ADCoupledSimpleRadiativeHeatFluxBC

Radiative heat transfer boundary condition with the far field temperature, of an assumed black body, given by auxiliary variables and constant emissivity

Description

This boundary condition computes the radiative heat flux from the specified boundary to an assumed surrounding blackbody. This boundary condition accounts for the effect of different phases present in the body, such as multiple microstructure phases or precipitates, by summing the heat transfer as a function of the fraction of each phase:

$var element = document.getElementById("moose-equation-cf340ff1-35bd-4bac-a521-2b8c313cc8c7");katex.render(" \\dot{Q} = \\sum_i \\left[ \\alpha_i \\epsilon_i \\sigma \\left( T^4 - T^4_{infinity}\\right) \\right]", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-db914d2b-e3e2-401c-a978-9ab681cf7894");katex.render("\\alpha_i", element, {displayMode:false,throwOnError:false});$ is the fraction of the phases present in the body on the boundary, $var element = document.getElementById("moose-equation-bab73e3c-6fb8-4c3a-b368-b3921cc04989");katex.render("\\epsilon_i", element, {displayMode:false,throwOnError:false});$ is the emissivity of each component, and $var element = document.getElementById("moose-equation-7ae0ee72-b01a-4dcf-905f-afc0e75ed629");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ is the Boltzmann constant (Cangel and Boles, 2007). Note that the user is responsible for ensuring that the values of the $var element = document.getElementById("moose-equation-811bc0ba-0624-45ab-85fe-b09234affc11");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ components sum to unity.

Example Input File Syntax

[BCs<<<{"href": "../../syntax/BCs/index.html"}>>>]
  [heatloss]
    type = ADCoupledSimpleRadiativeHeatFluxBC<<<{"description": "Radiative heat transfer boundary condition with the far field temperature, of an assumed black body, given by auxiliary variables and constant emissivity", "href": "ADCoupledSimpleRadiativeHeatFluxBC.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = right
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = temperature
    T_infinity<<<{"description": "Field holding the far-field temperature for each component"}>>> = '293 293'
    emissivity<<<{"description": "The emissivity of the surface to which this boundary belongs"}>>> = '0.95 0.07'
    alpha<<<{"description": "Volume fraction of components"}>>> = '0.4 0.6'
  []
[]

Input Parameters

T_infinityField holding the far-field temperature for each component
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Field holding the far-field temperature for each component
boundaryThe list of boundary IDs from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundary IDs from the mesh where this object applies
emissivityThe emissivity of the surface to which this boundary belongs
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:The emissivity of the surface to which this boundary belongs
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

alpha1.0Volume fraction of components
Default:1.0
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Volume fraction of components
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
sigma5.67e-08The Stefan-Boltzmann constant
Default:5.67e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The Stefan-Boltzmann constant

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
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
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
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<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
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.)
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
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<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
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.)
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
skip_execution_outside_variable_domainFalseWhether to skip execution of this boundary condition when the variable it applies to is not defined on the boundary. This can facilitate setups with moving variable domains and fixed boundaries. Note that the FEProblem boundary-restricted integrity checks will also need to be turned off if using this option
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip execution of this boundary condition when the variable it applies to is not defined on the boundary. This can facilitate setups with moving variable domains and fixed boundaries. Note that the FEProblem boundary-restricted integrity checks will also need to be turned off if using this option
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
Controllable:No
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.

Advanced Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(test/tests/example_testing/sample_three.i)
(test/tests/bcs/radiation_heat_loss/simple_radiation.i)
(test/tests/example_testing/sample_one.i)
(test/tests/bcs/radiation_heat_loss/multiple_phases_simple_radiation.i)
(test/tests/example_testing/sample_four.i)
(test/tests/interfacekernels/thermal_conductance/thermal_interface.i)

References

YA Cangel and Michael A Boles. Thermodynamics: An Engineering Approach 6th Edition in SI Units. Singapore (SI): McGraw-Hill, 2007.

@book{cangel2002thermodynamics,
    author = "Cangel, YA and Boles, Michael A",
    title = "Thermodynamics: An Engineering Approach 6th Edition in SI Units",
    publisher = "Singapore (SI): McGraw-Hill",
    year = "2007"
}

(test/tests/bcs/radiation_heat_loss/multiple_phases_simple_radiation.i)

# This is a simple 3D test of the simplistic radiation heat transfer loss. The
# body to which the heat is lost is considered as a pure blackbody.
# A rectangular prism is set to a uniform temperature, 400K, while the absolute
# temperature of the surrounding assumed blackbody is set to 293K. The emissivity
# is assumed to be 0.95 for 0.4 of the body and 0.07 for the remaining 0.6 of the
# body. A high thermal conductivity is used to obtain a nearly uniform temperature
# through the body needed to match to analytical solution. The heat flux loss
# through the right boundary with this radiative heat transfer boundary condition
# is calculated.
#
# The analytical solution is:
# Q = \sum_i (\alpha_i \epsilon_i * \sigma * (T^4_{body} - T^4_{infinity}))
#   = 0.4 * 0.95 * 5.67e-8 * (400^4 - 293^4) + 0.6 * 0.07 * 5.67e-8 * (400^4 - 293^4)
#   = 436.1953 W

[Mesh]
  type = GeneratedMesh
  dim = 3
  xmax = 0.01
  ymax = 1.0
  zmax = 1.0
  nx = 10
  ny = 5
  nz = 5
[]

[Variables]
  [temperature]
    initial_condition = 400.0
  []
[]

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

[BCs]
  [heatloss]
    type = ADCoupledSimpleRadiativeHeatFluxBC
    boundary = right
    variable = temperature
    T_infinity = '293 293'
    emissivity = '0.95 0.07'
    alpha = '0.4 0.6'
  []
  [insulation]
    type = DirichletBC
    boundary = 'left'
    variable = temperature
    value = 400
  []
[]

[Materials]
  [density]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '1e3'
  []
[]

[Executioner]
  type = Steady
  line_search = none
[]

[Postprocessors]
  [right_temperature]
    type = SideAverageValue
    variable = temperature
    boundary = right
  []
  [right_heatflux]
    type = SideDiffusiveFluxIntegral
    variable = temperature
    boundary = right
    diffusivity = thermal_conductivity
  []
[]

[Outputs]
  csv = true
  perf_graph = true
[]

(test/tests/example_testing/sample_three.i)

# Cincotti Sample III SPS System Electrothermal Example
# Configuration: Two stainless steel electrodes (with cooling channels) with two
#                large spacers, two small spacers, and one plunger in-between.
#                RZ, axisymmetric. Reproduces Figures 20(a) and 20(b) in Cincotti
#                reference (below)
#
# BCs:
#    Potential:
#       V (top electrode, top surface) --> Neumann condition specifiying potential
#                                          based on applied RMS Current (670 A)
#                                          and cross-sectional electrode area (see
#                                          elec_top BC below). Current turned off
#                                          at 1200 s.
#       V (bottom electrode, bottom surface) = 0 V
#       V (elsewhere) --> natural boundary conditions (no current external to circuit)
#    Temperature:
#       T (top electrode, top surface) = 293 K
#       T (bottom electrode, bottom surface) = 293 K
#       T (right side) --> simple radiative BC into black body at 293 K
#       T (water channel) --> simple convective BC into "water" with heat transfer coefficient parameter from Cincotti and temperature of 293 K
#       T (elsewhere) --> natural boundary conditions
# Interface Conditions:
#       V (SS-G upper and G-SS lower interface) --> ElectrostaticContactCondition
#       T (SS-G upper and G-SS lower interface) --> ThermalContactCondition
# Initial Conditions:
#       V = default (0 V)
#       T = 293 K
# Applied Mechanical Load: 3.5 kN
#
# Reference: Cincotti et al, DOI 10.1002/aic.11102

[Mesh]
  [import_mesh]
    type = FileMeshGenerator
    file = spsdie_table1model3_2d.e
  []
  coord_type = RZ
[]

[Variables]
  [temperature_graphite]
    initial_condition = 293.0
    block = graphite
  []
  [temperature_stainless_steel]
    initial_condition = 293.0
    block = stainless_steel
  []
  [potential_graphite]
    block = graphite
  []
  [potential_stainless_steel]
    block = stainless_steel
  []
[]

[AuxVariables]
  [electric_field_r]
    family = MONOMIAL
    order = CONSTANT
  []
  [electric_field_z]
    family = MONOMIAL
    order = CONSTANT
  []
  [current_density]
    family = NEDELEC_ONE
    order = FIRST
  []
  [T_infinity]
    initial_condition = 293.0
  []
  [heatflux_graphite_r]
    family = MONOMIAL
    order = CONSTANT
    block = graphite
  []
  [heatflux_graphite_z]
    family = MONOMIAL
    order = CONSTANT
    block = graphite
  []
  [heatflux_stainless_steel_r]
    family = MONOMIAL
    order = CONSTANT
    block = stainless_steel
  []
  [heatflux_stainless_steel_z]
    family = MONOMIAL
    order = CONSTANT
    block = stainless_steel
  []
[]

[Kernels]
  [HeatDiff_graphite]
    type = ADHeatConduction
    variable = temperature_graphite
    block = graphite
  []
  [HeatTdot_graphite]
    type = ADHeatConductionTimeDerivative
    variable = temperature_graphite
    specific_heat = heat_capacity
    block = graphite
  []
  [HeatSource_graphite]
    type = ADJouleHeatingSource
    variable = temperature_graphite
    elec = potential_graphite
    block = graphite
  []

  [HeatDiff_stainless_steel]
    type = ADHeatConduction
    variable = temperature_stainless_steel
    block = stainless_steel
  []
  [HeatTdot_stainless_steel]
    type = ADHeatConductionTimeDerivative
    variable = temperature_stainless_steel
    specific_heat = heat_capacity
    block = stainless_steel
  []
  [HeatSource_stainless_steel]
    type = ADJouleHeatingSource
    variable = temperature_stainless_steel
    elec = potential_stainless_steel
    block = stainless_steel
  []

  [electric_graphite]
    type = ADMatDiffusion
    variable = potential_graphite
    diffusivity = electrical_conductivity
    block = graphite
  []
  [electric_stainless_steel]
    type = ADMatDiffusion
    variable = potential_stainless_steel
    diffusivity = electrical_conductivity
    block = stainless_steel
  []
[]

[AuxKernels]
  [electrostatic_calculation_r_graphite]
    type = PotentialToFieldAux
    gradient_variable = potential_graphite
    variable = electric_field_r
    sign = negative
    component = x
    block = graphite
  []
  [electrostatic_calculation_z_graphite]
    type = PotentialToFieldAux
    gradient_variable = potential_graphite
    variable = electric_field_z
    sign = negative
    component = y
    block = graphite
  []
  [electrostatic_calculation_r_stainless_steel]
    type = PotentialToFieldAux
    gradient_variable = potential_stainless_steel
    variable = electric_field_r
    sign = negative
    component = x
    block = stainless_steel
  []
  [electrostatic_calculation_z_stainless_steel]
    type = PotentialToFieldAux
    gradient_variable = potential_stainless_steel
    variable = electric_field_z
    sign = negative
    component = y
    block = stainless_steel
  []
  [current_density_graphite]
    type = ADCurrentDensity
    variable = current_density
    potential = potential_graphite
    block = graphite
  []
  [current_density_stainless_steel]
    type = ADCurrentDensity
    variable = current_density
    potential = potential_stainless_steel
    block = stainless_steel
  []
  [heat_flux_graphite_r]
    type = DiffusionFluxAux
    diffusivity = nonad_thermal_conductivity
    diffusion_variable = temperature_graphite
    variable = heatflux_graphite_r
    component = x
    block = graphite
  []
  [heat_flux_graphite_z]
    type = DiffusionFluxAux
    diffusivity = nonad_thermal_conductivity
    diffusion_variable = temperature_graphite
    variable = heatflux_graphite_z
    component = y
    block = graphite
  []
  [heat_flux_stainless_r]
    type = DiffusionFluxAux
    diffusivity = nonad_thermal_conductivity
    diffusion_variable = temperature_stainless_steel
    variable = heatflux_stainless_steel_r
    block = stainless_steel
    component = x
  []
  [heat_flux_stainless_z]
    type = DiffusionFluxAux
    diffusivity = nonad_thermal_conductivity
    diffusion_variable = temperature_stainless_steel
    variable = heatflux_stainless_steel_z
    block = stainless_steel
    component = y
  []
[]

[BCs]
  [external_surface_stainless]
    type = ADCoupledSimpleRadiativeHeatFluxBC
    boundary = right_die_stainless_steel
    variable = temperature_stainless_steel
    T_infinity = T_infinity
    emissivity = 0.4
  []
  [external_surface_graphite]
    type = ADCoupledSimpleRadiativeHeatFluxBC
    boundary = right_die_graphite
    variable = temperature_graphite
    T_infinity = T_infinity
    emissivity = 0.85
  []
  [water_channel]
    type = CoupledConvectiveHeatFluxBC
    boundary = water_channel
    variable = temperature_stainless_steel
    T_infinity = 293
    htc = 4725
  []
  [temp_top]
    type = ADDirichletBC
    variable = temperature_stainless_steel
    boundary = top_die
    value = 293
  []
  [temp_bottom]
    type = ADDirichletBC
    variable = temperature_stainless_steel
    boundary = bottom_die
    value = 293
  []
  [elec_top]
    type = ADFunctionNeumannBC
    variable = potential_stainless_steel
    boundary = top_die
    function = 'if(t < 47, (670 / (pi * 0.00155))*((0.057531/2.6969)*t), if(t > 1200, 0, 670 / (pi * 0.00155)))' # RMS Current / Cross-sectional Area. Ramping for t < 47s approximately reflects Cincotti et al (DOI: 10.1002/aic.11102) Figure 20(b)
  []
  [elec_bottom]
    type = ADDirichletBC
    variable = potential_stainless_steel
    boundary = bottom_die
    value = 0
  []
[]

[InterfaceKernels]
  [electric_contact_conductance_ssg]
    type = ElectrostaticContactCondition
    variable = potential_stainless_steel
    neighbor_var = potential_graphite
    boundary = ssg_interface
    mean_hardness = graphite_stainless_mean_hardness
    mechanical_pressure = mechanical_pressure_func
  []
  [thermal_contact_conductance_calculated_ssg]
    type = ThermalContactCondition
    variable = temperature_stainless_steel
    neighbor_var = temperature_graphite
    primary_potential = potential_stainless_steel
    secondary_potential = potential_graphite
    primary_thermal_conductivity = thermal_conductivity
    secondary_thermal_conductivity = thermal_conductivity
    primary_electrical_conductivity = electrical_conductivity
    secondary_electrical_conductivity = electrical_conductivity
    mean_hardness = graphite_stainless_mean_hardness
    mechanical_pressure = mechanical_pressure_func
    boundary = ssg_interface
  []
  [electric_contact_conductance_gss]
    type = ElectrostaticContactCondition
    variable = potential_graphite
    neighbor_var = potential_stainless_steel
    boundary = gss_interface
    mean_hardness = graphite_stainless_mean_hardness
    mechanical_pressure = mechanical_pressure_func
  []
  [thermal_contact_conductance_calculated_gss]
    type = ThermalContactCondition
    variable = temperature_graphite
    neighbor_var = temperature_stainless_steel
    primary_potential = potential_graphite
    secondary_potential = potential_stainless_steel
    primary_thermal_conductivity = thermal_conductivity
    secondary_thermal_conductivity = thermal_conductivity
    primary_electrical_conductivity = electrical_conductivity
    secondary_electrical_conductivity = electrical_conductivity
    mean_hardness = graphite_stainless_mean_hardness
    mechanical_pressure = mechanical_pressure_func
    boundary = gss_interface
  []
[]

[Materials]
  #graphite
  [heat_conductor_graphite]
    type = ADGraphiteThermal
    temperature = temperature_graphite
    block = graphite
  []
  [rho_graphite]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = 1750
    block = graphite
  []
  [sigma_graphite]
    type = ADGraphiteElectricalConductivity
    temperature = temperature_graphite
    block = graphite
  []

  #stainless_steel
  [heat_conductor_stainless_steel]
    type = ADStainlessSteelThermal
    temperature = temperature_stainless_steel
    block = stainless_steel
  []
  [rho_stainless_steel]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = 8000
    block = stainless_steel
  []
  [sigma_stainless_steel]
    type = ADStainlessSteelElectricalConductivity
    temperature = temperature_stainless_steel
    block = stainless_steel
  []

  # harmonic mean of graphite and stainless steel hardness
  [mean_hardness]
    type = GraphiteStainlessMeanHardness
  []

  # Material property converter for DiffusionFluxAux object
  [converter]
    type = MaterialADConverter
    ad_props_in = thermal_conductivity
    reg_props_out = nonad_thermal_conductivity
  []
[]

[Functions]
  [mechanical_pressure_func]
    type = ParsedFunction
    symbol_names = 'radius force'
    symbol_values = '0.04 3.5' # 'm kN'
    expression = 'force * 1e3 / (pi * radius^2)' # (N / m^2)
  []
[]

# Tracking data locations specified in Cincotti paper
# [Postprocessors]
#   [./lower_big_spacer]
#     type = PointValue
#     variable = temperature_graphite
#     point = '0 0.28 0'
#   [../]
#   [./lower_small_spacer]
#     type = PointValue
#     variable = temperature_graphite
#     point = '0 0.315 0'
#   [../]
#   [./center_plunger]
#     type = PointValue
#     variable = temperature_graphite
#     point = '0 0.34 0'
#   [../]
#   [./potential_tracking]
#     type = PointValue
#     variable = potential_stainless_steel
#     point = '0.027 0.584 0'
#   [../]
# []

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

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = NEWTON
  dt = 1
  end_time = 3600
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Outputs]
  perf_graph = true
  file_base = sample_three_out
  active = 'normal_out'
  [normal_out]
    type = Exodus
  []
  [testing_out]
    # Due to platform diffs in *really* small auxvariable values
    type = Exodus
    show = 'temperature_graphite temperature_stainless_steel potential_graphite potential_stainless_steel'
  []
[]

(test/tests/bcs/radiation_heat_loss/simple_radiation.i)

# This is a simple 3D test of the simplistic radiation heat transfer loss. The
# body to which the heat is lost is considered as a pure blackbody.
# A rectangular prism is set to a uniform temperature, 302K, while the absolute
# temperature of the surrounding assumed blackbody is set to 293K. The emissivity
# of the body is assumed to be 0.95. A high thermal conductivity is used to
# obtain a nearly uniform temperature through the body needed to match to
# analytical solution. The heat flux loss through the right boundary with this
# radiative heat transfer boundary condition is calculated.
#
# The analytical solution is:
# Q = \epsilon * \sigma * (T^4_{body} - T^4_{infinity})
#   = 0.95 * 5.67e-8 * (302^4 - 293^4)
#   = 51.0704 W

[Mesh]
  type = GeneratedMesh
  dim = 3
  xmax = 0.01
  ymax = 1.0
  zmax = 1.0
  nx = 10
  ny = 5
  nz = 5
[]

[Variables]
  [temperature]
    initial_condition = 302.0
  []
[]

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

[BCs]
  [heatloss]
    type = ADCoupledSimpleRadiativeHeatFluxBC
    boundary = right
    variable = temperature
    T_infinity = 293
    emissivity = 0.95
  []
  [insulation]
    type = DirichletBC
    boundary = 'left'
    variable = temperature
    value = 302
  []
[]

[Materials]
  [density]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '9.5e3'
  []
[]

[Executioner]
  type = Steady
  line_search = none
  nl_rel_tol = 2e-8
[]

[Postprocessors]
  [right_temperature]
    type = SideAverageValue
    variable = temperature
    boundary = right
  []
  [right_heatflux]
    type = SideDiffusiveFluxIntegral
    variable = temperature
    boundary = right
    diffusivity = thermal_conductivity
  []
[]

[Outputs]
  csv = true
  perf_graph = true
[]

(test/tests/example_testing/sample_one.i)

# Cincotti Sample I SPS System Electrothermal Example
# Configuration: Two stainless steel electrodes (with cooling channels) with two
#                large spacers in-between. RZ, axisymmetric. Reproduces Figures
#                18(a), 18(b), and 19 in Cincotti reference (below)
#
# BCs:
#    Potential:
#       V (top electrode, top surface) --> Neumann condition specifiying potential
#                                          based on applied RMS Current (1200 A)
#                                          and cross-sectional electrode area (see
#                                          elec_top BC below). Current turned off
#                                          at 1200 s.
#       V (bottom electrode, bottom surface) = 0 V
#       V (elsewhere) --> natural boundary conditions (no current external to circuit)
#    Temperature:
#       T (top electrode, top surface) = 293 K
#       T (bottom electrode, bottom surface) = 293 K
#       T (right side) --> simple radiative BC into black body at 293 K
#       T (water channel) --> simple convective BC into "water" with heat transfer
#                             coefficient parameter from Cincotti and temperature of 293 K
#       T (elsewhere) --> natural boundary conditions
# Interface Conditions:
#       V (SS-G upper and G-SS lower interface) --> ElectrostaticContactCondition
#       T (SS-G upper and G-SS lower interface) --> ThermalContactCondition
# Initial Conditions:
#       V = default (0 V)
#       T = 293 K
# Applied Mechanical Load: 50 kN
#
# Reference: Cincotti et al, DOI 10.1002/aic.11102

[Mesh]
  [import_mesh]
    type = FileMeshGenerator
    file = spsdie_table1model1_2d.e
  []
  coord_type = RZ
[]

[Variables]
  [temperature_graphite]
    initial_condition = 293.0
    block = graphite
  []
  [temperature_stainless_steel]
    initial_condition = 293.0
    block = stainless_steel
  []
  [potential_graphite]
    block = graphite
  []
  [potential_stainless_steel]
    block = stainless_steel
  []
[]

[AuxVariables]
  [electric_field_r]
    family = MONOMIAL
    order = CONSTANT
  []
  [electric_field_z]
    family = MONOMIAL
    order = CONSTANT
  []
  [current_density]
    family = NEDELEC_ONE
    order = FIRST
  []
  [T_infinity]
    initial_condition = 293.0
  []
  [heatflux_graphite_r]
    family = MONOMIAL
    order = CONSTANT
    block = graphite
  []
  [heatflux_graphite_z]
    family = MONOMIAL
    order = CONSTANT
    block = graphite
  []
  [heatflux_stainless_steel_r]
    family = MONOMIAL
    order = CONSTANT
    block = stainless_steel
  []
  [heatflux_stainless_steel_z]
    family = MONOMIAL
    order = CONSTANT
    block = stainless_steel
  []
[]

[Kernels]
  [HeatDiff_graphite]
    type = ADHeatConduction
    variable = temperature_graphite
    block = graphite
  []
  [HeatTdot_graphite]
    type = ADHeatConductionTimeDerivative
    variable = temperature_graphite
    specific_heat = heat_capacity
    block = graphite
  []
  [HeatSource_graphite]
    type = ADJouleHeatingSource
    variable = temperature_graphite
    elec = potential_graphite
    block = graphite
  []

  [HeatDiff_stainless_steel]
    type = ADHeatConduction
    variable = temperature_stainless_steel
    block = stainless_steel
  []
  [HeatTdot_stainless_steel]
    type = ADHeatConductionTimeDerivative
    variable = temperature_stainless_steel
    specific_heat = heat_capacity
    block = stainless_steel
  []
  [HeatSource_stainless_steel]
    type = ADJouleHeatingSource
    variable = temperature_stainless_steel
    elec = potential_stainless_steel
    block = stainless_steel
  []

  [electric_graphite]
    type = ADMatDiffusion
    variable = potential_graphite
    diffusivity = electrical_conductivity
    block = graphite
  []
  [electric_stainless_steel]
    type = ADMatDiffusion
    variable = potential_stainless_steel
    diffusivity = electrical_conductivity
    block = stainless_steel
  []
[]

[AuxKernels]
  [electrostatic_calculation_r_graphite]
    type = PotentialToFieldAux
    gradient_variable = potential_graphite
    variable = electric_field_r
    sign = negative
    component = x
    block = graphite
  []
  [electrostatic_calculation_z_graphite]
    type = PotentialToFieldAux
    gradient_variable = potential_graphite
    variable = electric_field_z
    sign = negative
    component = y
    block = graphite
  []
  [electrostatic_calculation_r_stainless_steel]
    type = PotentialToFieldAux
    gradient_variable = potential_stainless_steel
    variable = electric_field_r
    sign = negative
    component = x
    block = stainless_steel
  []
  [electrostatic_calculation_z_stainless_steel]
    type = PotentialToFieldAux
    gradient_variable = potential_stainless_steel
    variable = electric_field_z
    sign = negative
    component = y
    block = stainless_steel
  []
  [current_density_graphite]
    type = ADCurrentDensity
    variable = current_density
    potential = potential_graphite
    block = graphite
  []
  [current_density_stainless_steel]
    type = ADCurrentDensity
    variable = current_density
    potential = potential_stainless_steel
    block = stainless_steel
  []
  [heat_flux_graphite_r]
    type = DiffusionFluxAux
    diffusivity = nonad_thermal_conductivity
    diffusion_variable = temperature_graphite
    variable = heatflux_graphite_r
    component = x
    block = graphite
  []
  [heat_flux_graphite_z]
    type = DiffusionFluxAux
    diffusivity = nonad_thermal_conductivity
    diffusion_variable = temperature_graphite
    variable = heatflux_graphite_z
    component = y
    block = graphite
  []
  [heat_flux_stainless_r]
    type = DiffusionFluxAux
    diffusivity = nonad_thermal_conductivity
    diffusion_variable = temperature_stainless_steel
    variable = heatflux_stainless_steel_r
    block = stainless_steel
    component = x
  []
  [heat_flux_stainless_z]
    type = DiffusionFluxAux
    diffusivity = nonad_thermal_conductivity
    diffusion_variable = temperature_stainless_steel
    variable = heatflux_stainless_steel_z
    block = stainless_steel
    component = y
  []
[]

[BCs]
  [external_surface_stainless]
    type = ADCoupledSimpleRadiativeHeatFluxBC
    boundary = right_die_stainless_steel
    variable = temperature_stainless_steel
    T_infinity = T_infinity
    emissivity = 0.4
  []
  [external_surface_graphite]
    type = ADCoupledSimpleRadiativeHeatFluxBC
    boundary = right_die_graphite
    variable = temperature_graphite
    T_infinity = T_infinity
    emissivity = 0.85
  []
  [water_channel]
    type = CoupledConvectiveHeatFluxBC
    boundary = water_channel
    variable = temperature_stainless_steel
    T_infinity = 293
    htc = 4725
  []
  [temp_top]
    type = ADDirichletBC
    variable = temperature_stainless_steel
    boundary = top_die
    value = 293
  []
  [temp_bottom]
    type = ADDirichletBC
    variable = temperature_stainless_steel
    boundary = bottom_die
    value = 293
  []
  [elec_top]
    type = ADFunctionNeumannBC
    variable = potential_stainless_steel
    boundary = top_die
    function = 'if(t < 43, (1200 / (pi * 0.00155))*((0.017703/0.75549)*t), if(t > 1200, 0, 1200 / (pi * 0.00155)))' # RMS Current / Cross-sectional Area. Ramping for t < 43s approximately reflects Cincotti et al (DOI: 10.1002/aic.11102) Figure 18(b)
  []
  [elec_bottom]
    type = ADDirichletBC
    variable = potential_stainless_steel
    boundary = bottom_die
    value = 0
  []
[]

[InterfaceKernels]
  [electric_contact_conductance_ssg]
    type = ElectrostaticContactCondition
    variable = potential_stainless_steel
    neighbor_var = potential_graphite
    boundary = ssg_interface
    mean_hardness = graphite_stainless_mean_hardness
    mechanical_pressure = mechanical_pressure_func
  []
  [thermal_contact_conductance_calculated_ssg]
    type = ThermalContactCondition
    variable = temperature_stainless_steel
    neighbor_var = temperature_graphite
    primary_potential = potential_stainless_steel
    secondary_potential = potential_graphite
    primary_thermal_conductivity = thermal_conductivity
    secondary_thermal_conductivity = thermal_conductivity
    primary_electrical_conductivity = electrical_conductivity
    secondary_electrical_conductivity = electrical_conductivity
    mean_hardness = graphite_stainless_mean_hardness
    mechanical_pressure = mechanical_pressure_func
    boundary = ssg_interface
  []
  [electric_contact_conductance_gss]
    type = ElectrostaticContactCondition
    variable = potential_graphite
    neighbor_var = potential_stainless_steel
    boundary = gss_interface
    mean_hardness = graphite_stainless_mean_hardness
    mechanical_pressure = mechanical_pressure_func
  []
  [thermal_contact_conductance_calculated_gss]
    type = ThermalContactCondition
    variable = temperature_graphite
    neighbor_var = temperature_stainless_steel
    primary_potential = potential_graphite
    secondary_potential = potential_stainless_steel
    primary_thermal_conductivity = thermal_conductivity
    secondary_thermal_conductivity = thermal_conductivity
    primary_electrical_conductivity = electrical_conductivity
    secondary_electrical_conductivity = electrical_conductivity
    mean_hardness = graphite_stainless_mean_hardness
    mechanical_pressure = mechanical_pressure_func
    boundary = gss_interface
  []
[]

[Materials]
  #graphite
  [heat_conductor_graphite]
    type = ADGraphiteThermal
    temperature = temperature_graphite
    block = graphite
  []
  [rho_graphite]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = 1750
    block = graphite
  []
  [sigma_graphite]
    type = ADGraphiteElectricalConductivity
    temperature = temperature_graphite
    block = graphite
  []

  #stainless_steel
  [heat_conductor_stainless_steel]
    type = ADStainlessSteelThermal
    temperature = temperature_stainless_steel
    block = stainless_steel
  []
  [rho_stainless_steel]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = 8000
    block = stainless_steel
  []
  [sigma_stainless_steel]
    type = ADStainlessSteelElectricalConductivity
    temperature = temperature_stainless_steel
    block = stainless_steel
  []

  # harmonic mean of graphite and stainless steel hardness
  [mean_hardness]
    type = GraphiteStainlessMeanHardness
  []

  # Material property converter for DiffusionFluxAux object
  [converter]
    type = MaterialADConverter
    ad_props_in = thermal_conductivity
    reg_props_out = nonad_thermal_conductivity
  []
[]

[Functions]
  [mechanical_pressure_func]
    type = ParsedFunction
    symbol_names = 'radius force'
    symbol_values = '0.04 50' # 'm kN'
    expression = 'force * 1e3 / (pi * radius^2)' # (N / m^2)
  []
[]

# Tracking data locations specified in Cincotti paper
# [Postprocessors]
#   [./temp_tracking]
#     type = PointValue
#     variable = temperature_graphite
#     point = '0 0.28 0'
#   [../]
#   [./potential_tracking]
#     type = PointValue
#     variable = potential_stainless_steel
#     point = '0.027 0.504 0'
#   [../]
# []

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

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = NEWTON
  dt = 1
  end_time = 3600
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Outputs]
  perf_graph = true
  file_base = sample_one_out
  active = 'normal_out'
  [normal_out]
    type = Exodus
  []
  [testing_out]
    # Due to platform diffs in *really* small auxvariable values
    type = Exodus
    show = 'temperature_graphite temperature_stainless_steel potential_graphite potential_stainless_steel'
  []
[]

(test/tests/bcs/radiation_heat_loss/multiple_phases_simple_radiation.i)

# This is a simple 3D test of the simplistic radiation heat transfer loss. The
# body to which the heat is lost is considered as a pure blackbody.
# A rectangular prism is set to a uniform temperature, 400K, while the absolute
# temperature of the surrounding assumed blackbody is set to 293K. The emissivity
# is assumed to be 0.95 for 0.4 of the body and 0.07 for the remaining 0.6 of the
# body. A high thermal conductivity is used to obtain a nearly uniform temperature
# through the body needed to match to analytical solution. The heat flux loss
# through the right boundary with this radiative heat transfer boundary condition
# is calculated.
#
# The analytical solution is:
# Q = \sum_i (\alpha_i \epsilon_i * \sigma * (T^4_{body} - T^4_{infinity}))
#   = 0.4 * 0.95 * 5.67e-8 * (400^4 - 293^4) + 0.6 * 0.07 * 5.67e-8 * (400^4 - 293^4)
#   = 436.1953 W

[Mesh]
  type = GeneratedMesh
  dim = 3
  xmax = 0.01
  ymax = 1.0
  zmax = 1.0
  nx = 10
  ny = 5
  nz = 5
[]

[Variables]
  [temperature]
    initial_condition = 400.0
  []
[]

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

[BCs]
  [heatloss]
    type = ADCoupledSimpleRadiativeHeatFluxBC
    boundary = right
    variable = temperature
    T_infinity = '293 293'
    emissivity = '0.95 0.07'
    alpha = '0.4 0.6'
  []
  [insulation]
    type = DirichletBC
    boundary = 'left'
    variable = temperature
    value = 400
  []
[]

[Materials]
  [density]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '1e3'
  []
[]

[Executioner]
  type = Steady
  line_search = none
[]

[Postprocessors]
  [right_temperature]
    type = SideAverageValue
    variable = temperature
    boundary = right
  []
  [right_heatflux]
    type = SideDiffusiveFluxIntegral
    variable = temperature
    boundary = right
    diffusivity = thermal_conductivity
  []
[]

[Outputs]
  csv = true
  perf_graph = true
[]

(test/tests/example_testing/sample_four.i)

# Cincotti Sample IV SPS System Electrothermal Example
# Configuration: Two stainless steel electrodes (with cooling channels) with two
#                large spacers, two small spacers, and one die-and-plungers
#                ensemble in-between. RZ, axisymmetric. Reproduces Figures 21(a)
#                and 21(b) in Cincotti reference (below)
#
# BCs:
#    Potential:
#       V (top electrode, top surface) --> Neumann condition specifiying potential
#                                          based on applied RMS Current (980 A)
#                                          and cross-sectional electrode area (see
#                                          elec_top BC below). Current turned off
#                                          at 1200 s.
#       V (bottom electrode, bottom surface) = 0 V
#       V (elsewhere) --> natural boundary conditions (no current external to circuit)
#    Temperature:
#       T (top electrode, top surface) = 293 K
#       T (bottom electrode, bottom surface) = 293 K
#       T (right side) --> simple radiative BC into black body at 293 K
#       T (water channel) --> simple convective BC into "water" with heat transfer coefficient parameter from Cincotti and temperature of 293 K
#       T (elsewhere) --> natural boundary conditions
# Interface Conditions:
#       V (SS-G upper and G-SS lower interface) --> ElectrostaticContactCondition
#       T (SS-G upper and G-SS lower interface) --> ThermalContactCondition
# Initial Conditions:
#       V = default (0 V)
#       T = 293 K
# Applied Mechanical Load: 3.5 kN
#
# Reference: Cincotti et al, DOI 10.1002/aic.11102

[Mesh]
  [import_mesh]
    type = FileMeshGenerator
    file = spsdie_table1model4_2d.e
  []
  coord_type = RZ
[]

[Variables]
  [temperature_graphite]
    initial_condition = 293.0
    block = graphite
  []
  [temperature_stainless_steel]
    initial_condition = 293.0
    block = stainless_steel
  []
  [potential_graphite]
    block = graphite
  []
  [potential_stainless_steel]
    block = stainless_steel
  []
[]

[AuxVariables]
  [electric_field_r]
    family = MONOMIAL
    order = CONSTANT
  []
  [electric_field_z]
    family = MONOMIAL
    order = CONSTANT
  []
  [current_density]
    family = NEDELEC_ONE
    order = FIRST
  []
  [T_infinity]
    initial_condition = 293.0
  []
  [heatflux_graphite_r]
    family = MONOMIAL
    order = CONSTANT
    block = graphite
  []
  [heatflux_graphite_z]
    family = MONOMIAL
    order = CONSTANT
    block = graphite
  []
  [heatflux_stainless_steel_r]
    family = MONOMIAL
    order = CONSTANT
    block = stainless_steel
  []
  [heatflux_stainless_steel_z]
    family = MONOMIAL
    order = CONSTANT
    block = stainless_steel
  []
[]

[Kernels]
  [HeatDiff_graphite]
    type = ADHeatConduction
    variable = temperature_graphite
    block = graphite
  []
  [HeatTdot_graphite]
    type = ADHeatConductionTimeDerivative
    variable = temperature_graphite
    specific_heat = heat_capacity
    block = graphite
  []
  [HeatSource_graphite]
    type = ADJouleHeatingSource
    variable = temperature_graphite
    elec = potential_graphite
    block = graphite
  []

  [HeatDiff_stainless_steel]
    type = ADHeatConduction
    variable = temperature_stainless_steel
    block = stainless_steel
  []
  [HeatTdot_stainless_steel]
    type = ADHeatConductionTimeDerivative
    variable = temperature_stainless_steel
    specific_heat = heat_capacity
    block = stainless_steel
  []
  [HeatSource_stainless_steel]
    type = ADJouleHeatingSource
    variable = temperature_stainless_steel
    elec = potential_stainless_steel
    block = stainless_steel
  []

  [electric_graphite]
    type = ADMatDiffusion
    variable = potential_graphite
    diffusivity = electrical_conductivity
    block = graphite
  []
  [electric_stainless_steel]
    type = ADMatDiffusion
    variable = potential_stainless_steel
    diffusivity = electrical_conductivity
    block = stainless_steel
  []
[]

[AuxKernels]
  [electrostatic_calculation_r_graphite]
    type = PotentialToFieldAux
    gradient_variable = potential_graphite
    variable = electric_field_r
    sign = negative
    component = x
    block = graphite
  []
  [electrostatic_calculation_z_graphite]
    type = PotentialToFieldAux
    gradient_variable = potential_graphite
    variable = electric_field_z
    sign = negative
    component = y
    block = graphite
  []
  [electrostatic_calculation_r_stainless_steel]
    type = PotentialToFieldAux
    gradient_variable = potential_stainless_steel
    variable = electric_field_r
    sign = negative
    component = x
    block = stainless_steel
  []
  [electrostatic_calculation_z_stainless_steel]
    type = PotentialToFieldAux
    gradient_variable = potential_stainless_steel
    variable = electric_field_z
    sign = negative
    component = y
    block = stainless_steel
  []
  [current_density_graphite]
    type = ADCurrentDensity
    variable = current_density
    potential = potential_graphite
    block = graphite
  []
  [current_density_stainless_steel]
    type = ADCurrentDensity
    variable = current_density
    potential = potential_stainless_steel
    block = stainless_steel
  []
  [heat_flux_graphite_r]
    type = DiffusionFluxAux
    diffusivity = nonad_thermal_conductivity
    diffusion_variable = temperature_graphite
    variable = heatflux_graphite_r
    component = x
    block = graphite
  []
  [heat_flux_graphite_z]
    type = DiffusionFluxAux
    diffusivity = nonad_thermal_conductivity
    diffusion_variable = temperature_graphite
    variable = heatflux_graphite_z
    component = y
    block = graphite
  []
  [heat_flux_stainless_r]
    type = DiffusionFluxAux
    diffusivity = nonad_thermal_conductivity
    diffusion_variable = temperature_stainless_steel
    variable = heatflux_stainless_steel_r
    block = stainless_steel
    component = x
  []
  [heat_flux_stainless_z]
    type = DiffusionFluxAux
    diffusivity = nonad_thermal_conductivity
    diffusion_variable = temperature_stainless_steel
    variable = heatflux_stainless_steel_z
    block = stainless_steel
    component = y
  []
[]

[BCs]
  [external_surface_stainless]
    type = ADCoupledSimpleRadiativeHeatFluxBC
    boundary = right_die_stainless_steel
    variable = temperature_stainless_steel
    T_infinity = T_infinity
    emissivity = 0.4
  []
  [external_surface_graphite]
    type = ADCoupledSimpleRadiativeHeatFluxBC
    boundary = right_die_graphite
    variable = temperature_graphite
    T_infinity = T_infinity
    emissivity = 0.85
  []
  [water_channel]
    type = CoupledConvectiveHeatFluxBC
    boundary = water_channel
    variable = temperature_stainless_steel
    T_infinity = 293
    htc = 4725
  []
  [temp_top]
    type = ADDirichletBC
    variable = temperature_stainless_steel
    boundary = top_die
    value = 293
  []
  [temp_bottom]
    type = ADDirichletBC
    variable = temperature_stainless_steel
    boundary = bottom_die
    value = 293
  []
  [elec_top]
    type = ADFunctionNeumannBC
    variable = potential_stainless_steel
    boundary = top_die
    function = 'if(t < 31, (980 / (pi * 0.00155))*((0.141301/4.3625)*t), if(t > 600, 0, 980 / (pi * 0.00155)))' # RMS Current / Cross-sectional Area. Ramping for t < 31s approximately reflects Cincotti et al (DOI: 10.1002/aic.11102) Figure 21(b)
  []
  [elec_bottom]
    type = ADDirichletBC
    variable = potential_stainless_steel
    boundary = bottom_die
    value = 0
  []
[]

[InterfaceKernels]
  [electric_contact_conductance_ssg]
    type = ElectrostaticContactCondition
    variable = potential_stainless_steel
    neighbor_var = potential_graphite
    boundary = ssg_interface
    mean_hardness = graphite_stainless_mean_hardness
    mechanical_pressure = mechanical_pressure_func
  []
  [thermal_contact_conductance_calculated_ssg]
    type = ThermalContactCondition
    variable = temperature_stainless_steel
    neighbor_var = temperature_graphite
    primary_potential = potential_stainless_steel
    secondary_potential = potential_graphite
    primary_thermal_conductivity = thermal_conductivity
    secondary_thermal_conductivity = thermal_conductivity
    primary_electrical_conductivity = electrical_conductivity
    secondary_electrical_conductivity = electrical_conductivity
    mean_hardness = graphite_stainless_mean_hardness
    mechanical_pressure = mechanical_pressure_func
    boundary = ssg_interface
  []
  [electric_contact_conductance_gss]
    type = ElectrostaticContactCondition
    variable = potential_graphite
    neighbor_var = potential_stainless_steel
    boundary = gss_interface
    mean_hardness = graphite_stainless_mean_hardness
    mechanical_pressure = mechanical_pressure_func
  []
  [thermal_contact_conductance_calculated_gss]
    type = ThermalContactCondition
    variable = temperature_graphite
    neighbor_var = temperature_stainless_steel
    primary_potential = potential_graphite
    secondary_potential = potential_stainless_steel
    primary_thermal_conductivity = thermal_conductivity
    secondary_thermal_conductivity = thermal_conductivity
    primary_electrical_conductivity = electrical_conductivity
    secondary_electrical_conductivity = electrical_conductivity
    mean_hardness = graphite_stainless_mean_hardness
    mechanical_pressure = mechanical_pressure_func
    boundary = gss_interface
  []
[]

[Materials]
  #graphite
  [heat_conductor_graphite]
    type = ADGraphiteThermal
    temperature = temperature_graphite
    block = graphite
  []
  [rho_graphite]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = 1750
    block = graphite
  []
  [sigma_graphite]
    type = ADGraphiteElectricalConductivity
    temperature = temperature_graphite
    block = graphite
  []

  #stainless_steel
  [heat_conductor_stainless_steel]
    type = ADStainlessSteelThermal
    temperature = temperature_stainless_steel
    block = stainless_steel
  []
  [rho_stainless_steel]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = 8000
    block = stainless_steel
  []
  [sigma_stainless_steel]
    type = ADStainlessSteelElectricalConductivity
    temperature = temperature_stainless_steel
    block = stainless_steel
  []

  # harmonic mean of graphite and stainless steel hardness
  [mean_hardness]
    type = GraphiteStainlessMeanHardness
  []

  # Material property converter for DiffusionFluxAux object
  [converter]
    type = MaterialADConverter
    ad_props_in = thermal_conductivity
    reg_props_out = nonad_thermal_conductivity
  []
[]

[Functions]
  [mechanical_pressure_func]
    type = ParsedFunction
    symbol_names = 'radius force'
    symbol_values = '0.04 3.5' # 'm kN'
    expression = 'force * 1e3 / (pi * radius^2)' # (N / m^2)
  []
[]

# Tracking data locations specified in Cincotti paper
# [Postprocessors]
#   [./lower_small_spacer]
#     type = PointValue
#     variable = temperature_graphite
#     point = '0 0.315 0'
#   [../]
#   [./inside_die]
#     type = PointValue
#     variable = temperature_graphite
#     point = '0.011 0.3525 0'
#   [../]
#   [./potential_tracking]
#     type = PointValue
#     variable = potential_stainless_steel
#     point = '0.027 0.609 0'
#   [../]
# []

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

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = NEWTON
  dt = 1
  end_time = 1800
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Outputs]
  perf_graph = true
  file_base = sample_four_out
  active = 'normal_out'
  [normal_out]
    type = Exodus
  []
  [testing_out]
    # Due to platform diffs in *really* small auxvariable values
    type = Exodus
    show = 'temperature_graphite temperature_stainless_steel potential_graphite potential_stainless_steel'
  []
[]

(test/tests/interfacekernels/thermal_conductance/thermal_interface.i)

# Input file block to generate this mesh can be found in thermal_interface_mesh.i
[Mesh]
  file = thermal_interface_regular_mesh.e
  coord_type = RZ
[]

[Variables]
  [temperature_graphite]
    initial_condition = 300.0
    block = graphite
  []
  [temperature_stainless_steel]
    initial_condition = 300.0
    block = stainless_steel
  []
  [potential_graphite]
    block = graphite
  []
  [potential_stainless_steel]
    block = stainless_steel
  []
[]

[AuxVariables]
  [T_infinity]
    initial_condition = 300.0
  []
[]

[Kernels]
  [HeatDiff_graphite]
    type = ADHeatConduction
    variable = temperature_graphite
    block = graphite
  []
  [HeatTdot_graphite]
    type = ADHeatConductionTimeDerivative
    variable = temperature_graphite
    block = graphite
  []
  [HeatSource_graphite]
    type = ADJouleHeatingSource
    variable = temperature_graphite
    elec = potential_graphite
    electrical_conductivity = electrical_conductivity
    block = graphite
  []

  [HeatDiff_stainless_steel]
    type = ADHeatConduction
    variable = temperature_stainless_steel
    block = stainless_steel
  []
  [HeatTdot_stainless_steel]
    type = ADHeatConductionTimeDerivative
    variable = temperature_stainless_steel
    block = stainless_steel
  []
  [HeatSource_stainless_steel]
    type = ADJouleHeatingSource
    variable = temperature_stainless_steel
    elec = potential_stainless_steel
    electrical_conductivity = electrical_conductivity
    block = stainless_steel
  []

  [electric_graphite]
    type = ADMatDiffusion
    variable = potential_graphite
    diffusivity = electrical_conductivity
    block = graphite
  []
  [electric_stainless_steel]
    type = ADMatDiffusion
    variable = potential_stainless_steel
    diffusivity = electrical_conductivity
    block = stainless_steel
  []
[]

[BCs]
  [external_surface_stainless]
    type = ADCoupledSimpleRadiativeHeatFluxBC
    boundary = right_stainless_steel
    variable = temperature_stainless_steel
    T_infinity = T_infinity
    emissivity = 0.85
  []
  [external_surface_graphite]
    type = ADCoupledSimpleRadiativeHeatFluxBC
    boundary = right_graphite
    variable = temperature_graphite
    T_infinity = T_infinity
    emissivity = 0.85
  []
  [elec_top]
    type = ADDirichletBC
    variable = potential_stainless_steel
    boundary = top_die
    value = 0.68 # Better reflects Cincotti et al (DOI: 10.1002/aic.11102) Figure 19
  []
  [elec_bottom]
    type = ADDirichletBC
    variable = potential_stainless_steel
    boundary = bottom_die
    value = 0
  []
[]

[InterfaceKernels]
  active = 'thermal_contact_conductance electric_contact_conductance'

  [thermal_contact_conductance]
    type = ThermalContactCondition
    variable = temperature_stainless_steel
    neighbor_var = temperature_graphite
    primary_potential = potential_stainless_steel
    secondary_potential = potential_graphite
    primary_thermal_conductivity = thermal_conductivity
    secondary_thermal_conductivity = thermal_conductivity
    primary_electrical_conductivity = electrical_conductivity
    secondary_electrical_conductivity = electrical_conductivity
    user_electrical_contact_conductance = 2.5e5 # as described in Cincotti et al (DOI: 10.1002/aic.11102)
    user_thermal_contact_conductance = 7 # also from Cincotti et al
    boundary = ssg_interface
  []
  [electric_contact_conductance]
    type = ElectrostaticContactCondition
    variable = potential_stainless_steel
    neighbor_var = potential_graphite
    primary_conductivity = electrical_conductivity
    secondary_conductivity = electrical_conductivity
    boundary = ssg_interface
    user_electrical_contact_conductance = 2.5e5 # as described in Cincotti et al (DOI: 10.1002/aic.11102)
  []

  [thermal_contact_conductance_calculated]
    type = ThermalContactCondition
    variable = temperature_stainless_steel
    neighbor_var = temperature_graphite
    primary_potential = potential_stainless_steel
    secondary_potential = potential_graphite
    primary_thermal_conductivity = thermal_conductivity
    secondary_thermal_conductivity = thermal_conductivity
    primary_electrical_conductivity = electrical_conductivity
    secondary_electrical_conductivity = electrical_conductivity
    mean_hardness = graphite_stainless_mean_hardness
    mechanical_pressure = 8.52842e10 # resulting in electrical contact conductance = ~1.4715e5, thermal contact conductance = ~3.44689e7
    boundary = ssg_interface
  []
[]

[Materials]
  active = 'heat_conductor_graphite rho_graphite sigma_graphite heat_conductor_stainless_steel rho_stainless_steel sigma_stainless_steel'

  #graphite
  [heat_conductor_graphite]
    type = ADHeatConductionMaterial
    thermal_conductivity = 630
    specific_heat = 60
    block = graphite
  []
  [rho_graphite]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = 1.75e3
    block = graphite
  []
  [sigma_graphite]
    type = ADElectricalConductivity
    temperature = temperature_graphite
    reference_temperature = 293.0
    reference_resistivity = 3.0e-3
    temperature_coefficient = 0 # makes conductivity constant
    block = graphite
  []

  #stainless_steel
  [heat_conductor_stainless_steel]
    type = ADHeatConductionMaterial
    thermal_conductivity = 17
    specific_heat = 502
    block = stainless_steel
  []
  [rho_stainless_steel]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = 8e3
    block = stainless_steel
  []
  [sigma_stainless_steel]
    type = ADElectricalConductivity
    temperature = temperature_stainless_steel
    reference_temperature = 293.0
    reference_resistivity = 7e-7
    temperature_coefficient = 0 # makes conductivity constant
    block = stainless_steel
  []

  # harmonic mean of graphite and stainless steel hardness
  [mean_hardness]
    type = GraphiteStainlessMeanHardness
  []
[]

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

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = NEWTON
  dt = 0.1
  end_time = 100
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

Description
Example Input File Syntax
Input Parameters
Input Files
References