- variableThe name of the variable that this boundary condition applies to
C++ Type:NonlinearVariableName

Description:The name of the variable that this boundary condition applies to

- boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector

Description:The list of boundary IDs from the mesh where this boundary condition applies

# GapHeatTransfer

Transfers heat across a gap between two surfaces dependant on the gap geometry specified.

## Description

GapHeatTransfer calculates the amount of heat transferred across unmeshed gaps between two different blocks.

The `quadrature`

option is generally recommended for most models. With this option, heat flux is computed and applied as an integrated boundary condition at the quadrature points on both faces. Use of the quadrature options generally gives smoother results, although there can be small differences in the heat flux on the two surfaces.

It is also important to use the appropriate `gap_geometry_type`

parameter (PLATE, CYLINDER, or SPHERE) for the model geometry.

Two-dimensional Cartesian geometries are not restricted to be in or parallel to the X-Y coordinate plane.

## Example Input syntax

```
[ThermalContact]
[./left_to_right]
slave = leftright
quadrature = true
master = rightleft
variable = temp
type = GapHeatTransfer
[../]
[]
```

(modules/heat_conduction/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/nonmatching.i)#### /opt/civet/build_0/moose/modules/heat_conduction/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]
slave = leftright
quadrature = true
master = 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 = SideFluxIntegral
variable = temp
boundary = leftright
diffusivity = thermal_conductivity
[../]
[./right]
type = SideFluxIntegral
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
[]
```

## Input Parameters

- gap_tempTemperature on the other side of the gap
C++ Type:std::vector

Options:

Description:Temperature on the other side of the gap

- disp_yThe y displacement
C++ Type:std::vector

Options:

Description:The y displacement

- gap_geometry_typeGap calculation type. Choices are: PLATE CYLINDER SPHERE
C++ Type:MooseEnum

Options:PLATE CYLINDER SPHERE

Description:Gap calculation type. Choices are: PLATE CYLINDER SPHERE

- disp_zThe z displacement
C++ Type:std::vector

Options:

Description:The z displacement

- min_gap1e-06A minimum gap size
Default:1e-06

C++ Type:double

Options:

Description:A minimum gap size

- disp_xThe x displacement
C++ Type:std::vector

Options:

Description:The x displacement

- warningsFalseWhether to output warning messages concerning nodes not being found
Default:False

C++ Type:bool

Options:

Description:Whether to output warning messages concerning nodes not being found

- appended_property_nameName appended to material properties to make them unique
C++ Type:std::string

Options:

Description:Name appended to material properties to make them unique

- max_gap1e+06A maximum gap size
Default:1e+06

C++ Type:double

Options:

Description:A maximum gap size

- quadratureFalseWhether or not to do Quadrature point based gap heat transfer. If this is true then gap_distance and gap_temp should NOT be provided (and will be ignored) however paired_boundary IS then required.
Default:False

C++ Type:bool

Options:

Description:Whether or not to do Quadrature point based gap heat transfer. If this is true then gap_distance and gap_temp should NOT be provided (and will be ignored) however paired_boundary IS then required.

- paired_boundaryThe boundary to be penetrated
C++ Type:BoundaryName

Options:

Description:The boundary to be penetrated

- sphere_originOrigin for sphere geometry
C++ Type:libMesh::VectorValue

Options:

Description:Origin for sphere geometry

- gap_distanceDistance across the gap
C++ Type:std::vector

Options:

Description:Distance across the gap

- cylinder_axis_point_1Start point for line defining cylindrical axis
C++ Type:libMesh::VectorValue

Options:

Description:Start point for line defining cylindrical axis

- cylinder_axis_point_2End point for line defining cylindrical axis
C++ Type:libMesh::VectorValue

Options:

Description:End point for line defining cylindrical axis

- orderFIRSTThe finite element order
Default:FIRST

C++ Type:MooseEnum

Options:CONSTANT FIRST SECOND THIRD FOURTH

Description:The finite element order

- displacementsThe displacements appropriate for the simulation geometry and coordinate system
C++ Type:std::vector

Options:

Description:The displacements appropriate for the simulation geometry and coordinate system

### Optional Parameters

- enableTrueSet the enabled status of the MooseObject.
Default:True

C++ Type:bool

Options:

Description:Set the enabled status of the MooseObject.

- save_inThe name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector

Options:

Description:The name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

- use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False

C++ Type:bool

Options:

Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector

Options:

Description:Adds user-defined labels for accessing object parameters via control logic.

- seed0The seed for the master random number generator
Default:0

C++ Type:unsigned int

Options:

Description:The seed for the master random number generator

- diag_save_inThe name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector

Options:

Description:The name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

- implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True

C++ Type:bool

Options:

Description:Determines whether this object is calculated using an implicit or explicit form

### Advanced Parameters

- vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime

C++ Type:MultiMooseEnum

Options:nontime time

Description:The tag for the vectors this Kernel should fill

- extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector

Options:

Description:The extra tags for the vectors this Kernel should fill

- matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system

C++ Type:MultiMooseEnum

Options:nontime system

Description:The tag for the matrices this Kernel should fill

- extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector

Options:

Description:The extra tags for the matrices this Kernel should fill

### Tagging Parameters

## Input Files

- modules/heat_conduction/test/tests/heat_conduction/3d_quadrature_gap_heat_transfer/second.i
- modules/combined/test/tests/gap_heat_transfer_convex/gap_heat_transfer_convex_sm.i
- modules/combined/test/tests/generalized_plane_strain_tm_contact/generalized_plane_strain_tm_contact.i
- modules/combined/test/tests/gap_heat_transfer_htonly/cyl3D.i
- modules/heat_conduction/test/tests/recover/recover.i
- modules/combined/test/tests/gap_heat_transfer_htonly/planar_yz.i
- modules/heat_conduction/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/nonmatching.i
- modules/heat_conduction/test/tests/meshed_gap_thermal_contact/meshed_gap_thermal_contact.i
- modules/heat_conduction/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/second_order.i
- modules/heat_conduction/test/tests/meshed_gap_thermal_contact/meshed_annulus_thermal_contact.i
- modules/combined/test/tests/gap_heat_transfer_convex/gap_heat_transfer_convex.i
- modules/combined/test/tests/gap_heat_transfer_htonly/planar_xz.i
- modules/combined/test/tests/gap_heat_transfer_htonly/gap_heat_transfer_htonly_test.i
- modules/combined/test/tests/gap_heat_transfer_htonly/cyl2D_yz.i
- modules/heat_conduction/test/tests/heat_conduction/3d_quadrature_gap_heat_transfer/moving.i
- modules/combined/test/tests/gap_heat_transfer_htonly/gap_heat_transfer_htonly_rspherical.i
- modules/heat_conduction/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/perfectQ9.i
- modules/heat_conduction/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/perfectQ8.i
- modules/heat_conduction/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/moving.i
- modules/combined/test/tests/gap_heat_transfer_htonly/sphere3D.i
- modules/heat_conduction/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/gap_conductivity_property.i
- modules/combined/test/tests/gap_heat_transfer_htonly/planar_xy.i
- modules/combined/test/tests/gap_heat_transfer_htonly/gap_heat_transfer_htonly_it_plot_test.i
- modules/combined/test/tests/gap_heat_transfer_htonly/cyl2D.i
- modules/combined/test/tests/gap_heat_transfer_htonly/cyl2D_xz.i
- modules/heat_conduction/test/tests/heat_conduction/2d_quadrature_gap_heat_transfer/perfect.i
- modules/combined/test/tests/gap_heat_transfer_htonly/gap_heat_transfer_htonly_rz_test.i
- modules/combined/test/tests/gap_heat_transfer_radiation/gap_heat_transfer_radiation_test.i
- modules/heat_conduction/test/tests/heat_conduction/3d_quadrature_gap_heat_transfer/nonmatching.i
- modules/combined/test/tests/gap_heat_transfer_htonly/sphere2DRZ.i

#### modules/heat_conduction/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]
slave = leftright
quadrature = true
master = rightleft
variable = temp
type = GapHeatTransfer
order = SECOND
[../]
[]
[Materials]
[./hcm]
type = HeatConductionMaterial
block = 'left right'
specific_heat = 1
thermal_conductivity = 1
[../]
[]
[Postprocessors]
[./left]
type = SideFluxIntegral
variable = temp
boundary = leftright
diffusivity = thermal_conductivity
[../]
[./right]
type = SideFluxIntegral
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/combined/test/tests/gap_heat_transfer_convex/gap_heat_transfer_convex_sm.i

```
[Mesh]
file = gap_heat_transfer_convex.e
displacements = 'disp_x disp_y disp_z'
[]
[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
master = 2
slave = 3
[../]
[]
[SolidMechanics]
[./solid]
disp_x = disp_x
disp_y = disp_y
disp_z = disp_z
[../]
[]
[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]
[./dummy]
type = Elastic
block = '1 2'
disp_x = disp_x
disp_y = disp_y
disp_z = disp_z
youngs_modulus = 1e6
poissons_ratio = .3
temp = temp
thermal_expansion = 0
[../]
[./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
disp_x = disp_x
disp_y = disp_y
disp_z = disp_z
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
start_time = 0.0
dt = 0.1
end_time = 2.0
[]
[Outputs]
file_base = gap_heat_transfer_convex_out
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
[../]
[]
[Modules]
[./TensorMechanics]
[./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
value = '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 = FunctionPresetBC
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]
master = 8
slave = 2
penalty = 1e+10
normalize_penalty = true
system = Constraint
tangential_tolerance = .1
normal_smoothing_distance = .1
model = frictionless
formulation = kinematic
[../]
[]
[ThermalContact]
[./thermal]
type = GapHeatTransfer
master = 8
slave = 2
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'
[../]
[]
[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/combined/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 slave (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
master = 3
slave = 2
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 = FunctionPresetBC
boundary = 5
variable = temp
function = temp
[../]
[./temp_far_right]
type = PresetBC
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 = SideFluxIntegral
variable = temp
boundary = 2
diffusivity = thermal_conductivity
[../]
[./flux_right]
type = SideFluxIntegral
variable = temp
boundary = 3
diffusivity = thermal_conductivity
[../]
[]
```

#### modules/heat_conduction/test/tests/recover/recover.i

```
[GlobalParams]
order = SECOND
family = LAGRANGE
[]
[Problem]
coord_type = RZ
[]
[Mesh]
file = recover_in.e
[]
[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 = 1e-2
function = 't'
[../]
[]
[ThermalContact]
[./thermal_contact]
type = GapHeatTransfer
variable = temp
master = 5
slave = 10
quadrature = true
[../]
[]
[BCs]
[./outside]
type = DirichletBC
value = 580
boundary = '1 2 3'
variable = temp
[../]
[./edge]
type = PresetBC
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 = SideFluxIntegral
variable = temp
boundary = 5
diffusivity = thermal_conductivity
execute_on = timestep_end
[../]
[./_dt]
type = TimestepSize
execute_on = timestep_end
[../]
[]
[Outputs]
exodus = true
[./console]
type = Console
max_rows = 25
[../]
[]
```

#### modules/combined/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 = simple_2D.e
[]
[MeshModifiers]
[./rotate]
type = Transform
transform = ROTATE
vector_value = '0 90 90'
[../]
[]
[Functions]
[./temp]
type = PiecewiseLinear
x = '0 1 2'
y = '100 200 200'
[../]
[]
[ThermalContact]
[./thermal_contact]
type = GapHeatTransfer
variable = temp
master = 3
slave = 2
[../]
[]
[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 = FunctionPresetBC
boundary = 1
variable = temp
function = temp
[../]
[./temp_far_top]
type = PresetBC
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 = Density
block = '1 2'
density = 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 = SideFluxIntegral
variable = temp
boundary = 2
diffusivity = thermal_conductivity
execute_on = 'initial timestep_end'
[../]
[./flux_top]
type = SideFluxIntegral
variable = temp
boundary = 3
diffusivity = thermal_conductivity
execute_on = 'initial timestep_end'
[../]
[]
[Outputs]
[./out]
type = Exodus
output_dimension = 3
[../]
[]
```

#### modules/heat_conduction/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]
slave = leftright
quadrature = true
master = 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 = SideFluxIntegral
variable = temp
boundary = leftright
diffusivity = thermal_conductivity
[../]
[./right]
type = SideFluxIntegral
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/heat_conduction/test/tests/meshed_gap_thermal_contact/meshed_gap_thermal_contact.i

```
[Mesh]
type = FileMesh
file = meshed_gap.e
dim = 2
[]
[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
master = 2
slave = 3
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_conduction/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]
slave = leftright
quadrature = true
master = rightleft
variable = temp
type = GapHeatTransfer
order = SECOND
[../]
[]
[Materials]
[./hcm]
type = HeatConductionMaterial
block = 'left right'
specific_heat = 1
thermal_conductivity = 1
[../]
[]
[Postprocessors]
[./left]
type = SideFluxIntegral
variable = temp
boundary = leftright
diffusivity = thermal_conductivity
[../]
[./right]
type = SideFluxIntegral
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_conduction/test/tests/meshed_gap_thermal_contact/meshed_annulus_thermal_contact.i

```
[Mesh]
type = FileMesh
file = meshed_annulus.e
dim = 2
[]
[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
master = 2
slave = 3
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/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
master = 2
slave = 3
[../]
[]
[Modules/TensorMechanics/Master/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
disp_x = disp_x
disp_y = disp_y
disp_z = disp_z
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
start_time = 0.0
dt = 0.1
end_time = 2.0
[]
[Outputs]
exodus = true
[]
```

#### modules/combined/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 = simple_2D.e
[]
[MeshModifiers]
[./rotate]
type = Transform
transform = ROTATE
vector_value = '0 90 0'
[../]
[]
[Functions]
[./temp]
type = PiecewiseLinear
x = '0 1 2'
y = '100 200 200'
[../]
[]
[ThermalContact]
[./thermal_contact]
type = GapHeatTransfer
variable = temp
master = 3
slave = 2
[../]
[]
[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 = FunctionPresetBC
boundary = 1
variable = temp
function = temp
[../]
[./temp_far_top]
type = PresetBC
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 = Density
block = '1 2'
density = 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 = SideFluxIntegral
variable = temp
boundary = 2
diffusivity = thermal_conductivity
execute_on = 'initial timestep_end'
[../]
[./flux_top]
type = SideFluxIntegral
variable = temp
boundary = 3
diffusivity = thermal_conductivity
execute_on = 'initial timestep_end'
[../]
[]
[Outputs]
[./out]
type = Exodus
output_dimension = 3
[../]
[]
```

#### modules/combined/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
master = 3
slave = 2
[../]
[./awesomium_contact]
type = GapHeatTransfer
variable = awesomium
master = 3
slave = 2
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 = FunctionPresetBC
boundary = 1
variable = temp
function = temp
[../]
[./temp_far_right]
type = PresetBC
boundary = 4
variable = temp
value = 100
[../]
[./awesomium_far_left]
type = FunctionPresetBC
boundary = 1
variable = awesomium
function = temp
[../]
[./awesomium_far_right]
type = PresetBC
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 = Density
block = '1 2'
density = 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 = SideFluxIntegral
variable = temp
boundary = 2
diffusivity = thermal_conductivity
execute_on = 'initial timestep_end'
[../]
[./flux_right]
type = SideFluxIntegral
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 = SideFluxIntegral
variable = awesomium
boundary = 2
diffusivity = thermal_conductivity
execute_on = 'initial timestep_end'
[../]
[./awe_flux_right]
type = SideFluxIntegral
variable = awesomium
boundary = 3
diffusivity = thermal_conductivity
execute_on = 'initial timestep_end'
[../]
[]
[Outputs]
exodus = true
[]
```

#### modules/combined/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 = cyl2D.e
[]
[MeshModifiers]
[./rotate]
type = Transform
transform = ROTATE
vector_value = '0 90 90'
[../]
[]
[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
master = 3
slave = 2
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 = FunctionPresetBC
boundary = 1
variable = temp
function = temp
[../]
[./temp_far_right]
type = PresetBC
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]
[./out]
type = Exodus
output_dimension = 3
[../]
[./Console]
type = Console
[../]
[]
[Postprocessors]
[./temp_left]
type = SideAverageValue
boundary = 2
variable = temp
[../]
[./temp_right]
type = SideAverageValue
boundary = 3
variable = temp
[../]
[./flux_left]
type = SideFluxIntegral
variable = temp
boundary = 2
diffusivity = thermal_conductivity
[../]
[./flux_right]
type = SideFluxIntegral
variable = temp
boundary = 3
diffusivity = thermal_conductivity
[../]
[]
```

#### modules/heat_conduction/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
value = 0.1*t
[../]
[./left_temp]
type = ParsedFunction
value = 1000+t
[../]
[]
[Kernels]
[./hc]
type = HeatConduction
variable = temp
[../]
[]
[AuxKernels]
[./disp_y]
type = FunctionAux
variable = disp_y
function = disp_y
block = left
[../]
[]
[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
master = rightleft
slave = leftright
quadrature = true
[../]
[]
[Materials]
[./hcm]
type = HeatConductionMaterial
block = 'left right'
specific_heat = 1
thermal_conductivity = 1
use_displaced_mesh = true
[../]
[]
[Postprocessors]
[./left]
type = SideFluxIntegral
variable = temp
boundary = leftright
diffusivity = thermal_conductivity
[../]
[./right]
type = SideFluxIntegral
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/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 slave (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.
#
#
[Problem]
coord_type = RSPHERICAL
[]
[Mesh]
file = gap_heat_transfer_htonly_rspherical.e
construct_side_list_from_node_list = true
[]
[Functions]
[./temp]
type = PiecewiseLinear
x = '0 1 2'
y = '100 200 200'
[../]
[]
[ThermalContact]
[./thermal_contact]
type = GapHeatTransfer
variable = temp
master = 3
slave = 2
[../]
[]
[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 = FunctionPresetBC
boundary = 1
variable = temp
function = temp
[../]
[./temp_far_right]
type = PresetBC
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 = Density
block = '1 2'
density = 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 = SideFluxIntegral
variable = temp
boundary = 2
diffusivity = thermal_conductivity
[../]
[./flux_right]
type = SideFluxIntegral
variable = temp
boundary = 3
diffusivity = thermal_conductivity
[../]
[]
[Outputs]
exodus = true
[]
```

#### modules/heat_conduction/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]
slave = leftright
quadrature = true
master = rightleft
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/heat_conduction/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]
slave = leftright
quadrature = true
master = rightleft
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_conduction/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
value = 0.1*t
[../]
[./left_temp]
type = ParsedFunction
value = 1000+t
[../]
[]
[Kernels]
[./hc]
type = HeatConduction
variable = temp
[../]
[]
[AuxKernels]
[./disp_y]
type = FunctionAux
variable = disp_y
function = disp_y
block = left
[../]
[]
[BCs]
[./left]
type = FunctionDirichletBC
variable = temp
boundary = leftleft
function = left_temp
[../]
[./right]
type = DirichletBC
variable = temp
boundary = rightright
value = 400
[../]
[]
[ThermalContact]
[./left_to_right]
slave = leftright
quadrature = true
master = rightleft
variable = temp
type = GapHeatTransfer
[../]
[]
[Materials]
[./hcm]
type = HeatConductionMaterial
block = 'left right'
specific_heat = 1
thermal_conductivity = 1
use_displaced_mesh = true
[../]
[]
[Postprocessors]
[./left]
type = SideFluxIntegral
variable = temp
boundary = leftright
diffusivity = thermal_conductivity
[../]
[./right]
type = SideFluxIntegral
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/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 slave (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
master = 3
slave = 2
gap_conductivity = 1
quadrature = true
gap_geometry_type = SPHERE
sphere_origin = '0 0 0'
[../]
[]
[BCs]
[./mid]
type = FunctionPresetBC
boundary = 5
variable = temp
function = temp
[../]
[./temp_far_right]
type = PresetBC
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 = SideFluxIntegral
variable = temp
boundary = 2
diffusivity = thermal_conductivity
[../]
[./flux_right]
type = SideFluxIntegral
variable = temp
boundary = 3
diffusivity = thermal_conductivity
[../]
[]
```

#### modules/heat_conduction/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]
slave = leftright
quadrature = true
master = rightleft
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/combined/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
master = 3
slave = 2
[../]
[]
[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 = FunctionPresetBC
boundary = 1
variable = temp
function = temp
[../]
[./temp_far_top]
type = PresetBC
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 = Density
block = '1 2'
density = 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 = SideFluxIntegral
variable = temp
boundary = 2
diffusivity = thermal_conductivity
execute_on = 'initial timestep_end'
[../]
[./flux_top]
type = SideFluxIntegral
variable = temp
boundary = 3
diffusivity = thermal_conductivity
execute_on = 'initial timestep_end'
[../]
[]
[Outputs]
exodus = true
[]
```

#### modules/combined/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
master = 3
slave = 2
[../]
[]
[Variables]
[./temp]
order = FIRST
family = LAGRANGE
initial_condition = 100
[../]
[]
[Kernels]
[./heat]
type = HeatConduction
variable = temp
[../]
[]
[BCs]
[./temp_far_left]
type = FunctionPresetBC
boundary = 1
variable = temp
function = temp
[../]
[./temp_far_right]
type = PresetBC
boundary = 4
variable = temp
value = 100
[../]
[]
[Materials]
[./heat1]
type = HeatConductionMaterial
block = '1 2'
specific_heat = 1.0
thermal_conductivity = 100000000.0
[../]
[./density]
type = Density
block = '1 2'
density = 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 = SideFluxIntegral
variable = temp
boundary = 2
diffusivity = thermal_conductivity
[../]
[./flux_right]
type = SideFluxIntegral
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/combined/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 slave (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
master = 3
slave = 2
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 = FunctionPresetBC
boundary = 1
variable = temp
function = temp
[../]
[./temp_far_right]
type = PresetBC
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 = SideFluxIntegral
variable = temp
boundary = 2
diffusivity = thermal_conductivity
[../]
[./flux_right]
type = SideFluxIntegral
variable = temp
boundary = 3
diffusivity = thermal_conductivity
[../]
[]
```

#### modules/combined/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 = cyl2D.e
[]
[MeshModifiers]
[./rotate]
type = Transform
transform = ROTATE
vector_value = '0 90 0'
[../]
[]
[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
master = 3
slave = 2
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 = FunctionPresetBC
boundary = 1
variable = temp
function = temp
[../]
[./temp_far_right]
type = PresetBC
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]
[./out]
type = Exodus
output_dimension = 3
[../]
[./Console]
type = Console
[../]
[]
[Postprocessors]
[./temp_left]
type = SideAverageValue
boundary = 2
variable = temp
[../]
[./temp_right]
type = SideAverageValue
boundary = 3
variable = temp
[../]
[./flux_left]
type = SideFluxIntegral
variable = temp
boundary = 2
diffusivity = thermal_conductivity
[../]
[./flux_right]
type = SideFluxIntegral
variable = temp
boundary = 3
diffusivity = thermal_conductivity
[../]
[]
```

#### modules/heat_conduction/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]
slave = leftright
quadrature = true
master = rightleft
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/combined/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.
#
[Problem]
coord_type = RZ
rz_coord_axis = Y # this is modified through CLI args to test Z-R as opposed to R-Z
[]
[Mesh]
file = gap_heat_transfer_htonly_rz_test.e
[]
[MeshModifiers]
active = '' # this is modified through CLI args to test Z-R as opposed to R-Z
[rotate]
type = Transform
transform = ROTATE
vector_value = '90 0 0'
[]
[]
[Functions]
[./ramp]
type = PiecewiseLinear
x = '0 1 2'
y = '100 200 200'
[../]
[]
[ThermalContact]
[./thermal_contact]
type = GapHeatTransfer
variable = temp
master = 3
slave = 2
[../]
[./thermal_contact2]
type = GapHeatTransfer
variable = temp2
master = 3
slave = 2
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 = FunctionPresetBC
boundary = 1
variable = temp
function = ramp
[../]
[./temp_far_right]
type = PresetBC
boundary = 4
variable = temp
value = 100
[../]
[./temp_far_left2]
type = FunctionPresetBC
boundary = 1
variable = temp2
function = ramp
[../]
[./temp_far_right2]
type = PresetBC
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 = Density
block = '1 2'
density = 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 = SideFluxIntegral
variable = temp
boundary = 2
diffusivity = thermal_conductivity
[../]
[./flux_right]
type = SideFluxIntegral
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 = SideFluxIntegral
variable = temp2
boundary = 2
diffusivity = thermal_conductivity
[../]
[./flux_right2]
type = SideFluxIntegral
variable = temp2
boundary = 3
diffusivity = thermal_conductivity
[../]
[]
[Outputs]
exodus = true
[]
```

#### modules/combined/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
master = 3
slave = 2
gap_conductivity = 0.09187557
emissivity_1 = 0.5
emissivity_2 = 0.5
[../]
[]
[Materials]
[./heat1]
type = HeatConductionMaterial
block = '1 2'
specific_heat = 1.0
thermal_conductivity = 10000000.0
[../]
[./density]
type = Density
block = '1 2'
density = 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 = SideFluxIntegral
variable = temp
boundary = 2
diffusivity = thermal_conductivity
[../]
[./flux_right]
type = SideFluxIntegral
variable = temp
boundary = 3
diffusivity = thermal_conductivity
[../]
[]
[Outputs]
exodus = true
[]
```

#### modules/heat_conduction/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]
slave = leftright
quadrature = true
master = rightleft
variable = temp
type = GapHeatTransfer
[../]
[]
[Materials]
[./hcm]
type = HeatConductionMaterial
block = 'left right'
specific_heat = 1
thermal_conductivity = 1
[../]
[]
[Postprocessors]
[./left]
type = SideFluxIntegral
variable = temp
boundary = leftright
diffusivity = thermal_conductivity
[../]
[./right]
type = SideFluxIntegral
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/combined/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 slave (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
[]
[Problem]
coord_type = RZ
[]
[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
master = 3
slave = 2
gap_conductivity = 1
quadrature = true
gap_geometry_type = SPHERE
sphere_origin = '0 0 0'
[../]
[]
[BCs]
[./mid]
type = FunctionPresetBC
boundary = 1
variable = temp
function = temp
[../]
[./temp_far_right]
type = PresetBC
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 = SideFluxIntegral
variable = temp
boundary = 2
diffusivity = thermal_conductivity
[../]
[./flux_right]
type = SideFluxIntegral
variable = temp
boundary = 3
diffusivity = thermal_conductivity
[../]
[]
```