boundary = 'left_bottom left_back left_right left_front left_left left_top'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []

  [right_block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 4
    ny = 8
    nz = 8
    xmin = 0.5
    xmax = 1
    ymin = -0.5
    ymax = 0.5
    zmin = -0.5
    zmax = 0.5
    elem_type = HEX27
  []
  [right_block_sidesets]
    type = RenameBoundaryGenerator
    input = right_block
    old_boundary = '0 1 2 3 4 5'
    # new_boundary = 'right_bottom right_back right_right right_front right_left right_top'
    new_boundary = '100 101 102 103 104 105'
  []
  [right_block_sidesets_rename]
    type = RenameBoundaryGenerator
    input = right_block_sidesets
    old_boundary = '100 101 102 103 104 105'
    new_boundary = 'right_bottom right_back right_right right_front right_left right_top'
  []
  [right_block_id]
    type = SubdomainIDGenerator
    input = right_block_sidesets_rename
    subdomain_id = 2
  []

  [combined_mesh]
    type = MeshCollectionGenerator
    inputs = 'left_block_id right_block_id'
  []

  [left_lower]
    type = LowerDBlockFromSidesetGenerator
    input = combined_mesh
    sidesets = 'left_right'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
  []
  [right_lower]
    type = LowerDBlockFromSidesetGenerator
    input = left_lower
    sidesets = 'right_left'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
  []
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
  [lm]
    order = SECOND
    family = LAGRANGE
    block = 'secondary_lower'
  []
[]

[AuxVariables]
  [power_density]
    block = 1
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
    block = '1 2'
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = '1'
    v = power_density
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[UserObjects]
  [radiation]
    type = GapFluxModelRadiation
    temperature = temp
    boundary = 'left_right'
    primary_emissivity = 0.0
    secondary_emissivity = 0.0
  []
  [conduction]
    type = GapFluxModelConduction
    temperature = temp
    boundary = 'left_right'
    gap_conductivity = 5.0
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = temp
    primary_boundary = 'right_left'
    primary_subdomain = 'primary_lower'
    secondary_boundary = 'left_right'
    secondary_subdomain = 'secondary_lower'
    gap_flux_models = 'radiation conduction'
    gap_geometry_type = PLATE
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = 'right_right' # outer RPV
    coefficient = ${outer_htc}
    T_infinity = ${outer_Tinf}
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-8
[]

[Outputs]
  exodus = true
  csv = true
  [Console]
    type = Console
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 'left_right'
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 'right_left'
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 'left_right'
    diffusivity = thermal_conductivity
  []
  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 'right_left'
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 1
  []
  [convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = 'right_right' # outer RVP
    T_fluid = ${outer_Tinf}
    htc = ${outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(convective_out - ptot) / ptot'
    pp_names = 'convective_out ptot'
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = 'left_right right_left'
    variable = temp
  []
[]

(modules/heat_transfer/test/tests/radiative_bcs/function_radiative_bc.i)

#
# If we assume that epsilon*sigma*(T_inf^4-T_s^4) is approximately equal to
#   epsilon*sigma*4*T_inf^3*(T_inf-T_s), that form is equivalent to
#   h*(T_inf-T_s), the convective flux bc.  So, the radiative and convective
#   flux bcs should give nearly the same answer if the leading terms are equal.
#
[Mesh]
  [top]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    bias_x = 0.8
    ymin = 1.2
    ymax = 2.2
    boundary_name_prefix = top
  []
  [bottom]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    bias_x = 0.8
    boundary_name_prefix = bot
    boundary_id_offset = 6
  []
  [two_blocks]
    type = MeshCollectionGenerator
    inputs = 'top bottom'
  []
[]

[Variables]
  [temp]
    initial_condition = 600.0
  []
[]

[Kernels]
  [heat_dt]
    type = TimeDerivative
    variable = temp
  []
  [heat_conduction]
    type = HeatConduction
    variable = temp
  []
[]

[BCs]
  [./top_right]
    type = ConvectiveHeatFluxBC
    variable = temp
    boundary = top_right
    T_infinity = 300.0
    heat_transfer_coefficient = 3.0
    heat_transfer_coefficient_dT = 0
  [../]
  [./bot_right]
    type = FunctionRadiativeBC
    variable = temp
    boundary = bot_right
    # htc/(stefan-boltzmann*4*T_inf^3)
    emissivity_function = '3/(5.670367e-8*4*300*300*300)'
    # Using previous default
    Tinfinity = 0
  [../]
[]

[Materials]
  [./thermal]
    type = GenericConstantMaterial
    prop_names = 'density  thermal_conductivity specific_heat'
    prop_values = '1 10 100'
  [../]
[]

[Postprocessors]
  [./top_left_temp]
    type = SideAverageValue
    variable = temp
    boundary = top_left
    execute_on = 'TIMESTEP_END initial'
  [../]
  [./bot_left_temp]
    type = SideAverageValue
    variable = temp
    boundary = bot_left
    execute_on = 'TIMESTEP_END initial'
  [../]
  [./top_right_temp]
    type = SideAverageValue
    variable = temp
    boundary = top_right
  [../]
  [./bot_right_temp]
    type = SideAverageValue
    variable = temp
    boundary = bot_right
  [../]
[]

[Executioner]
  type = Transient

  num_steps = 10
  dt = 1e1

  nl_abs_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/heat_conduction_patch/heat_conduction_patch_rz_quad8.i)

#
# This problem is taken from the Abaqus verification manual:
#   "1.5.8 Patch test for heat transfer elements"
#
# The temperature on the exterior nodes is -2e5+200x+100y.
#
# This gives a constant flux at all Gauss points.
#
# In addition, the temperature at all nodes follows the same formula.
#
# Node x         y          Temperature
#    1 1e3       0          0
#    2 1.00024e3 0          48
#    3 1.00018e3 3e-2       39
#    4 1.00004e3 2e-2       10
#    9 1.00008e3 8e-2       24
#   10 1e3       1.2e-1     12
#   14 1.00016e3 8e-2       40
#   17 1.00024e3 1.2e-1     60

[Mesh]#Comment
  file = heat_conduction_patch_rz_quad8.e
  coord_type = RZ
[] # Mesh

[Functions]
  [./temps]
    type = ParsedFunction
    expression ='-2e5+200*x+100*y'
  [../]
[] # Functions

[Variables]

  [./temp]
    order = SECOND
    family = LAGRANGE
  [../]

[] # Variables

[Kernels]

  [./heat_r]
    type = HeatConduction
    variable = temp
  [../]

[] # Kernels

[BCs]

  [./temps]
    type = FunctionDirichletBC
    variable = temp
    boundary = 10
    function = temps
  [../]

[] # BCs

[Materials]

  [./heat]
    type = HeatConductionMaterial
    block = 1

    specific_heat = 0.116
    thermal_conductivity = 4.85e-4
  [../]

[] # Materials

[Executioner]

  type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -ksp_gmres_restart'
  petsc_options_value = 'lu       101'

  line_search = 'none'

  nl_abs_tol = 1e-11
  nl_rel_tol = 1e-10

  l_max_its = 20

  [./Quadrature]
    order = THIRD
  [../]

[] # Executioner

[Outputs]
  exodus = true
[] # Outputs

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/gap_heat_transfer_htonly_it_plot_test.i)

#
# 1-D Gap Heat Transfer Test without mechanics
#
# This test exercises 1-D gap heat transfer for a constant conductivity gap.
#
# The mesh consists of two element blocks containing one element each.  Each
#   element is a unit cube.  They sit next to one another with a unit between them.
#
# The conductivity of both blocks is set very large to achieve a uniform temperature
#  across each block. The temperature of the far left boundary
#  is ramped from 100 to 200 over one time unit, and then held fixed for an additional
#  time unit.  The temperature of the far right boundary is held fixed at 100.
#
# A simple analytical solution is possible for the heat flux between the blocks:
#
#  Flux = (T_left - T_right) * (gapK/gap_width)
#
# The gap conductivity is specified as 1, thus
#
#  gapK(Tavg) = 1.0*Tavg
#
#
# The heat flux across the gap at time = 2 is then:
#
#  Flux(2) = 100 * (1.0/1.0) = 100
#
# For comparison, see results from the flux post processors
#


[Mesh]
  file = gap_heat_transfer_htonly_test.e
[]

[Functions]

  [./temp]
    type = PiecewiseLinear
    x = '0   1   2'
    y = '100 200 200'
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
  [../]
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]


[BCs]
  [./temp_far_left]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  [../]

  [./temp_far_right]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
[]

[Materials]

  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 100000000.0
  [../]

  [./density]
    type = GenericConstantMaterial
    block = '1 2'
    prop_names = 'density'
    prop_values = '1.0'
  [../]
[]

[Executioner]
  type = Transient

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'




  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'


  line_search = 'none'


  nl_abs_tol = 1e-5
  nl_rel_tol = 1e-12

  l_tol = 1e-10
  l_max_its = 100

  start_time = 0.0
  dt = 1e-1
  end_time = 2.0
[]

[Postprocessors]

  [./temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  [../]

  [./temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  [../]

  [./flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  [../]

  [./flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  [../]
[]


[Outputs]
  file_base = out_it_plot
  [./exodus]
    type = Exodus
    execute_on = 'initial timestep_end nonlinear'
    nonlinear_residual_dt_divisor = 100
  [../]
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_sphere.i)

sphere_outer_htc = 10 # W/m^2/K
sphere_outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = cyl2D.e
  []
  allow_renumbering = false
  coord_type = RZ
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
[]

[AuxVariables]
  [gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  []
  [power_density]
    block = 'fuel'
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = 'fuel'
    v = power_density
  []
[]

[AuxKernels]
  [gap_cond]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_conductance
    boundary = 2
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0.0
    emissivity_secondary = 0.0
    gap_conductivity = 5
  #  quadrature = true
    gap_geometry_type = SPHERE
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = '4' # outer RPV
    coefficient = ${sphere_outer_htc}
    T_infinity = ${sphere_outer_Tinf}
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = '2 3'
    variable = temp
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

  [Quadrature]
    order = fifth
    side_order = seventh
  []
[]

[Outputs]
  exodus = true
  csv = true
  [Console]
    type = Console
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  []

  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 'fuel'
  []
  [sphere_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = '4' # outer RVP
    T_fluid = ${sphere_outer_Tinf}
    htc = ${sphere_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(sphere_convective_out - ptot) / ptot'
    pp_names = 'sphere_convective_out ptot'
  []
[]

(modules/combined/test/tests/heat_convection/heat_convection_3d_test.i)

# Test cases for convective boundary conditions.
# Input file for htc_3dtest1

# TKLarson
# 11/02/11
# Revision 0
#
# Goals of this test are:
#  1) show that the 'fluid' temperature for convective boundary condition
#    is behaving as expected/desired
#  2) show that expected results ensue from application of convective boundary conditions
# Convective boundary condition:
#  q = h*A*(Tw - Tf)
#  where
#    q - heat transfer rate (w)
#    h - heat transfer coefficient (w/m^2-K)
#    A - surface area (m^2)
#    Tw - surface temperature (K)
#    Tf - fluid temperature adjacent to the surface (K)
# The heat transfer coefficient (h) is input as a variable called 'rate'
# Tf is a two valued function specified by 'initial' and 'final' along with a variable
#  called 'duration,' the length of time in seconds that it takes initial to linearly ramp
#  to 'final.'

# The mesh for this test case is concocted from an ASTM standard for the so-called Brazillian Cylinder test
# (ASTM International, Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete
# Specimens, C 496/C 496M-04, 2004).  I turned a cylinder model into a rectangular parallelpiped,
# because I already had the cylinder model.
# The model is 3-d xyz coordinates.
#
# Brazillian Parallelpiped sample dimensions:
#       z = 10.3 cm, 0.103 m, (4 in)
#       y = 5.08 cm, 0.0508 m, (2 in)
#       x = 5.08 cm, 0.0508 m, (2 in)

# Material properties are:
#   density = 2405.28 km/m^3
#   specific heat = 826.4 J/kg-K
#   thermal conductivity 1.937 w/m-K
#  alpha (thermal conductivity/(density*specific heat) is then 9.74e-7 m^2/s
#
# Initial parallelpiped temperature is room temperature 294.26 K (70 F)
# The initial fluid temperature is room temperature. We will ramp it to 477.6 K (400 F) in 10 minutes.
# We will use an h representative of natural convection conditions as the boundary condition for all sides
# on the parallelpiped.  Akin to putting the object in an oven and turning the oven on.
#  This is essentially a thermal soak.
#
# What we expect for this problem:
#  1) Use of h = 284 w/m^2-K (50 BTU/hr-ft^2-F) should cause the parallelpiped to slowly heat up to 477K.
#  2) The fluid temperature should rise from initial (294.26 K) to final (477.6 K) in 600 s.
#  3) 1) and 2) should show the convective BC is working as desired.
#
[Mesh]    # Mesh Start
# 5cm x 5cm x 10cm parallelpiped not so detailed mesh, 4 elements each end, 8 elements each long face
# Only one block (Block 1), all concrete
# Sideset definitions:
#    1 - xy plane at z=0,
#    2 - xy plane at z=-0.103,
#    3 - xz plane at y=0,
#    4 - yz plane at x=0,
#    5 - xz plane at y=0.0508,
#    6 - yz plane at x=0.0508
  file = heat_convection_3d_mesh.e
#
[]    # Mesh END

[Variables]  # Variables Start
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 294.26 # Initial parallelpiped temperature
  [../]

[]    # Variables END


[Kernels]  # Kernels Start
  [./heat]
#    type = HeatConductionRZ
     type = HeatConduction
     variable = temp
  [../]

  [./heat_ie]
#  type = HeatConductionTimeDerivativeRZ
  type = HeatConductionTimeDerivative
  variable = temp
  [../]

[]    # Kernels END


[BCs]    # Boundary Conditions Start
# Heat transfer coefficient on outer parallelpiped radius and ends
  [./convective_clad_surface]    # Convective Start
#         type = ConvectiveFluxRZ  # Convective flux, e.g. q'' = h*(Tw - Tf)
         type = ConvectiveFluxBC  # Convective flux, e.g. q'' = h*(Tw - Tf)
         boundary = '1 2 3 4 5 6'  # BC applied on top, along length, and bottom
         variable = temp
   rate = 284.      # convective heat transfer coefficient (w/m^2-K)[50 BTU/hr-ft^2-F]
         initial = 294.26    # initial ambient (lab or oven) temperature (K)
         final = 477.6      # final ambient (lab or oven) temperature (K)
   duration = 600.    # length of time in seconds that it takes the ambient
           #     temperature to ramp from initial to final
  [../]          # Convective End

[]    # BCs END

[Materials]    # Materials Start
  [./thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 826.4
    #thermal_conductivity = 1.937  # this makes alpha 9.74e-7 m^2/s
    thermal_conductivity = 193.7  # this makes alpha 9.74e-5 m^2/s
          # above conductivity arbitrarily increased by 2 decades to make the
          #   object soak faster for the present purposes

  [../]

  [./density]
    type = Density
    block = 1
    density = 2405.28
  [../]
[]      # Materials END

[Executioner]    # Executioner Start
   type = Transient
#   type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'


   petsc_options = '-snes_ksp_ew '
   petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type'
   petsc_options_value = '70 hypre boomeramg'
   l_max_its = 60
   nl_rel_tol = 1e-8
   nl_abs_tol = 1e-10
   l_tol = 1e-5

   start_time = 0.0
  dt = 60.
  num_steps = 20  # Total run time 1200 s

[]      # Executioner END

[Outputs]    # Output Start
  # Output Start
  file_base = out_3d
  exodus = true
[]      # Output END
#      # Input file END

(modules/combined/test/tests/heat_convection/heat_convection_3d_tf_test.i)

# Test cases for convective boundary conditions.
# Input file for htc_3dtest0

# TKLarson
# 11/02/11
# Revision 0
#
# Goals of this test are:
#  1) show that the 'fluid' temperature for convective boundary condition
#    is behaving as expected/desired
#  2) show that expected results ensue from application of convective boundary conditions
# Convective boundary condition:
#  q = h*A*(Tw - Tf)
#  where
#    q - heat transfer rate (w)
#    h - heat transfer coefficient (w/m^2-K)
#    A - surface area (m^2)
#    Tw - surface temperature (K)
#    Tf - fluid temperature adjacent to the surface (K)
# The heat transfer coefficient (h) is input as a variable called 'rate'
# Tf is a two valued function specified by 'initial' and 'final' along with a variable
#  called 'duration,' the length of time in seconds that it takes initial to linearly ramp
#  to 'final.'

# The mesh for this test case is concocted from an ASTM standard for the so-called Brazillian Cylinder test
# (ASTM International, Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete
# Specimens, C 496/C 496M-04, 2004).  I turned a cylinder model into a rectangular parallelpiped,
# because I already had the cylinder model.
# The model is 3-d xyz coordinates.
#
# Brazillian Parallelpiped sample dimensions:
#       z = 10.3 cm, 0.103 m, (4 in)
#       y = 5.08 cm, 0.0508 m, (2 in)
#       x = 5.08 cm, 0.0508 m, (2 in)

# Material properties are:
#   density = 2405.28 km/m^3
#   specific heat = 826.4 J/kg-K
#   thermal conductivity 1.937 w/m-K
#  alpha (thermal conductivity/(density*specific heat) is then 9.74e-7 m^2/s
#
# Initial parallelpiped temperature is room temperature 294.26 K (70 F)
# The initial fluid temperature is room temperature. We will ramp it to 477.6 K (400 F) in 10 minutes.
# We will use a very large h (1000000) to make the surface temperature mimick the fluid temperature.

# What we expect for this problem:
#  1) Use of h = 1000000 should cause the parallelpiped surface temperature to track the fluid temperature
#  2) The fluid temperature should rise from initial (294.26 K) to final (477.6 K) in 600 s.
#  3) 1) and 2) should prove that the Tf boundary condition is ramping as desired.
# Note, we do the above because there is no way to plot a variable that is not on a mesh node!

[Mesh]    # Mesh Start
# 5cm x 5cm x 10cm parallelpiped not so detailed mesh, 4 elements each end, 8 elements each long face
# Only one block (Block 1), all concrete
# Sideset definitions:
#    1 - xy plane at z=0,
#    2 - xy plane at z=-0.103,
#    3 - xz plane at y=0,
#    4 - yz plane at x=0,
#    5 - xz plane at y=0.0508,
#    6 - yz plane at x=0.0508
  file = heat_convection_3d_mesh.e
#
[]    # Mesh END

[Variables]  # Variables Start
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 294.26 # Initial parallelpiped temperature
  [../]

[]    # Variables END


[Kernels]  # Kernels Start
  [./heat]
#    type = HeatConductionRZ
     type = HeatConduction
     variable = temp
  [../]

  [./heat_ie]
#  type = HeatConductionTimeDerivativeRZ
  type = HeatConductionTimeDerivative
  variable = temp
  [../]

[]    # Kernels END


[BCs]    # Boundary Conditions Start
# Heat transfer coefficient on outer parallelpiped radius and ends
  [./convective_clad_surface]    # Convective Start
#         type = ConvectiveFluxRZ  # Convective flux, e.g. q'' = h*(Tw - Tf)
         type = ConvectiveFluxBC  # Convective flux, e.g. q'' = h*(Tw - Tf)
         boundary = '1 2 3 4 5 6'  # BC applied on top, along length, and bottom
         variable = temp
   rate = 1000000.   # convective heat transfer coefficient (w/m^2-K)[176000 "]
#         #  the above h is ~ infinity for present purposes
         initial = 294.26         # initial ambient (lab or oven) temperature (K)
         final = 477.6            # final ambient (lab or oven) temperature (K)
   duration = 600.   # length of time in seconds that it takes the ambient
         #     temperature to ramp from initial to final
  [../]          # Convective End

[]    # BCs END

[Materials]    # Materials Start
  [./thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 826.4
    thermal_conductivity = 1.937  # this makes alpha 9.74e-7 m^2/s
  [../]
  [./density]
    type = Density
    block = 1
    density = 2405.28
  [../]
[]      # Materials END

[Executioner]    # Executioner Start
   type = Transient
#   type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'


   petsc_options = '-snes_ksp_ew '
   petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type'
   petsc_options_value = '70 hypre boomeramg'
   l_max_its = 60
   nl_rel_tol = 1e-8
   nl_abs_tol = 1e-10
   l_tol = 1e-5

   start_time = 0.0
  dt = 60.
  num_steps = 20  # Total run time 1200 s

[]      # Executioner END

[Outputs]    # Output Start
  # Output Start
  file_base = out_3d_tf
  exodus = true
[]      # Output END
#      # Input file END

(modules/combined/test/tests/elastic_thermal_patch/elastic_thermal_jacobian_rz_smp.i)

# This problem is intended to exercise the Jacobian for coupled RZ
# problems.  Only two iterations should be needed.

[GlobalParams]
  temperature = temp
  volumetric_locking_correction = true
[]

[Mesh]
  file = elastic_thermal_patch_rz_test.e
  coord_type = RZ
[]

[Functions]
  [./ur]
    type = ParsedFunction
    expression = '0'
  [../]
  [./uz]
    type = ParsedFunction
    expression = '0'
  [../]
  [./body]
    type = ParsedFunction
    expression = '-400/x'
  [../]
  [./temp]
    type = ParsedFunction
    expression = '117.56+100*t'
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]

  [./temp]
    initial_condition = 117.56
  [../]
[]

[Physics]
    [SolidMechanics]
        [QuasiStatic]
            displacements = 'disp_x disp_y'
            [All]
                displacements = 'disp_x disp_y'
                add_variables = true
                strain = SMALL
                incremental = true
                eigenstrain_names = eigenstrain
                generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_yz stress_zx'
            [../]
        [../]
    [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./ur]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 1
    function = ur
  [../]
  [./uz]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 2
    function = uz
  [../]

  [./temp]
    type = FunctionDirichletBC
    variable = temp
    boundary = 10
    function = temp
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e6
    poissons_ratio = 0.25
  [../]
  [./thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    stress_free_temperature = 117.56
    thermal_expansion_coeff = 1e-6
    eigenstrain_name = eigenstrain
  [../]
  [./stress]
    type = ComputeStrainIncrementBasedStress
  [../]

  [./heat]
    type = HeatConductionMaterial
    specific_heat = 0.116
    thermal_conductivity = 4.85e-4
  [../]

  [./density]
    type = Density
    density = 0.283
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  nl_abs_tol = 1e-9
  nl_rel_tol = 1e-12

  l_max_its = 20

  start_time = 0.0
  dt = 1.0
  num_steps = 1
  end_time = 1.0
[]

[Outputs]
  file_base = elastic_thermal_jacobian_rz_smp_out
  [./exodus]
    type = Exodus
    execute_on = 'initial timestep_end nonlinear'
    nonlinear_residual_dt_divisor = 100
  [../]
[]

(modules/heat_transfer/test/tests/truss_heat_conduction/line.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 10
    xmax = 0.5
    xmin = -0.5
  []
  [left_line]
    type = SubdomainBoundingBoxGenerator
    input = gmg
    bottom_left = '-0.5 0 0'
    top_right = '0 0 0'
    block_id = 1
    block_name = 'left_line'
    location = INSIDE
  []
  [right_line]
    type = SubdomainBoundingBoxGenerator
    input = left_line
    bottom_left = '0 0 0'
    top_right = '0.5 0 0'
    block_id = 2
    block_name = 'right_line'
    location = INSIDE
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time_derivative]
    # type = HeatConductionTimeDerivative
    type = TrussHeatConductionTimeDerivative
    variable = temperature
    area = area
  []
  [heat_conduction]
    # type = HeatConduction
    type = TrussHeatConduction
    variable = temperature
    area = area
  []
[]

[AuxVariables]
  [area]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [area]
    type = ConstantAux
    variable = area
    value = 0.1
    execute_on = 'initial timestep_begin'
  []
[]

[Materials]
  [left_line]
    type = GenericConstantMaterial
    block = 'left_line'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '0.1                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
  [right_line]
    type = GenericConstantMaterial
    block = 'right_line'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '5.0e-3                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
[]

[BCs]
  [right]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'right'
    function = '10*t'
  []
[]

[VectorPostprocessors]
  [center]
    type = LineValueSampler
    start_point = '-0.5 0 0'
    end_point = '0.5 0 0'
    num_points = 40
    variable = 'temperature'
    sort_by = id
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1
  end_time = 1
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'csv/line'
    time_data = true
  []
[]

(modules/heat_transfer/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/perfectQ8.i)

[GlobalParams]
  order = SECOND
[]

[Mesh]
  file = perfectQ8.e
[]

[Variables]
  [./temp]
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temp
    boundary = leftleft
    value = 300
  [../]
  [./right]
    type = DirichletBC
    variable = temp
    boundary = rightright
    value = 400
  [../]
[]

[ThermalContact]
  [./left_to_right]
    secondary = leftright
    quadrature = true
    primary = rightleft
    emissivity_primary = 0
    emissivity_secondary = 0
    variable = temp
    type = GapHeatTransfer
  [../]
[]

[Materials]
  [./hcm]
    type = HeatConductionMaterial
    block = 'left right'
    specific_heat = 1
    thermal_conductivity = 1
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'

  [./Quadrature]
    order = THIRD
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_sphere_mortar.i)

sphere_outer_htc = 10 # W/m^2/K
sphere_outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Problem]
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = cyl2D.e
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '2'
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    input = file
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '3'
    new_block_id = 10000
    new_block_name = 'primary_lower'
    input = secondary
  []
  allow_renumbering = false
  coord_type = RZ
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
  [lm]
    order = SECOND
    family = LAGRANGE
    block = 'secondary_lower'
  []
[]

[AuxVariables]
  [power_density]
    block = 'fuel'
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
    block = '1 2'
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = 'fuel'
    v = power_density
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[UserObjects]
  [radiation]
    type = GapFluxModelRadiation
    temperature = temp
    boundary = 2
    primary_emissivity = 0.0
    secondary_emissivity = 0.0
  []
  [conduction]
    type = GapFluxModelConduction
    temperature = temp
    boundary = 2
    gap_conductivity = 5.0
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = temp
    primary_boundary = 3
    primary_subdomain = 10000
    secondary_boundary = 2
    secondary_subdomain = 10001
    gap_flux_models = 'radiation conduction'
    gap_geometry_type = SPHERE
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = '4' # outer RPV
    coefficient = ${sphere_outer_htc}
    T_infinity = ${sphere_outer_Tinf}
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

[]

[Outputs]
  exodus = true
  csv = true
  [Console]
    type = Console
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = '2 3'
    variable = temp
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  []

  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 'fuel'
  []
  [sphere_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = '4' # outer RVP
    T_fluid = ${sphere_outer_Tinf}
    htc = ${sphere_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(sphere_convective_out - ptot) / ptot'
    pp_names = 'sphere_convective_out ptot'
  []
[]

(modules/heat_transfer/test/tests/truss_heat_conduction/block_w_line.i)

[Mesh]
  parallel_type = 'replicated'
  [block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 3
    ny = 50
    nz = 1
    xmin = -0.5
    xmax = 0.5
    ymin = -1.25
    ymax = 1.25
    zmin = -0.04
    zmax = 0.04
    boundary_name_prefix = block
  []
  [block_id]
    type = SubdomainIDGenerator
    input = block
    subdomain_id = 1
  []
  [line]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = -0.5
    xmax = 0.5
    nx = 10
    boundary_name_prefix = line
    boundary_id_offset = 10
  []
  [line_id]
    type = SubdomainIDGenerator
    input = line
    subdomain_id = 2
  []
  [combined]
    type = MeshCollectionGenerator
    inputs = 'block_id line_id'
  []
  [line_rename]
    type = RenameBlockGenerator
    input = combined
    old_block = '1 2'
    new_block = 'block line'
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = temperature
    block = 'block'
  []
  [heat_conduction]
    type = HeatConduction
    variable = temperature
    block = 'block'
  []
  [time_derivative_line]
    type = TrussHeatConductionTimeDerivative
    variable = temperature
    area = area
    block = 'line'
  []
  [heat_conduction_line]
    type = TrussHeatConduction
    variable = temperature
    area = area
    block = 'line'
  []
[]

[AuxVariables]
  [area]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [area]
    type = ConstantAux
    variable = area
    value = 0.008
    execute_on = 'initial timestep_begin'
  []
[]

[Constraints]
  [equalvalue]
    type = EqualValueEmbeddedConstraint
    secondary = 'line'
    primary = 'block'
    penalty = 1e6
    formulation = kinematic
    primary_variable = temperature
    variable = temperature
  []
[]

[Materials]
  [block]
    type = GenericConstantMaterial
    block = 'block'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
  [line]
    type = GenericConstantMaterial
    block = 'line'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '10.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
[]

[BCs]
  [right]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'block_right line_right'
    function = '10*t'
  []
[]

[VectorPostprocessors]
  [x_n0_25]
    type = LineValueSampler
    start_point = '-0.25 0 0'
    end_point = '-0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
  [x_0_25]
    type = LineValueSampler
    start_point = '0.25 0 0'
    end_point = '0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1
  end_time = 1
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'csv/block_w_line'
    time_data = true
  []
[]

(modules/heat_transfer/test/tests/truss_heat_conduction/strip.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 1
    xmax = 0.5
    xmin = -0.5
    ymin = -0.05
    ymax = 0.05
  []
  [left_line]
    type = SubdomainBoundingBoxGenerator
    input = gmg
    bottom_left = '-0.5 0 0'
    top_right = '0 0 0'
    block_id = 1
    block_name = 'left_strip'
    location = INSIDE
  []
  [right_line]
    type = SubdomainBoundingBoxGenerator
    input = left_line
    bottom_left = '0 0 0'
    top_right = '0.5 0 0'
    block_id = 2
    block_name = 'right_strip'
    location = INSIDE
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat_conduction]
    type = HeatConduction
    variable = temperature
  []
[]

[Materials]
  [left_strip]
    type = GenericConstantMaterial
    block = 'left_strip'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '0.1                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
  [right_strip]
    type = GenericConstantMaterial
    block = 'right_strip'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '5.0e-3                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
[]

[BCs]
  [right]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'right'
    function = '10*t'
  []
[]

[VectorPostprocessors]
  [center]
    type = LineValueSampler
    start_point = '-0.5 0 0'
    end_point = '0.5 0 0'
    num_points = 40
    variable = 'temperature'
    sort_by = id
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1
  end_time = 1
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'csv/strip'
    time_data = true
  []
[]

(modules/heat_transfer/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/second_order.i)

[Mesh]
  file = nonmatching.e
  second_order = true
[]

[Variables]
  [./temp]
    order = SECOND
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temp
    boundary = leftleft
    value = 1000
  [../]
  [./right]
    type = DirichletBC
    variable = temp
    boundary = rightright
    value = 400
  [../]
[]

[ThermalContact]
  [./left_to_right]
    emissivity_primary = 0
    emissivity_secondary = 0
    secondary = leftright
    quadrature = true
    primary = rightleft
    variable = temp
    type = GapHeatTransfer
    order = SECOND
  [../]
[]

[Materials]
  [./hcm]
    type = HeatConductionMaterial
    block = 'left right'
    specific_heat = 1
    thermal_conductivity = 1
  [../]
[]

[Postprocessors]
  [./left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = leftright
    diffusivity = thermal_conductivity
  [../]
  [./right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = rightleft
    diffusivity = thermal_conductivity
  [../]
[]

[Executioner]
  type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(modules/functional_expansion_tools/examples/2D_volumetric_Cartesian/main.i)

# Basic example coupling a master and sub app in a 2D Cartesian volume.
#
# The master app provides field values to the sub app via Functional Expansions, which then performs
# its calculations. The sub app's solution field values are then transferred back to the master app
# and coupled into the solution of the master app solution.
#
# This example couples Functional Expansions via AuxVariable.
[Mesh]
  type = GeneratedMesh
  dim = 2

  xmin = 0.0
  xmax = 10.0
  nx = 15

  ymin = 1.0
  ymax = 11.0
  ny = 25
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./s_in] # Add in the contribution from the SubApp
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'top bottom left right'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3   4'
    physical_bounds = '0.0  10.0    1.0 11.0'
    x = Legendre
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(modules/subchannel/test/tests/auxkernels/q_prime/test.i)

pin_diameter = 0.4
heated_length = 1.0

[Mesh]
  second_order = true
  [bisonMesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 0.2 # pin diameter / 2.0
    bias_x = 1.0
    nx = 5
    ymax = 1.0 # heated length
    ny = 10 # number of axial cells
  []
  coord_type = RZ
  rz_coord_axis = Y
[]

[Variables]
  [temperature]
    order = SECOND
    family = LAGRANGE
  []
[]

[AuxVariables]
  [q_prime]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [QPrime]
    type = SCMRZPinQPrimeAux
    diffusivity = 'thermal_conductivity'
    variable = q_prime
    diffusion_variable = temperature
    component = normal
    boundary = 'right'
    execute_on = 'timestep_end'
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temperature
  []
  [heat_source]
    type = HeatSource
    variable = temperature
    value = '${fparse 4.0 * 1000 / (pi * pin_diameter * pin_diameter * heated_length)}'
  []
[]

[Materials]
  [heat_conductor]
    type = HeatConductionMaterial
    thermal_conductivity = 1.0
    block = 0
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = temperature
    boundary = 'left'
  []
  [right]
    type = DirichletBC
    variable = temperature
    boundary = 'right'
    value = 200.0
  []
[]

[UserObjects]
  [q_prime_uo]
    type = LayeredSideAverage
    boundary = right
    variable = q_prime
    num_layers = 10
    direction = y
    execute_on = 'TIMESTEP_END'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
[]

[Outputs]
  exodus = true
[]

(modules/functional_expansion_tools/examples/3D_volumetric_cylindrical/main.i)

# Basic example coupling a master and sub app in a 3D cylindrical mesh from an input file
#
# The master app provides field values to the sub app via Functional Expansions, which then performs
# its calculations. The sub app's solution field values are then transferred back to the master app
# and coupled into the solution of the master app solution.
#
# This example couples Functional Expansions via AuxVariable, the recommended approach.
#
# Note: this problem is not light, and may take a few minutes to solve.
[Mesh]
  type = FileMesh
  file = cyl-tet.e
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./s_in] # Add in the contribution from the SubApp
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'top bottom outside'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = CylindricalDuo
    orders = '5   3' # Axial first, then (r, t) FX
    physical_bounds = '-2.5 2.5   0 0 1' # z_min z_max   x_center y_center radius
    z = Legendre # Axial in z
    disc = Zernike # (r, t) default to unit disc in x-y plane
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(modules/functional_expansion_tools/examples/2D_interface_different_submesh/main.i)

# Derived from the example '2D_interface' with the following differences:
#
#   1) The number of y divisions in the sub app is not the same as the master app
#   2) The subapp mesh is skewed in y
#   3) The Functional Expansion order for the flux term was increased to 7
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.0
  xmax = 0.4
  nx = 6
  ymin = 0.0
  ymax = 10.0
  ny = 20
[]

[Variables]
  [./m]
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./source_m]
    type = BodyForce
    variable = m
    value = 100
  [../]
[]

[Materials]
  [./Impervium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '0.00001              50.0          100.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    value = 2
    variable = m
  [../]
[]

[BCs]
  [./interface_value]
    type = FXValueBC
    variable = m
    boundary = right
    function = FX_Basis_Value_Main
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = right
    variable = m
    function = FX_Basis_Flux_Main
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '7'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Flux_UserObject_Main]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Main
    variable = m
    boundary = right
    diffusivity = thermal_conductivity
  [../]
[]

[Postprocessors]
  [./average_interface_value]
    type = SideAverageValue
    variable = m
    boundary = right
  [../]
  [./total_flux]
    type = SideDiffusiveFluxIntegral
    variable = m
    boundary = right
    diffusivity = thermal_conductivity
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
    sub_cycling = true
  [../]
[]

[Transfers]
  [./FluxToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Flux_UserObject_Main
    multi_app_object_name = FX_Basis_Flux_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
  [./FluxToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Flux_Main
    multi_app_object_name = FX_Flux_UserObject_Sub
  [../]
[]

(modules/heat_transfer/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/moving.i)

[Mesh]
  file = nonmatching.e
  displacements = 'disp_x disp_y'
[]

[Variables]
  [temp]
  []
[]

[AuxVariables]
  [disp_x]
  []
  [disp_y]
  []
[]

[Functions]
  [disp_y]
    type = ParsedFunction
    expression = 0.1*t
  []
  [left_temp]
    type = ParsedFunction
    expression = 1000+t
  []
[]

[Kernels]
  [hc]
    type = HeatConduction
    variable = temp
  []
[]

[AuxKernels]
  [disp_y]
    type = FunctionAux
    variable = disp_y
    function = disp_y
    block = left
    execute_on = 'INITIAL TIMESTEP_BEGIN'
  []
[]

[BCs]
  [left]
    type = FunctionDirichletBC
    variable = temp
    boundary = leftleft
    function = left_temp
  []
  [right]
    type = DirichletBC
    variable = temp
    boundary = rightright
    value = 400
  []
[]

[ThermalContact]
  [left_to_right]
    secondary = leftright
    quadrature = true
    primary = rightleft
    emissivity_primary = 0
    emissivity_secondary = 0
    variable = temp
    type = GapHeatTransfer
  []
[]

[Materials]
  [hcm]
    type = HeatConductionMaterial
    block = 'left right'
    specific_heat = 1
    thermal_conductivity = 1
    use_displaced_mesh = true
  []
[]

[Postprocessors]
  [left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = leftright
    diffusivity = thermal_conductivity
  []
  [right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = rightleft
    diffusivity = thermal_conductivity
  []
[]

[Executioner]
  type = Transient
  num_steps = 9
  dt = 1

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(modules/subchannel/examples/coupling/thermo_mech/quad/one_pin_problem_sub.i)

pin_diameter = 0.00950
heated_length = 1.0
T_in = 359.15
[GlobalParams]
    displacements = 'disp_x disp_y'
[]

[Mesh]
    second_order = true
    [PinMesh]
        type = GeneratedMeshGenerator
        dim = 2
        xmax = '${fparse pin_diameter / 2.0}'
        bias_x = 1.0
        nx = 20
        ymax = ${heated_length}
        ny = 100 # number of axial cells
    []
    coord_type = RZ
    rz_coord_axis = Y
    beta_rotation = 90
[]

[Functions]
    [volumetric_heat_rate] # Defined such as to be consistent with the IC in SCM
        type = ParsedFunction
        expression = '(4.0 * 100000.0 / (pi * D * D * L)) * (pi/2)*sin(pi*y/L)'
        symbol_names = 'L D'
        symbol_values = '${heated_length} ${pin_diameter}'
    []
[]

[Variables]
    [temperature]
        order = SECOND
        family = LAGRANGE
    []
[]

[AuxVariables]
    [Pin_surface_temperature]
    []
    [pin_diameter_deformed]
        # order = CONSTANT
        # family = MONOMIAL
    []
    [q_prime]
        order = CONSTANT
        family = MONOMIAL
    []
[]

[Physics]
    [SolidMechanics]
        [QuasiStatic]
            add_variables = true
            strain = SMALL
            incremental = true
            generate_output = 'stress_xx stress_yy stress_xy'
            temperature = temperature

            [block0]
                eigenstrain_names = eigenstrain
                block = 0
            []
        []
    []
[]

[AuxKernels]
    [QPrime]
        type = SCMRZPinQPrimeAux # This kernel calculates linear heat rate for the 2D-RZ pin model
        diffusivity = 'thermal_conductivity'
        variable = q_prime
        diffusion_variable = temperature
        component = normal
        boundary = 'right'
        execute_on = 'TIMESTEP_END'
        use_displaced_mesh = true
    []
    [Deformation]
        type = ParsedAux
        variable = pin_diameter_deformed
        coupled_variables = 'disp_x'
        expression = '2.0 * disp_x + ${pin_diameter}'
        execute_on = 'timestep_end'
    []
[]

[Kernels]
    [heat_conduction]
        type = HeatConduction
        variable = temperature
        use_displaced_mesh = true
    []
    [heat_source]
        type = HeatSource
        variable = temperature
        function = volumetric_heat_rate
        use_displaced_mesh = false
    []
[]

[Materials]
    [elasticity_tensor]
        type = ComputeIsotropicElasticityTensor
        block = 0
        bulk_modulus = 0.333333333333e6
        poissons_ratio = 0.0
    []
    [thermal_strain]
        type = ComputeThermalExpansionEigenstrain
        block = 0
        temperature = temperature
        stress_free_temperature = 117.56
        thermal_expansion_coeff = 1e-5
        eigenstrain_name = eigenstrain
    []
    [stress]
        type = ComputeStrainIncrementBasedStress
        block = 0
    []
    [heat_conductor]
        type = HeatConductionMaterial
        thermal_conductivity = 1.0
        block = 0
    []
    [density]
        type = Density
        block = 0
        density = 1.0
    []
[]

[BCs]
    [left]
        type = NeumannBC
        variable = temperature
        boundary = 'left'
    []
    [right]
        type = MatchedValueBC
        variable = temperature
        boundary = 'right'
        v = Pin_surface_temperature
    []
    [no_x]
        type = DirichletBC
        variable = disp_x
        boundary = 'left'
        value = 0.0
    []
    [no_y]
        type = DirichletBC
        variable = disp_y
        boundary = 'bottom top'
        value = 0.0
    []
[]

[ICs]
    [temperature_ic]
        type = ConstantIC
        variable = temperature
        value = ${T_in}
    []
    [q_prime_ic]
        type = ConstantIC
        variable = q_prime
        value = 0.0
    []
    [RD_IC]
        type = ConstantIC
        variable = pin_diameter_deformed
        value = ${pin_diameter}
    []
[]

[Preconditioning]
    [smp]
        type = SMP
        full = true
    []
[]

[Executioner]
    type = Transient
    solve_type = 'PJFNK'
    nl_abs_tol = 1e-7
    l_max_its = 20
    start_time = 0.0
    dt = 0.5
    num_steps = 2
    end_time = 1.0
    petsc_options_iname = '-pc_type -mat_fd_coloring_err -mat_fd_type'
    petsc_options_value = 'lu       1e-6                 ds'

    [Quadrature]
        order = FIFTH
        side_order = SEVENTH
    []
[]

[Postprocessors]
    [total_power]
        type = ElementIntegralFunctorPostprocessor
        functor = volumetric_heat_rate
        use_displaced_mesh = false
    []
    [total_power_disp]
        type = ElementIntegralFunctorPostprocessor
        functor = volumetric_heat_rate
        use_displaced_mesh = true
    []
    [volume]
        type = VolumePostprocessor
    []
    [volume_disp]
        type = VolumePostprocessor
        use_displaced_mesh = true
    []
[]

[Outputs]
    exodus = true
[]

(modules/heat_transfer/test/tests/code_verification/cartesian_test_no4.i)

# Problem I.4
#
# An infinite plate with constant thermal conductivity k and internal
# heat generation q. The left boundary is exposed to a constant heat flux q0.
# The right boundary is exposed to a fluid with constant temperature uf and
# heat transfer coefficient h, which results in the convective boundary condition.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    nx = 1
  [../]
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./exact]
    type = ParsedFunction
    symbol_names = 'q q0 k L uf h'
    symbol_values = '1200 200 1 1 100 10.0'
    expression = 'uf + (q0 + L * q)/h + 0.5 * ( 2 * q0 + q * (L + x)) * (L-x) / k'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
  [./heatsource]
    type = HeatSource
    function = 1200
    variable = u
  [../]
[]

[BCs]
  [./ui]
    type = NeumannBC
    boundary = left
    variable = u
    value = 200
  [../]
  [./uo]
    type = CoupledConvectiveHeatFluxBC
    boundary = right
    variable = u
    htc = 10.0
    T_infinity = 100
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat thermal_conductivity'
    prop_values = '1.0 1.0 1.0'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/verify_against_analytical/1D_transient.i)

# This test solves a 1D transient heat equation
# The error is caclulated by comparing to the analytical solution
# The problem setup and analytical solution are taken from "Advanced Engineering
# Mathematics, 10th edition" by Erwin Kreyszig.
# http://www.amazon.com/Advanced-Engineering-Mathematics-Erwin-Kreyszig/dp/0470458364
# It is Example 1 in section 12.6 on page 561

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 160
  xmax = 80
[]

[Variables]
  [./T]
  [../]
[]

[ICs]
  [./T_IC]
    type = FunctionIC
    variable = T
    function = '100*sin(pi*x/80)'
  [../]
[]

[Kernels]
  [./HeatDiff]
    type = HeatConduction
    variable = T
  [../]
  [./HeatTdot]
    type = HeatConductionTimeDerivative
    variable = T
  [../]
[]

[BCs]
  [./sides]
    type = DirichletBC
    variable = T
    boundary = 'left right'
    value = 0
  [../]
[]

[Materials]
  [./k]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '0.95' #copper in cal/(cm sec C)
  [../]
  [./cp]
    type = GenericConstantMaterial
    prop_names = 'specific_heat'
    prop_values = '0.092' #copper in cal/(g C)
  [../]
  [./rho]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = '8.92' #copper in g/(cm^3)
  [../]
[]

[Postprocessors]
  [./error]
    type = NodalL2Error
    function = '100*sin(pi*x/80)*exp(-0.95/(0.092*8.92)*pi^2/80^2*t)'
    variable = T
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  l_tol = 1e-6
  dt = 2
  end_time = 100
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/heat_conduction_patch/heat_conduction_patch.i)

#
# This problem is taken from the Abaqus verification manual:
#   "1.5.8 Patch test for heat transfer elements"
#
# The temperature on the exterior nodes is 200x+100y+200z.
#
# This gives a constant flux at all Gauss points.
#
# In addition, the temperature at all nodes follows the same formula.
#
# Node x         y         z        Temperature
#   1  1.00E+00  0.00E+00  1.00E+00  400
#   2  6.77E-01  3.05E-01  6.83E-01  302.5
#   3  3.20E-01  1.86E-01  6.43E-01  211.2
#   4  0.00E+00  0.00E+00  1.00E+00  200
#   5  1.00E+00  1.00E+00  1.00E+00  500
#   6  7.88E-01  6.93E-01  6.44E-01  355.7
#   7  1.65E-01  7.45E-01  7.02E-01  247.9
#   8  0.00E+00  1.00E+00  1.00E+00  300
#   9  1.00E+00  0.00E+00  0.00E+00  200
#  10  0.00E+00  0.00E+00  0.00E+00  0
#  11  8.26E-01  2.88E-01  2.88E-01  251.6
#  12  2.49E-01  3.42E-01  1.92E-01  122.4
#  13  2.73E-01  7.50E-01  2.30E-01  175.6
#  14  0.00E+00  1.00E+00  0.00E+00  100
#  15  8.50E-01  6.49E-01  2.63E-01  287.5
#  16  1.00E+00  1.00E+00  0.00E+00  300

[Mesh]#Comment
  file = heat_conduction_patch.e
[] # Mesh

[Functions]
  [./temps]
    type = ParsedFunction
    expression ='200*x+100*y+200*z'
  [../]
[] # Functions

[Variables]

  [./temp]
    order = FIRST
    family = LAGRANGE
  [../]

[] # Variables

[Kernels]

  [./heat]
    type = HeatConduction
    variable = temp
  [../]

[] # Kernels

[BCs]

  [./temps]
    type = FunctionDirichletBC
    variable = temp
    boundary = 10
    function = temps
  [../]

[] # BCs

[Materials]

  [./heat]
    type = HeatConductionMaterial
    block = 1

    specific_heat = 0.116
    thermal_conductivity = 4.85e-4
  [../]

[] # Materials

[Executioner]

  type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -ksp_gmres_restart'
  petsc_options_value = 'lu       101'

  line_search = 'none'

  nl_abs_tol = 1e-11
  nl_rel_tol = 1e-10

  l_max_its = 20

[] # Executioner

[Outputs]
  exodus = true
[] # Output

(modules/heat_transfer/test/tests/convective_flux_function/convective_flux_function.i)

# This is a test of the ConvectiveFluxFunction BC.
# There is a single 1x1 element with a prescribed temperature
# on the left side and a convective flux BC on the right side.
# The temperature on the left is 100, and the far-field temp is 200.
# The conductance of the body (conductivity * length) is 10
#
# If the conductance in the BC is also 10, the temperature on the
# right side of the solid element should be 150 because half of the
# temperature drop should occur over the body and half in the BC.
#
# The integrated flux is deltaT * conductance, or -50 * 10 = -500.
# The negative sign indicates that heat is going into the body.
#
# The conductance is defined multiple ways using this input, and
# as long as it evaluates to 10, the result described above will
# be obtained.

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
[]

[Problem]
  extra_tag_vectors = 'bcs'
[]

[Variables]
  [temp]
    initial_condition = 100.0
  []
[]

[AuxVariables]
  [flux]
  []
[]

[AuxKernels]
  [flux]
    type = TagVectorAux
    variable = flux
    v = temp
    vector_tag = 'bcs'
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 10.0
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 100.0
  []
  [right]
    type = ConvectiveFluxFunction
    variable = temp
    boundary = right
    T_infinity = 200.0
    coefficient = 10.0 #This will behave as described in the header of this file if this evaluates to 10
    extra_vector_tags = 'bcs'
  []
[]

[Postprocessors]
  [integrated_flux]
    type = NodalSum
    variable = flux
    boundary = right
  []
[]

[Executioner]
  type = Transient
  start_time = 0.0
  end_time = 1.0
  dt = 1.0
  nl_rel_tol=1e-12
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/radiation_transfer_action/radiative_transfer_action.i)

[Problem]
  kernel_coverage_check = false
[]

[Mesh]
  type = MeshGeneratorMesh

  [./cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1.3 1.9'
    ix = '3 3 3'
    dy = '2 1.2 0.9'
    iy = '3 3 3'
    subdomain_id = '0 1 0
                    4 5 2
                    0 3 0'
  [../]

  [./inner_bottom]
    type = SideSetsBetweenSubdomainsGenerator
    input = cmg
    primary_block = 1
    paired_block = 5
    new_boundary = 'inner_bottom'
  [../]

  [./inner_left]
    type = SideSetsBetweenSubdomainsGenerator
    input = inner_bottom
    primary_block = 4
    paired_block = 5
    new_boundary = 'inner_left'
  [../]

  [./inner_right]
    type = SideSetsBetweenSubdomainsGenerator
    input = inner_left
    primary_block = 2
    paired_block = 5
    new_boundary = 'inner_right'
  [../]

  [./inner_top]
    type = SideSetsBetweenSubdomainsGenerator
    input = inner_right
    primary_block = 3
    paired_block = 5
    new_boundary = 'inner_top'
  [../]

  [./rename]
    type = RenameBlockGenerator
    old_block = '1 2 3 4'
    new_block = '0 0 0 0'
    input = inner_top
  [../]
[]

[Variables]
  [./temperature]
    block = 0
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temperature
    block = 0
    diffusion_coefficient = 5
  [../]
[]

[GrayDiffuseRadiation]
  [./cavity]
    boundary = '4 5 6 7'
    emissivity = '0.9 0.8 0.4 1'
    n_patches = '2 2 2 3'
    partitioners = 'centroid centroid centroid centroid'
    centroid_partitioner_directions = 'x y y x'
    temperature = temperature
    adiabatic_boundary = '7'
    fixed_temperature_boundary = '4'
    fixed_boundary_temperatures = '1200'
    view_factor_calculator = analytical
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 600
  [../]

  [./right]
    type = DirichletBC
    variable = temperature
    boundary = right
    value = 300
  [../]
[]

[Postprocessors]
  [./average_T_inner_right]
    type = SideAverageValue
    variable = temperature
    boundary = inner_right
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/combined_plasticity_temperature/plasticity_temperature_dep_yield.i)

#
# This is a test of the piece-wise linear strain hardening model using the
# small strain formulation.  This test exercises the temperature-dependent
# yield stress.
#
# Test procedure:
# 1. The element is pulled to and then beyond the yield stress for a given
# temperature.
# 2. The displacement is then constant while the temperature increases and
# the yield stress decreases.  This results in a lower stress with more
# plastic strain.
# 3. The temperature decreases beyond its original value giving a higher
# yield stress.  The displacement increases, causing increases stress to
# the new yield stress.
# 4. The temperature and yield stress are constant with increasing
# displacement giving a constant stress and more plastic strain.
#
# Plotting total_strain_yy on the x axis and stress_yy on the y axis shows
# the stress history in a clear way.
#
#  s |
#  t |            *****
#  r |           *
#  e |   *****  *
#  s |  *    * *
#  s | *     *
#    |*
#    +------------------
#           total strain
#

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Physics/SolidMechanics/QuasiStatic]
  [./all]
    strain = FINITE
    incremental = true
    add_variables = true
    generate_output = 'stress_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
  [../]
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Functions]
  [./top_pull]
    type = PiecewiseLinear
    x = '0 1     2    4    5    6'
    y = '0 0.025 0.05 0.05 0.06 0.085'
  [../]
  [./yield]
    type = PiecewiseLinear
    x = '400 500 600'
    y = '6e3 5e3 4e3'
  [../]
  [./temp]
    type = PiecewiseLinear
    x = '0   1   2   3   4'
    y = '500 500 500 600 400'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./y_pull_function]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = top
    function = top_pull
  [../]
  [./x_bot]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./y_bot]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./z_bot]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  [../]
  [./temp]
    type = FunctionDirichletBC
    variable = temp
    function = temp
    boundary = left
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 0
    youngs_modulus = 2.0e5
    poissons_ratio = 0.3
  [../]
  [./creep_plas]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    block = 0
    inelastic_models = 'plasticity'
    max_iterations = 50
    absolute_tolerance = 1e-05
  [../]
  [./plasticity]
    type = IsotropicPlasticityStressUpdate
    block = 0
    hardening_constant = 0
    yield_stress_function = yield
    temperature = temp
  [../]
  [./heat_conduction]
    type = HeatConductionMaterial
    block = 0
    specific_heat = 1
    thermal_conductivity = 1
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-9

  start_time = 0.0
  end_time = 6
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(modules/functional_expansion_tools/examples/1D_volumetric_Cartesian/main.i)

# Basic example coupling a master and sub app in a 1D Cartesian volume.
#
# The master app provides field values to the sub app via Functional Expansions, which then performs
# its calculations. The sub app's solution field values are then transferred back to the master app
# and coupled into the solution of the master app solution.
#
# This example couples Functional Expansions via AuxVariable.
[Mesh]
  type = GeneratedMesh
  dim = 1

  xmin = 0.0
  xmax = 10.0
  nx = 15
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./s_in] # Add in the contribution from the SubApp
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'left right'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3'
    physical_bounds = '0.0  10.0'
    x = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(modules/heat_transfer/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/nonmatching.i)

[Mesh]
  file = nonmatching.e
[]

[Variables]
  [./temp]
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temp
    boundary = leftleft
    value = 1000
  [../]
  [./right]
    type = DirichletBC
    variable = temp
    boundary = rightright
    value = 400
  [../]
[]

[ThermalContact]
  [./left_to_right]
    emissivity_primary = 0
    emissivity_secondary = 0
    secondary = leftright
    quadrature = true
    primary = rightleft
    variable = temp
    type = GapHeatTransfer
  [../]
[]

[Materials]
  [./hcm]
    type = HeatConductionMaterial
    block = 'left right'
    specific_heat = 1
    thermal_conductivity = 1
  [../]
  [./gap_conductance]
    type = GenericConstantMaterial
    prop_names = 'gap_conductance gap_conductance_dT'
    boundary = 'leftright rightleft'
    prop_values = '1 0'
  [../]
[]

[Postprocessors]
  [./left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = leftright
    diffusivity = thermal_conductivity
  [../]
  [./right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = rightleft
    diffusivity = thermal_conductivity
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/elastic_thermal_patch/elastic_thermal_patch_rz_smp.i)

#
# This problem is modified from the Abaqus verification manual:
#   "1.5.4 Patch test for axisymmetric elements"
# The original stress solution is given as:
#   xx = yy = zz = 2000
#   xy = 400
#
# Here, E=1e6 and nu=0.25.
# However, with a +100 degree change in temperature and a coefficient
#   of thermal expansion of 1e-6, the solution becomes:
#   xx = yy = zz = 1800
#   xy = 400
#   since
#   E*(1-nu)/(1+nu)/(1-2*nu)*(1+2*nu/(1-nu))*(1e-3-1e-4) = 1800
#
# Also,
#
#   dSrr   dSrz   Srr-Stt
#   ---- + ---- + ------- + br = 0
#    dr     dz       r
#
# and
#
#   dSrz   Srz   dSzz
#   ---- + --- + ---- + bz = 0
#    dr     r     dz
#
# where
#   Srr = stress in rr
#   Szz = stress in zz
#   Stt = stress in theta-theta
#   Srz = stress in rz
#   br  = body force in r direction
#   bz  = body force in z direction
#
# This test is meant to exercise the Jacobian.  To that end, the body
# force has been turned off.  This makes the results differ slightly
# from the original values, but requires a correct Jacobian for minimal
# iterations.  Iteration plotting is turned on to ensure that the
# number of iterations needed does not increase.

[GlobalParams]
  temperature = temp
  volumetric_locking_correction = true
[]

[Mesh]
  file = elastic_thermal_patch_rz_test.e
  coord_type = RZ
[]

[Functions]
  [./ur]
    type = ParsedFunction
    expression = '1e-3*x'
  [../]
  [./uz]
    type = ParsedFunction
    expression = '1e-3*(x+y)'
  [../]
  [./body]
    type = ParsedFunction
    expression = '-400/x'
  [../]
  [./temp]
    type = ParsedFunction
    expression = '117.56+100*t'
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]

  [./temp]
    initial_condition = 117.56
  [../]
[]

[Physics]
    [SolidMechanics]
        [QuasiStatic]
            displacements = 'disp_x disp_y'
            [All]
                displacements = 'disp_x disp_y'
                add_variables = true
                strain = SMALL
                incremental = true
                eigenstrain_names = eigenstrain
                generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_yz stress_zx'
            [../]
        [../]
    [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./ur]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 10
    function = ur
  [../]
  [./uz]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 10
    function = uz
  [../]

  [./temp]
    type = FunctionDirichletBC
    variable = temp
    boundary = 10
    function = temp
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    bulk_modulus = 666666.6666666667
    poissons_ratio = 0.25
  [../]
  [./thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 1e-6
    stress_free_temperature = 117.56
    eigenstrain_name = eigenstrain
  [../]
  [./stress]
    type = ComputeStrainIncrementBasedStress
  [../]

  [./heat]
    type = HeatConductionMaterial
    specific_heat = 0.116
    thermal_conductivity = 4.85e-4
  [../]

  [./density]
    type = Density
    block = 1
    density = 0.283
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  nl_abs_tol = 1e-11
  nl_rel_tol = 1e-12

  l_max_its = 20

  start_time = 0.0
  dt = 1.0
  num_steps = 1
  end_time = 1.0
[]

[Outputs]
  file_base = elastic_thermal_patch_rz_smp_out
  [./exodus]
    type = Exodus
    execute_on = 'initial timestep_end nonlinear'
    nonlinear_residual_dt_divisor = 100
  [../]
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/planar_yz.i)

# 1-D Gap Heat Transfer Test without mechanics
#
# This test exercises 1-D gap heat transfer for a constant conductivity gap.
#
# The mesh consists of two element blocks in the y-z plane.  Each element block
# is a square. They sit next to one another with a unit between them.
#
# The conductivity of both blocks is set very large to achieve a uniform temperature
# across each block. The temperature of the far bottom boundary
# is ramped from 100 to 200 over one time unit.  The temperature of the far top
# boundary is held fixed at 100.
#
# A simple analytical solution is possible for the heat flux between the blocks:
#
# Flux = (T_left - T_right) * (gapK/gap_width)
#
# The gap conductivity is specified as 1, thus
#
# gapK(Tavg) = 1.0*Tavg
#
# The heat flux across the gap at time = 1 is then:
#
# Flux = 100 * (1.0/1.0) = 100
#
# For comparison, see results from the flux post processors.  These results
# are the same as for the unit 1-D gap heat transfer between two unit cubes.

[Mesh]
  [file]
    type = FileMeshGenerator
    file = simple_2D.e
  []
  [./rotate]
    type = TransformGenerator
    transform = ROTATE
    vector_value = '0 90 90'
    input = file
  [../]
[]

[Functions]
  [./temp]
    type = PiecewiseLinear
    x = '0   1   2'
    y = '100 200 200'
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
  [../]
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  [../]
[]

[AuxVariables]
  [./gap_cond]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]


[BCs]
  [./temp_far_bottom]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  [../]
  [./temp_far_top]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
[]

[AuxKernels]
  [./conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 2
  [../]
[]

[Materials]
  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 100000000.0
  [../]
  [./density]
    type = GenericConstantMaterial
    block = '1 2'
    prop_names = 'density'
    prop_values = '1.0'
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'
  nl_rel_tol = 1e-12
  l_tol = 1e-3
  l_max_its = 100

  dt = 1e-1
  end_time = 1.0
[]

[Postprocessors]
  [./temp_bottom]
    type = SideAverageValue
    boundary = 2
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./temp_top]
    type = SideAverageValue
    boundary = 3
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./flux_bottom]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  [../]

  [./flux_top]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_radiation/cylinder.i)

#
# This problem is one of radiation boundary conditions between two
# cylindrical surfaces.
#
#            S(T1^4 - T2^4)                       R1
# flux1 = - ---------------- and flux2 = -flux1 * --
#           1    1 - e2   R1                      R2
#           -- + ------ * --
#           e1     e2     R2
#
# where S is the Stefan Boltzmann constant         5.67e-8 W/m^2/K^4
#       T1 is the temperature on the left surface  278 K
#       T2 is the temperature on the right surface 333 K
#       e1 is the emissivity for the left surface  0.8
#       e2 is the emissivity for the left surface  0.9
#       R1 is the radius of the inner surface      0.1 m
#       R2 is the radius of the outer surface      0.11 m
#
# Flux1:
# Exact           Code
# -------------   -------------
# -265.29 W/m^2   -265.26 W/m^2
#
# Flux2:
# Exact           Code
# -------------   -------------
#  241.26 W/m^2    241.15 W/m^2
#

thick = 0.01
R1 = 0.1
R2 = 0.11

[GlobalParams]
  order = second
  family = lagrange
[]

[Mesh]
  coord_type = RZ
  [mesh1]
    type = GeneratedMeshGenerator
    dim = 2
    elem_type = quad8
    nx = 4
    ny = 1
    xmin = '${fparse R1 - thick}'
    xmax = '${R1}'
    ymin = 0
    ymax = '${R1}'
    boundary_name_prefix = left
  []
  [mesh2]
    type = GeneratedMeshGenerator
    dim = 2
    elem_type = quad8
    nx = 4
    ny = 1
    xmin = '${R2}'
    xmax = '${fparse R2 + thick}'
    ymin = 0
    ymax = '${R1}'
    boundary_id_offset = 4
    boundary_name_prefix = right
  []
  [final]
    type = CombinerGenerator
    inputs = 'mesh1 mesh2'
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temperature
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = temperature
    boundary = left_left
    value = 278
  []
  [right]
    type = DirichletBC
    variable = temperature
    boundary = right_right
    value = 333
  []
[]

[Materials]
  [heat]
    type = HeatConductionMaterial
    thermal_conductivity = 200 # W/m/K
    specific_heat = 4.2e5
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temperature
    primary = left_right
    secondary = right_left
    emissivity_primary = 0.8
    emissivity_secondary = 0.9
    quadrature = true
    gap_conductivity = 1e-40 # requires a positive value
    gap_geometry_type = cylinder
  []
[]

[Functions]
  [analytic_flux_1]
    type = ParsedFunction
    symbol_names = 'S        T1  T2  e1  e2  R1    R2'
    symbol_values = '5.67e-8 278 333 0.8 0.9 ${R1} ${R2}'
    expression = 'T14 := T1*T1*T1*T1;
                  T24 := T2*T2*T2*T2;
                  S*(T14-T24)/(1/e1+(1-e2)/e2*R1/R2)'
  []
  [analytic_flux_2]
    type = ParsedFunction
    symbol_names = 'S        T1  T2  e1  e2  R1    R2'
    symbol_values = '5.67e-8 278 333 0.8 0.9 ${R1} ${R2}'
    expression = 'T14 := T1*T1*T1*T1;
                  T24 := T2*T2*T2*T2;
                  -S*(T14-T24)/(1/e1+(1-e2)/e2*R1/R2)*R1/R2'
  []
[]

[Postprocessors]
  [code_flux_1]
    type = SideDiffusiveFluxAverage
    variable = temperature
    boundary = left_right
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [analytic_flux_1]
    type = FunctionValuePostprocessor
    function = analytic_flux_1
    execute_on = 'initial timestep_end'
  []
  [error_1]
    type = ParsedPostprocessor
    pp_names = 'code_flux_1 analytic_flux_1'
    expression = '(analytic_flux_1 - code_flux_1)/analytic_flux_1*100'
    execute_on = 'initial timestep_end'
  []
  [code_flux_2]
    type = SideDiffusiveFluxAverage
    variable = temperature
    boundary = right_left
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [analytic_flux_2]
    type = FunctionValuePostprocessor
    function = analytic_flux_2
    execute_on = 'initial timestep_end'
  []
  [error_2]
    type = ParsedPostprocessor
    pp_names = 'code_flux_2 analytic_flux_2'
    expression = '(analytic_flux_2 - code_flux_2)/analytic_flux_2*100'
    execute_on = 'initial timestep_end'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = newton

  num_steps = 1
  dt = 1
  end_time = 1

  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-10
[]

[Outputs]
  csv = true
[]

(modules/combined/test/tests/thermal_conductivity_temperature_function_test/thermal_conductivity_temperature_function_test.i)

#
# This test evaluates the capability of HeatConductionMaterial to define
# thermal conductivity as a function of temperature.  The test uses the patch test
# cube mesh with a flux bc on one side and a temperature bc on the opposite side.
# The temperature bc changes as a function of time from 100 to 200.  The thermal
# conductivity is a function of temperature, with k = 1 for temps = 100-199, k = 2
# for temps _>_ 200. The flux, q = 10 is constant.  The Transient Executioner is used here
# although the interial kernel is omitted, so this is really a series of two steady-state
# solutions.
#
#                         ---------------
#                        |               |
#                        |               |
#                q    -> |       k       |  T2
#                        |               |
#             T1 = ?     |               |
#                         ---------------
#                              dx = 1
#
#
#                         q = -k dT/dx
#
#                         q = -k (T1 - T2)/dx
#
#                         T1 = (q/-k)*dx + T2
#
#                         for: T2 = 100, k = 1, q = -10
#
#                         T1 = 110
#                         --------
#
#                         for: T2 = 200, k = 2, q = -10
#
#                         T1 = 205
#                         --------
#

[Mesh]#Comment
  file = fe_patch.e
[] # Mesh

[Functions]
  [./k_func]
    type = PiecewiseLinear
    x = '100 199 200'
    y = '1   1   2'
  [../]

  [./c_func]
    type = PiecewiseLinear
    x = '100    200'
    y = '0.116  0.116'
  [../]

  [./t_func]
    type = PiecewiseLinear
    x = '0   1   2'
    y = '100 100 200'
  [../]
[] # Functions

[Variables]

  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  [../]

[] # Variables

[Kernels]

  [./heat_r]
    type = HeatConduction
    variable = temp
  [../]


[] # Kernels

[BCs]

  [./temps_function]
    type = FunctionDirichletBC
    variable = temp
    boundary = 1000
    function = t_func
  [../]

  [./flux_in]
    type = NeumannBC
    variable = temp
    boundary = 100
    value = 10
  [../]

[] # BCs

[Materials]

  [./heat]
    type = HeatConductionMaterial
    block = 1
    temp = temp
    thermal_conductivity_temperature_function = k_func
    specific_heat_temperature_function = c_func
  [../]

  [./density]
    type = Density
    block = 1
    density = 0.283
  [../]

[] # Materials


[Executioner]

  type = Transient


  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'



  petsc_options_iname = '-pc_type -ksp_gmres_restart'
  petsc_options_value = 'lu       101'


  line_search = 'none'


  l_max_its = 100
  l_tol = 8e-3

  nl_max_its = 15
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-10

  start_time = 0.0
  dt = 1
  end_time = 2
  num_steps = 2


[] # Executioner

[Outputs]
  file_base = out
  exodus = true
[] # Outputs

(modules/combined/test/tests/gap_heat_transfer_convex/gap_heat_transfer_convex_gap_offsets.i)

#The two blocks were moved apart by the value of 0.005 in the y-direction, respectively.
#This value was compensated by the gap offsets from both secondary and primary sides
[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  temperature = temp
[]

[Mesh]
  file = gap_heat_transfer_convex_gap_offsets.e
[]

[Functions]
  [./disp]
    type = PiecewiseLinear
    x = '0 2.0'
    y = '0 1.0'
  [../]
  [./temp]
    type = PiecewiseLinear
    x = '0     1'
    y = '200 200'
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]

  [./temp]
    initial_condition = 100
  [../]
[]

[AuxVariables]
  [./primary_gap_offset]
  [../]
  [./secondary_gap_offset]
  [../]
  [./mapped_primary_gap_offset]
  [../]
[]

[AuxKernels]
  [./primary_gap_offset]
    type = ConstantAux
    variable = primary_gap_offset
    value = -0.005
    boundary = 2
  [../]
  [./mapped_primary_gap_offset]
    type = GapValueAux
    variable = mapped_primary_gap_offset
    paired_variable = primary_gap_offset
    boundary = 3
    paired_boundary = 2
  [../]
  [./secondary_gap_offset]
    type = ConstantAux
    variable = secondary_gap_offset
    value = -0.005
    boundary = 3
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 2
    secondary = 3
    emissivity_primary = 0
    emissivity_secondary = 0
    secondary_gap_offset = secondary_gap_offset
    mapped_primary_gap_offset = mapped_primary_gap_offset
  [../]
[]

[Physics/SolidMechanics/QuasiStatic/All]
  volumetric_locking_correction = true
  strain = FINITE
  eigenstrain_names = eigenstrain
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./move_right]
    type = FunctionDirichletBC
    boundary = '3'
    variable = disp_x
    function = disp
  [../]

  [./fixed_x]
    type = DirichletBC
    boundary = '1'
    variable = disp_x
    value = 0
  [../]
  [./fixed_y]
    type = DirichletBC
    boundary = '1 2 3 4'
    variable = disp_y
    value = 0
  [../]
  [./fixed_z]
    type = DirichletBC
    boundary = '1 2 3 4'
    variable = disp_z
    value = 0
  [../]

  [./temp_bottom]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  [../]
  [./temp_top]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2'
    youngs_modulus = 1e6
    poissons_ratio = 0.3
  [../]
  [./thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    stress_free_temperature = 100
    thermal_expansion_coeff = 0
    eigenstrain_name = eigenstrain
  [../]
  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]

  [./heat1]
    type = HeatConductionMaterial
    block = 1

    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]
  [./heat2]
    type = HeatConductionMaterial
    block = 2

    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./density]
    type = Density
    block = '1 2'
    density = 1.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  start_time = 0.0
  dt = 0.1
  end_time = 2.0
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/1D.i)

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  coord_type = RZ
  [fred]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 25
    xmin = 0
    xmax = 1
    boundary_name_prefix = left
    elem_type = edge3
  []
  [wilma]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 25
    xmin = 2
    xmax = 3
    boundary_id_offset = 10
    boundary_name_prefix = right
    elem_type = edge3
  []
  [combine]
    type = CombinerGenerator
    inputs = 'fred wilma'
  []
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1   2'
    y = '100 200 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 100
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
[]

[BCs]
  [temp_far_left]
    type = FunctionDirichletBC
    boundary = left_left
    variable = temp
    function = temp
  []

  [temp_far_right]
    type = DirichletBC
    boundary = right_right
    variable = temp
    value = 100
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = right_left
    secondary = left_right
    emissivity_primary = 0
    emissivity_secondary = 0
  []
[]

[Materials]
  [heat]
    type = HeatConductionMaterial
    specific_heat = 1.0
    thermal_conductivity = 1.0e6
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  nl_abs_tol = 1e-3
  nl_rel_tol = 1e-12

  l_tol = 1e-8
  l_max_its = 100

  start_time = 0.0
  dt = 2e-1
  end_time = 2.0
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = left_right
    variable = temp
    execute_on = 'initial timestep_end'
  []

  [temp_right]
    type = SideAverageValue
    boundary = right_left
    variable = temp
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/optimization/thermal_sensitivity/2d_root.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-4
power = 1

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 20
    xmin = 0
    xmax = 40
    ymin = 0
    ymax = 40
  []
[]

[Variables]
  [T]
    initial_condition = 100
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    diffusion_coefficient = k
    variable = T
  []
  [heat_source]
    type = HeatSource
    function = 1e-2
    variable = T
  []
[]
[DiracKernels]
  [src]
    type = ConstantPointSource
    variable = T
    point = '0 5 0'
    value = 10
  []
[]

[BCs]
  [no_x]
    type = DirichletBC
    variable = T
    boundary = 'right top bottom'
    value = 0.0
  []
[]

[Materials]
  [k]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = k
  []
  [dc]
    type = ThermalSensitivity
    temperature = T
    design_density = mat_den
    thermal_conductivity = k
  []
  #only needed for objective function output in postprocessor
  [thermal_compliance]
    type = ThermalCompliance
    temperature = T
    thermal_conductivity = k
  []
[]

[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 3
    weights = linear
    prop_name = thermal_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [update]
    type = DensityUpdate
    density_sensitivity = Dc
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
  []
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-8
  dt = 1.0
  dtmin = 1.0
  num_steps = 20
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'FINAL'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = thermal_sensitivity
  []
  [objective_thermal]
    type = ElementIntegralMaterialProperty
    mat_prop = thermal_compliance
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_htonly/gap_heat_transfer_htonly_rz_test.i)

#
# 2-D RZ Gap Heat Transfer Test without mechanics
#
# This test exercises 1-D gap heat transfer for a constant conductivity gap.
#
# The mesh consists of two element blocks containing one element each.  Each
#   element is a unit cube.  They sit next to one another with a unit between them.
#
# The conductivity of both blocks is set very large to achieve a uniform temperature
#  across each block. The temperature of the far left boundary
#  is ramped from 100 to 200 over one time unit, and then held fixed for an additional
#  time unit.  The temperature of the far right boundary is held fixed at 100.
#
# A simple analytical solution is possible for the heat flux between the blocks, or cylinders in the case of RZ.:
#
#  Flux = (T_left - T_right) * (gapK/(r*ln(r2/r1)))
#
# For gapK = 1 (default value)
#
# The integrated heat flux across the gap at time 2 is then:
#
# 2*pi*h*k*delta_T/(ln(r2/r1))
# 2*pi*1*1*100/(ln(2/1)) = 906.5 watts
#
# For comparison, see results from the flux post processors.
#
# As a second test, use the rectilinear (parallel plate) form of the gap heat transfer.
#
#  Flux = (T_left - T_right) * (gapK/gapL)
#
# For gapK = 1 (default value)
#
# The integrated heat flux across the gap at time 2 is then:
#
# 2*pi*h*k*delta_T/(1)
# 2*pi*1*1*100/(1) = 628.3 watts
#
# For comparison, see results from the flux post processors.
#

[Mesh]
  active = 'file'
  [file]
    type = FileMeshGenerator
    file = gap_heat_transfer_htonly_rz_test.e
  []
  [rotate]
    type = TransformGenerator
    transform = ROTATE
    vector_value = '90 0 0'
    input = file
  []
  rz_coord_axis = Y # this is modified through CLI args to test Z-R as opposed to R-Z
  coord_type = RZ
[]
[Functions]

  [./ramp]
    type = PiecewiseLinear
    x = '0   1   2'
    y = '100 200 200'
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
  [../]
  [./thermal_contact2]
    type = GapHeatTransfer
    variable = temp2
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_geometry_type = PLATE
    appended_property_name = 2
  [../]
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  [../]
  [./temp2]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
  [../]
[]

[AuxVariables]
  [./gap_cond]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./gap_cond2]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./heat2]
    type = HeatConduction
    variable = temp2
  [../]
[]


[BCs]
  [./temp_far_left]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = ramp
  [../]

  [./temp_far_right]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  [../]

  [./temp_far_left2]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp2
    function = ramp
  [../]

  [./temp_far_right2]
    type = DirichletBC
    boundary = 4
    variable = temp2
    value = 100
  [../]
[]

[AuxKernels]
  [./conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 2
  [../]
  [./conductance2]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond2
    boundary = 2
  [../]
[]

[Materials]

  [./heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 1e6
  [../]
  [./density]
    type = GenericConstantMaterial
    block = '1 2'
    prop_names = 'density'
    prop_values = '1.0'
  [../]
[]

[Executioner]
  type = Transient
#  petsc_options = '-snes_mf_operator -ksp_monitor -snes_ksp_ew'

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'




#  petsc_options_iname = '-snes_type -snes_ls -snes_linesearch_type -ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
#  petsc_options_value = 'ls         basic    basic                    201                hypre    boomeramg      4'
#  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
#  petsc_options_value = '201                hypre    boomeramg      4'

  nl_abs_tol = 1e-3
  nl_rel_tol = 1e-8

  l_tol = 1e-6
  l_max_its = 100

  start_time = 0.0
  dt = 1e-1
  dtmin = 1e-1
  end_time = 2.0
[]

[Postprocessors]

  [./temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  [../]

  [./flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  [../]

  [./temp_left2]
    type = SideAverageValue
    boundary = 2
    variable = temp2
    execute_on = 'initial timestep_end'
  [../]

  [./temp_right2]
    type = SideAverageValue
    boundary = 3
    variable = temp2
    execute_on = 'initial timestep_end'
  [../]

  [./flux_left2]
    type = SideDiffusiveFluxIntegral
    variable = temp2
    boundary = 2
    diffusivity = thermal_conductivity
  [../]

  [./flux_right2]
    type = SideDiffusiveFluxIntegral
    variable = temp2
    boundary = 3
    diffusivity = thermal_conductivity
  [../]

[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/gap_heat_transfer_radiation_test.i)

#
# This test replicates the legacy heat transfter test
# gap_heat_transfer_radiation/gap_heat_transfer_radiation_test.i
# The flux post processors give 3.753945e+01
#

[Mesh]
  [file]
    type = FileMeshGenerator
    file = gap_heat_transfer_radiation_test.e
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '2'
    new_block_id = '200'
    new_block_name = 'secondary_lower'
    input = file
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '3'
    new_block_id = '300'
    new_block_name = 'primary_lower'
    input = secondary
  []
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '200 200'
  []
[]

[Variables]
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 100
    scaling = 1e-8
  []
  [lm]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
    scaling = 1e-1
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
    block = '1 2'
  []
[]

[BCs]
  [temp_far_left]
    type = FunctionDirichletBC
    boundary = 1
    variable = temp
    function = temp
  []

  [temp_far_right]
    type = DirichletBC
    boundary = 4
    variable = temp
    value = 100
  []
[]

[UserObjects]
  [radiative]
    type = GapFluxModelRadiative
    secondary_emissivity = 0.5
    primary_emissivity = 0.5
    temperature = temp
    boundary = 3
  []
  [simple]
    type = GapFluxModelSimple
    k = 0.09187557
    temperature = temp
    boundary = 3
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = temp
    primary_boundary = 3
    primary_subdomain = 300
    secondary_boundary = 2
    secondary_subdomain = 200
    gap_flux_models = 'simple radiative'
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 10000000.0
  []
  [density]
    type = GenericConstantMaterial
    block = '1 2'
    prop_names = 'density'
    prop_values = '1.0'
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  end_time = 1.0
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
    execute_on = 'initial timestep_end'
  []

  [temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
    execute_on = 'initial timestep_end'
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  []

  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  []
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/thin_layer_heat_transfer/transient_3d.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    nx = 10
    ny = 10
    nz = 2
    zmax = 0.2
    dim = 3
  []
  [block1]
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '0 0 0'
    top_right = '0.5 1 0.2'
    input = gen
  []
  [block2]
    type = SubdomainBoundingBoxGenerator
    block_id = 2
    bottom_left = '0.5 0 0'
    top_right = '1 1 0.2'
    input = block1
  []
  [breakmesh]
    input = block2
    type = BreakMeshByBlockGenerator
    block_pairs = '1 2'
    split_interface = true
    add_interface_on_two_sides = true
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [thermal_cond]
    type = HeatConduction
    variable = temperature
  []
[]

[InterfaceKernels]
  [thin_layer]
    type = ThinLayerHeatTransfer
    thermal_conductivity = thermal_conductivity_layer
    specific_heat = specific_heat_layer
    density = density_layer
    heat_source = heat_source_layer
    thickness = 0.01
    variable = temperature
    neighbor_var = temperature
    boundary = Block1_Block2
  []
[]

[BCs]
  [left_temp]
    type = DirichletBC
    value = 0
    variable = temperature
    boundary = left
  []
  [right_temp]
    type = DirichletBC
    value = 0
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [thermal_cond]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '1 1 1'
  []
  [thermal_cond_layer]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity_layer specific_heat_layer heat_source_layer density_layer'
    prop_values = '0.05 1 10000 1'
    boundary = Block1_Block2
  []
[]
[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10

  dt = 0.05
  num_steps = 2
[]

[Outputs]
  print_linear_residuals = false
  exodus = true
[]

(modules/heat_transfer/test/tests/heat_conduction/3d_quadrature_gap_heat_transfer/moving.i)

[Mesh]
  file = nonmatching.e
  displacements = 'disp_x disp_y disp_z'
[]

[Variables]
  [temp]
  []
[]

[AuxVariables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[Functions]
  [disp_y]
    type = ParsedFunction
    expression = 0.1*t
  []
  [left_temp]
    type = ParsedFunction
    expression = 1000+t
  []
[]

[Kernels]
  [hc]
    type = HeatConduction
    variable = temp
  []
[]

[AuxKernels]
  [disp_y]
    type = FunctionAux
    variable = disp_y
    function = disp_y
    block = left
    execute_on = 'INITIAL TIMESTEP_BEGIN'
  []
[]

[BCs]
  [left]
    type = FunctionDirichletBC
    variable = temp
    boundary = leftleft
    function = left_temp
  []
  [right]
    type = DirichletBC
    variable = temp
    boundary = rightright
    value = 400
  []
[]

[ThermalContact]
  [left_to_right]
    type = GapHeatTransfer
    variable = temp
    primary = rightleft
    secondary = leftright
    emissivity_primary = 0
    emissivity_secondary = 0
    quadrature = true
  []
[]

[Materials]
  [hcm]
    type = HeatConductionMaterial
    block = 'left right'
    specific_heat = 1
    thermal_conductivity = 1
    use_displaced_mesh = true
  []
[]

[Postprocessors]
  [left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = leftright
    diffusivity = thermal_conductivity
  []
  [right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = rightleft
    diffusivity = thermal_conductivity
  []
[]

[Executioner]
  type = Transient
  num_steps = 9
  dt = 1

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(modules/combined/examples/effective_properties/effective_th_cond.i)

# This example calculates the effective thermal conductivity across a microstructure
# with circular second phase precipitates. Two methods are used to calculate the effective thermal conductivity,
# the direct method that applies a temperature to one side and a heat flux to the other,
# and the AEH method.
[Mesh] #Sets mesh size to 10 microns by 10 microns
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 100
    ny = 100
    xmax = 10
    ymax = 10
  []
  [new_nodeset]
    input = gen
    type = ExtraNodesetGenerator
    coord = '5 5'
    new_boundary = 100
  []
[]

[Variables] #Adds variables needed for two ways of calculating effective thermal cond.
  [T] #Temperature used for the direct calculation
    initial_condition = 800
  []
  [Tx_AEH] #Temperature used for the x-component of the AEH solve
    initial_condition = 800
    scaling = 1.0e4 #Scales residual to improve convergence
  []
  [Ty_AEH] #Temperature used for the y-component of the AEH solve
    initial_condition = 800
    scaling = 1.0e4  #Scales residual to improve convergence
  []
[]

[AuxVariables] #Creates second constant phase
  [phase2]
  []
[]

[ICs] #Sets the IC for the second constant phase
  [phase2_IC] #Creates circles with smooth interfaces at random locations
    variable = phase2
    type = MultiSmoothCircleIC
    int_width = 0.3
    numbub = 20
    bubspac = 1.5
    radius = 0.5
    outvalue = 0
    invalue = 1
    block = 0
  []
[]

[Kernels]
  [HtCond] #Kernel for direct calculation of thermal cond
    type = HeatConduction
    variable = T
  []
  [heat_x] #All other kernels are for AEH approach to calculate thermal cond.
    type = HeatConduction
    variable = Tx_AEH
  []
  [heat_rhs_x]
    type = HomogenizedHeatConduction
    variable = Tx_AEH
    component = 0
  []
  [heat_y]
    type = HeatConduction
    variable = Ty_AEH
  []
  [heat_rhs_y]
    type = HomogenizedHeatConduction
    variable = Ty_AEH
    component = 1
  []
[]

[BCs]
  [Periodic]
    [all]
      auto_direction = 'x y'
      variable = 'Tx_AEH Ty_AEH'
    []
  []
  [left_T] #Fix temperature on the left side
    type = DirichletBC
    variable = T
    boundary = left
    value = 800
  []
  [right_flux] #Set heat flux on the right side
    type = NeumannBC
    variable = T
    boundary = right
    value = 5e-6
  []
  [fix_x] #Fix Tx_AEH at a single point
    type = DirichletBC
    variable = Tx_AEH
    value = 800
    boundary = 100
  []
  [fix_y] #Fix Ty_AEH at a single point
    type = DirichletBC
    variable = Ty_AEH
    value = 800
    boundary = 100
  []
[]

[Materials]
  [thcond] #The equation defining the thermal conductivity is defined here, using two ifs
    # The k in the bulk is k_b, in the precipitate k_p2, and across the interaface k_int
    type = ParsedMaterial
    block = 0
    constant_names = 'length_scale k_b k_p2 k_int'
    constant_expressions = '1e-6 5 1 0.1'
    expression = 'sk_b:= length_scale*k_b; sk_p2:= length_scale*k_p2; sk_int:= k_int*length_scale; if(phase2>0.1,if(phase2>0.95,sk_p2,sk_int),sk_b)'
    outputs = exodus
    f_name = thermal_conductivity
    coupled_variables = phase2
  []
[]

[Postprocessors]
  [right_T]
    type = SideAverageValue
    variable = T
    boundary = right
  []
  [k_x_direct] #Effective thermal conductivity from direct method
    # This value is lower than the AEH value because it is impacted by second phase
    # on the right boundary
    type = ThermalConductivity
    variable = T
    flux = 5e-6
    length_scale = 1e-06
    T_hot = 800
    dx = 10
    boundary = right
  []
  [k_x_AEH] #Effective thermal conductivity in x-direction from AEH
    type = HomogenizedThermalConductivity
    chi = 'Tx_AEH Ty_AEH'
    row = 0
    col = 0
    scale_factor = 1e6 #Scale due to length scale of problem
  []
  [k_y_AEH] #Effective thermal conductivity in x-direction from AEH
    type = HomogenizedThermalConductivity
    chi = 'Tx_AEH Ty_AEH'
    row = 1
    col = 1
    scale_factor = 1e6 #Scale due to length scale of problem
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    off_diag_row = 'Tx_AEH Ty_AEH'
    off_diag_column = 'Ty_AEH Tx_AEH'
  []
[]

[Executioner]
  type = Steady
  l_max_its = 15
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart -pc_hypre_boomeramg_strong_threshold'
  petsc_options_value = 'hypre boomeramg 31 0.7'
  l_tol = 1e-04
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
  csv = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/modular_gap_heat_transfer_mortar.i)

[Mesh]
  [file]
    type = FileMeshGenerator
    file = 2blk-gap.e
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '101'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
    input = file
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '100'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
    input = secondary
  []
[]

[Problem]
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Variables]
  [temp]
    order = FIRST
    family = LAGRANGE
    block = '1 2'
  []

  [lm]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  []
[]

[Materials]
  [left]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1000
    specific_heat = 1
  []

  [right]
    type = HeatConductionMaterial
    block = 2
    thermal_conductivity = 500
    specific_heat = 1
  []
[]

[Kernels]
  [hc]
    type = HeatConduction
    variable = temp
    use_displaced_mesh = false
    block = '1 2'
  []
[]

[UserObjects]
  [simple]
    type = GapFluxModelSimple
    k = 100
    temperature = temp
    boundary = 100
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = temp
    primary_boundary = 100
    primary_subdomain = 10000
    secondary_boundary = 101
    secondary_subdomain = 10001
    gap_flux_models = simple
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = temp
    boundary = 'left'
    value = 1
  []

  [right]
    type = DirichletBC
    variable = temp
    boundary = 'right'
    value = 0
  []
[]

[Preconditioning]
  [fmp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  nl_rel_tol = 1e-11
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/heat_conduction/3d_quadrature_gap_heat_transfer/nonmatching.i)

[Mesh]
  file = nonmatching.e
[]

[Variables]
  [./temp]
  [../]
[]

[Kernels]
  [./hc]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temp
    boundary = leftleft
    value = 1000
  [../]
  [./right]
    type = DirichletBC
    variable = temp
    boundary = rightright
    value = 400
  [../]
[]

[ThermalContact]
  [./left_to_right]
    secondary = leftright
    quadrature = true
    primary = rightleft
    variable = temp
    emissivity_primary = 0
    emissivity_secondary = 0
    type = GapHeatTransfer
  [../]
[]

[Materials]
  [./hcm]
    type = HeatConductionMaterial
    block = 'left right'
    specific_heat = 1
    thermal_conductivity = 1
  [../]
[]

[Postprocessors]
  [./left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = leftright
    diffusivity = thermal_conductivity
  [../]
  [./right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = rightleft
    diffusivity = thermal_conductivity
  [../]
[]

[Executioner]
  type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/recover/recover.i)

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  file = recover_in.e
  coord_type = RZ
[]

[Variables]
  [./temp]
    initial_condition = 580.0
  [../]
[]

[AuxVariables]
  [./gap_cond]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./heat_source]
    type = BodyForce
    variable = temp
    block = pellet_type_1
    value = 1e3
    function = 't'
  [../]
[]

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 5
    secondary = 10
    emissivity_primary = 0
    emissivity_secondary = 0
    quadrature = true
  [../]
[]

[BCs]
  [./outside]
    type = DirichletBC
    value = 580
    boundary = '1 2 3'
    variable = temp
  [../]
  [./edge]
    type = DirichletBC
    value = 700
    boundary = 10
    variable = temp
  [../]
[]

[Materials]
  [./thermal_3]
    type = HeatConductionMaterial
    block = 3
    thermal_conductivity = 5
    specific_heat = 12
  [../]
  [./thermal_1]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 16.0
    specific_heat = 330.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = ' lu       superlu_dist'

  nl_rel_tol = 1e-9
  nl_abs_tol = 1e-11

  start_time = -200
  n_startup_steps = 1
  end_time = 1.02e5
  num_steps = 10

  dtmax = 2e6
  dtmin = 1

  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 2.0e2
    optimal_iterations = 15
    iteration_window = 2
  [../]

  [./Quadrature]
    order = FIFTH
    side_order = SEVENTH
  [../]
[]

[Postprocessors]
  [./ave_temp_interior]
     type = SideAverageValue
     boundary = 9
     variable = temp
     execute_on = 'initial linear'
  [../]
  [./avg_clad_temp]
    type = SideAverageValue
    boundary = 7
    variable = temp
    execute_on = 'initial timestep_end'
  [../]
  [./flux_from_clad]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 5
    diffusivity = thermal_conductivity
  [../]
  [./_dt]
    type = TimestepSize
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/code_verification/cylindrical_test_no2.i)

# Problem II.2
#
# The thermal conductivity of an infinitely long hollow tube varies
# linearly with temperature. It is exposed on the inner
# and outer surfaces to constant temperatures.
#
# REFERENCE:
# A. Toptan, et al. (Mar.2020). Tech. rep. CASL-U-2020-1939-000, SAND2020-3887 R. DOI:10.2172/1614683.

[Mesh]
  [./geom]
    type = GeneratedMeshGenerator
    dim = 1
    elem_type = EDGE2
    xmin = 0.2
    nx = 4
  [../]
  coord_type = RZ
[]

[Variables]
  [./u]
    order = FIRST
  [../]
[]

[Functions]
  [./exact]
    type = ParsedFunction
    symbol_names = 'ri ro beta ki ko ui uo'
    symbol_values = '0.2 1.0 1e-3 5.3 5 300 0'
    expression = 'uo+(ko/beta)* ( ( 1 + beta*(ki+ko)*(ui-uo)*( log(x/ro) / log(ri/ro) )/(ko^2))^0.5 -1 )'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = u
  [../]
[]

[BCs]
  [./ui]
    type = DirichletBC
    boundary = left
    variable = u
    value = 300
  [../]
  [./uo]
    type = DirichletBC
    boundary = right
    variable = u
    value = 0
  [../]
[]

[Materials]
  [./property]
    type = GenericConstantMaterial
    prop_names = 'density specific_heat'
    prop_values = '1.0 1.0'
  [../]
  [./thermal_conductivity]
    type = ParsedMaterial
    property_name = 'thermal_conductivity'
    coupled_variables = u
    expression = '5 + 1e-3 * (u-0)'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = exact
    variable = u
  [../]
  [./h]
    type = AverageElementSize
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/radiation_transfer_action/radiative_transfer_no_action.i)

[Problem]
  kernel_coverage_check = false
[]

[Mesh]
  type = MeshGeneratorMesh

  [./cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1.3 1.9'
    ix = '3 3 3'
    dy = '2 1.2 0.9'
    iy = '3 3 3'
    subdomain_id = '0 1 0
                    4 5 2
                    0 3 0'
  [../]

  [./inner_bottom]
    type = SideSetsBetweenSubdomainsGenerator
    input = cmg
    primary_block = 1
    paired_block = 5
    new_boundary = 'inner_bottom'
  [../]

  [./inner_left]
    type = SideSetsBetweenSubdomainsGenerator
    input = inner_bottom
    primary_block = 4
    paired_block = 5
    new_boundary = 'inner_left'
  [../]

  [./inner_right]
    type = SideSetsBetweenSubdomainsGenerator
    input = inner_left
    primary_block = 2
    paired_block = 5
    new_boundary = 'inner_right'
  [../]

  [./inner_top]
    type = SideSetsBetweenSubdomainsGenerator
    input = inner_right
    primary_block = 3
    paired_block = 5
    new_boundary = 'inner_top'
  [../]

  [./rename]
    type = RenameBlockGenerator
    old_block = '1 2 3 4'
    new_block = '0 0 0 0'
    input = inner_top
  [../]

  [./split_inner_bottom]
    type = PatchSidesetGenerator
    boundary = 4
    n_patches = 2
    partitioner = centroid
    centroid_partitioner_direction = x
    input = rename
  [../]

  [./split_inner_left]
    type = PatchSidesetGenerator
    boundary = 5
    n_patches = 2
    partitioner = centroid
    centroid_partitioner_direction = y
    input = split_inner_bottom
  [../]

  [./split_inner_right]
    type = PatchSidesetGenerator
    boundary = 6
    n_patches = 2
    partitioner = centroid
    centroid_partitioner_direction = y
    input = split_inner_left
  [../]

  [./split_inner_top]
    type = PatchSidesetGenerator
    boundary = 7
    n_patches = 3
    partitioner = centroid
    centroid_partitioner_direction = x
    input = split_inner_right
  [../]
[]

[Variables]
  [./temperature]
    block = 0
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temperature
    block = 0
    diffusion_coefficient = 5
  [../]
[]

[UserObjects]
  [./gray_lambert]
    type = ViewFactorObjectSurfaceRadiation
    boundary = 'inner_bottom_0 inner_bottom_1
                inner_left_0 inner_left_1
                inner_right_0 inner_right_1
                inner_top_0 inner_top_1 inner_top_2'
    fixed_temperature_boundary = 'inner_bottom_0 inner_bottom_1'
    fixed_boundary_temperatures = '1200          1200'
    adiabatic_boundary = 'inner_top_0 inner_top_1 inner_top_2'
    emissivity = '0.9 0.9
                  0.8 0.8
                  0.4 0.4
                  1 1 1'
    temperature = temperature
    view_factor_object_name = view_factor
    execute_on = 'LINEAR TIMESTEP_END'
  [../]

  [./view_factor]
    type = UnobstructedPlanarViewFactor
    boundary = 'inner_bottom_0 inner_bottom_1
                inner_left_0 inner_left_1
                inner_right_0 inner_right_1
                inner_top_0 inner_top_1 inner_top_2'
    normalize_view_factor = true
    execute_on = 'INITIAL'
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 600
  [../]

  [./right]
    type = DirichletBC
    variable = temperature
    boundary = right
    value = 300
  [../]

  [./radiation]
    type = GrayLambertNeumannBC
    variable = temperature
    surface_radiation_object_name = gray_lambert
    boundary = 'inner_left_0 inner_left_1
                inner_right_0 inner_right_1'
  [../]
[]

[Postprocessors]
  [./average_T_inner_right]
    type = SideAverageValue
    variable = temperature
    boundary = inner_right
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_cylinder_mortar.i)

rpv_core_gap_size = 0.15

core_outer_radius = 2
rpv_inner_radius = '${fparse 2 + rpv_core_gap_size}'
rpv_outer_radius = '${fparse 2.5 + rpv_core_gap_size}'

rpv_outer_htc = 10 # W/m^2/K
rpv_outer_Tinf = 300 # K

core_blocks = '1'
rpv_blocks = '3'

[Mesh]
  [core_gap_rpv]
    type = ConcentricCircleMeshGenerator
    num_sectors = 10
    radii = '${core_outer_radius} ${rpv_inner_radius} ${rpv_outer_radius}'
    rings = '2 1 2'
    has_outer_square = false
    preserve_volumes = true
    portion = full
  []
  [rename_core_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = core_gap_rpv
    primary_block = 1
    paired_block = 2
    new_boundary = 'core_outer'
  []
  [rename_inner_rpv_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = rename_core_bdy
    primary_block = 3
    paired_block = 2
    new_boundary = 'rpv_inner'
  []
  [2d_mesh]
    type = BlockDeletionGenerator
    input = rename_inner_rpv_bdy
    block = 2
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'rpv_inner'
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    input = 2d_mesh
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'core_outer'
    new_block_id = 10000
    new_block_name = 'primary_lower'
    input = secondary
  []
  allow_renumbering = false
[]

[Variables]
  [Tsolid]
    initial_condition = 500
  []
  [lm]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  []
[]

[Kernels]
  [heat_source]
    type = CoupledForce
    variable = Tsolid
    block = '${core_blocks}'
    v = power_density
  []
  [heat_conduction]
    type = HeatConduction
    variable = Tsolid
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = Tsolid
    boundary = 'outer' # outer RPV
    coefficient = ${rpv_outer_htc}
    T_infinity = ${rpv_outer_Tinf}
  []
[]

[UserObjects]
  [radiation]
    type = GapFluxModelRadiation
    temperature = Tsolid
    boundary = 'rpv_inner'
    primary_emissivity = 0.8
    secondary_emissivity = 0.8
  []
  [conduction]
    type = GapFluxModelConduction
    temperature = Tsolid
    boundary = 'rpv_inner'
    gap_conductivity = 0.1
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = Tsolid
    primary_boundary = 'core_outer'
    primary_subdomain = 10000
    secondary_boundary = 'rpv_inner'
    secondary_subdomain = 10001
    gap_flux_models = 'radiation conduction'
    gap_geometry_type = 'CYLINDER'
  []
[]

[AuxVariables]
  [power_density]
    block = '${core_blocks}'
    initial_condition = 50e3
  []
[]

[Materials]
  [simple_mat]
    type = HeatConductionMaterial
    thermal_conductivity = 34.6 # W/m/K
  []
[]

[Postprocessors]
  [Tcore_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Trpv_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = '${core_blocks}'
  []
  [rpv_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = Tsolid
    boundary = 'outer' # outer RVP
    T_fluid = ${rpv_outer_Tinf}
    htc = ${rpv_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(rpv_convective_out - ptot) / ptot'
    pp_names = 'rpv_convective_out ptot'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = 'rpv_inner core_outer'
    variable = 'Tsolid'
  []
[]

[Executioner]
  type = Steady

  petsc_options = '-snes_converged_reason -pc_svd_monitor'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = ' lu       superlu_dist                  1e-5          NONZERO               1e-15'
  snesmf_reuse_base = false

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_max_its = 100

  line_search = none
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/heat_transfer/test/tests/radiative_bcs/radiative_bc_cyl.i)

#
# Thin cylindrical shell with very high thermal conductivity
# so that temperature is almost uniform at 500 K. Radiative
# boundary conditions is applied. Heat flux out of boundary
# 'right' should be 3723.36; this is approached as the mesh
# is refined
#

[Mesh]
  type = MeshGeneratorMesh
  [./cartesian]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1'
    ix = '1 10'
    dy = '1 1'
    subdomain_id = '1 2 1 2'
  [../]

  [./remove_1]
    type = BlockDeletionGenerator
    block = 1
    input = cartesian
  [../]

  [./readd_left]
    type = ParsedGenerateSideset
    combinatorial_geometry = 'abs(x - 1) < 1e-4'
    new_sideset_name = left
    input = remove_1
  [../]
  coord_type = RZ
[]

[Variables]
  [./temp]
    initial_condition = 800.0
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./lefttemp]
    type = DirichletBC
    boundary = left
    variable = temp
    value = 800
  [../]

  [./radiative_bc]
    type = InfiniteCylinderRadiativeBC
    boundary = right
    variable = temp
    boundary_radius = 2
    boundary_emissivity = 0.2
    cylinder_radius = 3
    cylinder_emissivity = 0.7
    Tinfinity = 500
  [../]
[]

[Materials]
  [./density]
    type = GenericConstantMaterial
    prop_names = 'density  thermal_conductivity'
    prop_values = '1 1.0e5'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Steady
  petsc_options = '-snes_converged_reason'
  line_search = none
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-7
[]

[Postprocessors]
  [./right]
    type = SideDiffusiveFluxAverage
    variable = temp
    boundary = right
    diffusivity = thermal_conductivity
  [../]

  [./min_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = min
  [../]

  [./max_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = max
  [../]
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/convective_heat_flux/flux.i)

# This is a test of the ConvectiveHeatFluxBC.
# There is a single 1x1 element with a prescribed temperature
# on the left side and a convective flux BC on the right side.
# The temperature on the left is 100, and the far-field temp is 200.
# The conductance of the body (conductivity * length) is 10
#
# If the conductance in the BC is also 10, the temperature on the
# right side of the solid element should be 150 because half of the
# temperature drop should occur over the body and half in the BC.
#
# The integrated flux is deltaT * conductance, or -50 * 10 = -500.
# The negative sign indicates that heat is going into the body.

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[Problem]
  extra_tag_vectors = 'bcs'
[]

[Variables]
  [./temp]
    initial_condition = 100.0
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temp
    diffusion_coefficient = 10
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 100.0
  [../]
  [./right]
    type = ConvectiveHeatFluxBC
    variable = temp
    boundary = right
    T_infinity = 200.0
    heat_transfer_coefficient = 10
    heat_transfer_coefficient_dT = 0
  [../]
[]

[Postprocessors]
  [./right_flux]
    type = SideDiffusiveFluxAverage
    variable = temp
    boundary = right
    diffusivity = 10
  [../]
[]

[Executioner]
  type = Transient

  num_steps = 1.0
  nl_rel_tol = 1e-12
[]

[Outputs]
  csv = true
[]

(modules/combined/test/tests/elastic_thermal_patch/elastic_thermal_patch_rz.i)

#
# This problem is modified from the Abaqus verification manual:
#   "1.5.4 Patch test for axisymmetric elements"
# The original stress solution is given as:
#   xx = yy = zz = 2000
#   xy = 400
#
# Here, E=1e6 and nu=0.25.
# However, with a +100 degree change in temperature and a coefficient
#   of thermal expansion of 1e-6, the solution becomes:
#   xx = yy = zz = 1800
#   xy = 400
#   since
#   E*(1-nu)/(1+nu)/(1-2*nu)*(1+2*nu/(1-nu))*(1e-3-1e-4) = 1800
#
# Also,
#
#   dSrr   dSrz   Srr-Stt
#   ---- + ---- + ------- + br = 0
#    dr     dz       r
#
# and
#
#   dSrz   Srz   dSzz
#   ---- + --- + ---- + bz = 0
#    dr     r     dz
#
# where
#   Srr = stress in rr
#   Szz = stress in zz
#   Stt = stress in theta-theta
#   Srz = stress in rz
#   br  = body force in r direction
#   bz  = body force in z direction
#
[GlobalParams]
  displacements = 'disp_x disp_y'
  temperature = temp
  volumetric_locking_correction = true
[]

[Mesh]
  file = elastic_thermal_patch_rz_test.e
  coord_type = RZ
[]

[Functions]
  [./ur]
    type = ParsedFunction
    expression = '1e-3*x'
  [../]
  [./uz]
    type = ParsedFunction
    expression = '1e-3*(x+y)'
  [../]
  [./body]
    type = ParsedFunction
    expression = '-400/x'
  [../]
  [./temp]
    type = ParsedFunction
    expression = '117.56+100*t'
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]

  [./temp]
    initial_condition = 117.56
  [../]
[]

[Physics/SolidMechanics/QuasiStatic/All]
  add_variables = true
  strain = SMALL
  incremental = true
  eigenstrain_names = eigenstrain
  generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_yz stress_zx'
[]

[Kernels]
  [./body]
    type = BodyForce
    variable = disp_y
    value = 1
    function = body
  [../]

  [./heat]
    type = HeatConduction
    variable = temp
  [../]
[]

[BCs]
  [./ur]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 10
    function = ur
  [../]
  [./uz]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 10
    function = uz
  [../]

  [./temp]
    type = FunctionDirichletBC
    variable = temp
    boundary = 10
    function = temp
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    lambda = 400000.0
    poissons_ratio = 0.25
  [../]
  [./thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 1e-6
    stress_free_temperature = 117.56
    eigenstrain_name = eigenstrain
  [../]
  [./stress]
    type = ComputeStrainIncrementBasedStress
  [../]

  [./heat]
    type = HeatConductionMaterial
    specific_heat = 0.116
    thermal_conductivity = 4.85e-4
  [../]

  [./density]
    type = Density
    density = 0.283
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  nl_abs_tol = 1e-11
  nl_rel_tol = 1e-12

  l_max_its = 20

  start_time = 0.0
  dt = 1.0
  num_steps = 1
  end_time = 1.0
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/thermal_test.i)

vol_frac = 0.4
cost_frac = 10.0

power = 2.0

E0 = 1.0e-6
E1 = 1.0

rho0 = 0.0
rho1 = 1.0

C0 = 1.0e-6
C1 = 1.0

TC0 = 1.0e-16
TC1 = 1.0

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = 0
    xmax = 40
    ymin = 0
    ymax = 40
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push_left]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push_left
    coord = '16 0 0'
  []
  [push_center]
    type = ExtraNodesetGenerator
    input = push_left
    new_boundary = push_center
    coord = '24 0 0'
  []
  [extra]
    type = SideSetsFromBoundingBoxGenerator
    input = push_center
    bottom_left = '-0.01 17.999  0'
    top_right = '5 22.001  0'
    boundary_new = n1
    included_boundaries = left
  []
  [dirichlet_bc]
    type = SideSetsFromNodeSetsGenerator
    input = extra
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 100.0
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [Cc]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [Tc]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [Cost]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = FIRST
    initial_condition = ${vol_frac}
  []
[]

[AuxKernels]
  [Cost]
    type = MaterialRealAux
    variable = Cost
    property = Cost_mat
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
    diffusion_coefficient = thermal_cond
  []
  [heat_source]
    type = HeatSource
    value = 1e-2 # W/m^3
    variable = temp
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_x_symm]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [left_n1]
    type = DirichletBC
    variable = temp
    boundary = n1
    value = 0.0
  []
  [top]
    type = NeumannBC
    variable = temp
    boundary = top
    value = 0
  []
  [bottom]
    type = NeumannBC
    variable = temp
    boundary = bottom
    value = 0
  []
  [right]
    type = NeumannBC
    variable = temp
    boundary = right
    value = 0
  []
  [left]
    type = NeumannBC
    variable = temp
    boundary = left
    value = 0
  []
[]

[NodalKernels]
  [push_left]
    type = NodalGravity
    variable = disp_y
    boundary = push_left
    gravity_value = 0.0 # -1e-8
    mass = 1
  []
  [push_center]
    type = NodalGravity
    variable = disp_y
    boundary = push_center
    gravity_value = 0.0 # -1e-8
    mass = 1
  []
[]

[Materials]
  [thermal_cond]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${TC0}-${TC1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${TC0}-A1*${rho0}^${power}; TC1:=A1*mat_den^${power}+B1; TC1"
    coupled_variables = 'mat_den'
    property_name = thermal_cond
    outputs = 'exodus'
  []
  [thermal_compliance]
    type = ThermalCompliance
    temperature = temp
    thermal_conductivity = thermal_cond
    outputs = 'exodus'
  []
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; E1"
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [Cost_mat]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${C0}-${C1})/(${rho0}^(1/${power})-${rho1}^(1/${power})); "
                 "B1:=${C0}-A1*${rho0}^(1/${power}); C1:=A1*mat_den^(1/${power})+B1; C1"
    coupled_variables = 'mat_den'
    property_name = Cost_mat
  []
  [CostDensity]
    type = ParsedMaterial
    property_name = CostDensity
    coupled_variables = 'mat_den Cost'
    expression = 'mat_den*Cost'
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
  [cc]
    type = CostSensitivity
    design_density = mat_den
    cost = Cost_mat
    outputs = 'exodus'
  []
  [tc]
    type = ThermalSensitivity
    design_density = mat_den
    thermal_conductivity = thermal_cond
    temperature = temp
    outputs = 'exodus'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 0.1
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_cost]
    type = RadialAverage
    radius = 0.1
    weights = linear
    prop_name = cost_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_thermal]
    type = RadialAverage
    radius = 0.1
    weights = linear
    prop_name = thermal_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [update]
    type = DensityUpdateTwoConstraints
    density_sensitivity = Dc
    cost_density_sensitivity = Cc
    cost = Cost
    cost_fraction = ${cost_frac}
    design_density = mat_den
    volume_fraction = ${vol_frac}

    bisection_lower_bound = 0
    bisection_upper_bound = 1.0e12 # 100

    use_thermal_compliance = true
    thermal_sensitivity = Tc
    weight_mechanical_thermal = '0 1'

    relative_tolerance = 1.0e-12
    bisection_move = 0.015
    adaptive_move = false
    execute_on = TIMESTEP_BEGIN
  []
  # Provides Dc
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Cc
  [calc_sense_cost]
    type = SensitivityFilter
    density_sensitivity = Cc
    design_density = mat_den
    filter_UO = rad_avg_cost
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Tc
  [calc_sense_thermal]
    type = SensitivityFilter
    density_sensitivity = Tc
    design_density = mat_den
    filter_UO = rad_avg_thermal
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-12
  dt = 1.0
  num_steps = 5
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [right_flux]
    type = SideDiffusiveFluxAverage
    variable = temp
    boundary = right
    diffusivity = 10
  []
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
  [cost_sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = cost_sensitivity
  []
  [cost]
    type = ElementIntegralMaterialProperty
    mat_prop = CostDensity
  []
  [cost_frac]
    type = ParsedPostprocessor
    expression = 'cost / mesh_volume'
    pp_names = 'cost mesh_volume'
  []
  [objective]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [objective_thermal]
    type = ElementIntegralMaterialProperty
    mat_prop = thermal_compliance
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]