SideSetHeatTransferKernel

Modeling conduction, convection, and radiation across internal side set.

Description

This kernel models the heat transfer across a side set using all three heat transfer mechanisms. The purpose is to model the heat transfer across a small gap without modeling the gap itself. The heat transfer mechanisms for each side of the gap are described by the following equations: $var element = document.getElementById("moose-equation-a2f84b54-c793-45cc-9e45-e29e5c52ec15");katex.render(" q''^{+}_{\\mathrm{conduction}} = q''^{-}_{\\mathrm{conduction}} = -C_{\\mathrm{gap}} (T_{+}-T_{-}),", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ $var element = document.getElementById("moose-equation-9662da7d-756b-47e2-a3c6-691d52634d48");katex.render(" q''^{\\pm}_{\\mathrm{convection}} = \\pm h_{\\mathrm{gap}}^{\\pm} (T_{\\mathrm{bulk}} - T_{\\pm}),", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ $var element = document.getElementById("moose-equation-45798fa2-c2cf-4228-907a-6579e4227229");katex.render(" q''^+_{\\mathrm{radiation}} = q''^-_{\\mathrm{radiation}} = \\epsilon^{-}_{\\mathrm{eff}}T_{-}^4 - \\epsilon^{+}_{\\mathrm{eff}}T_{+}^4,", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where the $var element = document.getElementById("moose-equation-c7b2eeb2-13f5-49d1-849a-5f90948ff3d7");katex.render("+", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-ad65f12e-64ca-4da6-9e76-72c2e2df300e");katex.render("-", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ indices indicate the master and neighbor side of the boundary, respectively.

- $var element = document.getElementById("moose-equation-eede5b84-2a6e-4e52-ae2d-e319ccf37908");katex.render("C_{\\mathrm{gap}}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the gap conductance typically defined as conductivity divided by gap width: conductance

- $var element = document.getElementById("moose-equation-95acfa6f-f82e-41ca-93c8-b230306a4b46");katex.render("h_{\\mathrm{gap}}^{\\pm}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the convective heat transfer coefficient: h_master/h_neighbor

- $var element = document.getElementById("moose-equation-05243752-30ba-4ff8-bd92-fdf6c84064f9");katex.render("T_{\\mathrm{bulk}}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the bulk temperature of the gap, either defined by a material property or variable: Tbulk_mat or Tbulk_var

- $var element = document.getElementById("moose-equation-5f5b70dd-6fe4-4b20-a695-388b51e35f43");katex.render("\\epsilon^{\\pm}_{\\mathrm{eff}}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the effective emmissivity: emissivity_eff_master/emissivity_eff_neighbor

$var element = document.getElementById("moose-equation-bae59aea-68a8-4f30-a1fc-1a738c42ca6b");katex.render(" \\epsilon^{\\pm}_{\\mathrm{eff}} = \\sigma\\epsilon^{\\pm}\\frac{1-\\rho^{\\mp}}{1-\\rho^{+}\\rho^{-}}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

Example Input File Syntax

Using material properties generated from SideSetHeatTransferMaterial:

[gap]
  type = SideSetHeatTransferKernel
  variable = T
  neighbor_var = T
  boundary = 'interface0'
[]

/opt/civet/build_0/moose/modules/heat_conduction/test/tests/sideset_heat_transfer/gap_thermal_1D.i

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 2
    xmax = 2
  []
  [split]
    type = SubdomainBoundingBoxGenerator
    input = mesh
    block_id = 1
    bottom_left = '1 0 0'
    top_right = '2 0 0'
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = split
    master_block = 1
    paired_block = 0
    new_boundary = 'interface0'
  []
  uniform_refine = 4
[]

[Variables]
  # Defining a DFEM variable to handle gap discontinuity
  [T]
    order = FIRST
    family = MONOMIAL
  []
[]

[AuxVariables]
  # Auxvariable containing bulk temperature of gap
  [Tbulk]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300 # K
  []
[]

[Kernels]
  [diff]
    type = MatDiffusion
    variable = T
    diffusivity = conductivity
  []
  [source]
    type = BodyForce
    variable = T
    value = 1.0
  []
[]

[DGKernels]
  # DG kernel to represent diffusion accross element faces
  [./dg_diff]
    type = DGDiffusion
    variable = T
    epsilon = -1
    sigma = 6
    diff = conductivity
    # Ignoring gap side set because no diffusion accross there
    exclude_boundary = 'interface0'
  [../]
[]

[InterfaceKernels]
  active = 'gap'
  # Heat transfer kernel using Tbulk as material
  [gap]
    type = SideSetHeatTransferKernel
    variable = T
    neighbor_var = T
    boundary = 'interface0'
  []
  # Heat transfer kernel using Tbulk as auxvariable
  [gap_var]
    type = SideSetHeatTransferKernel
    variable = T
    neighbor_var = T
    boundary = 'interface0'
    Tbulk_var = Tbulk
  []
[]

[Functions]
  [bc_func]
    type = ConstantFunction
    value = 300
  []
  [exact]
    type = ParsedFunction
    value = '
            A := if(x < 1, -0.5, -0.25);
            B := if(x < 1, -0.293209850655001, 0.0545267662299068);
            C := if(x < 1, 300.206790149345, 300.19547323377);
            d := -1;
            A * (x+d) * (x+d) + B * (x+d) + C'
  []
[]

[BCs]
  [bc_left]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'left'
    variable = T
    diff = 'conductivity'
    epsilon = -1
    sigma = 6
    function = bc_func
  []
  [bc_right]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'right'
    variable = T
    diff = 'conductivity'
    epsilon = -1
    sigma = 6
    function = bc_func
  []
[]

[Materials]
  [k0]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 1.0
    block = 0
  []
  [k1]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 2.0
    block = 1
  []
  [gap_mat]
    type = SideSetHeatTransferMaterial
    boundary = 'interface0'
    conductivity = 1.5
    gap_length = 1.0
    h_master = 1
    h_neighbor = 1
    Tbulk = 300
    emissivity_master = 1
    emissivity_neighbor = 1
  []
[]

[Postprocessors]
  [error]
    type = ElementL2Error
    variable = T
    function = exact
  []
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

Using bulk gap temperature (for convection) as auxiliary variable:

[gap_var]
  type = SideSetHeatTransferKernel
  variable = T
  neighbor_var = T
  boundary = 'interface0'
  Tbulk_var = Tbulk
[]

/opt/civet/build_0/moose/modules/heat_conduction/test/tests/sideset_heat_transfer/gap_thermal_1D.i

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 2
    xmax = 2
  []
  [split]
    type = SubdomainBoundingBoxGenerator
    input = mesh
    block_id = 1
    bottom_left = '1 0 0'
    top_right = '2 0 0'
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = split
    master_block = 1
    paired_block = 0
    new_boundary = 'interface0'
  []
  uniform_refine = 4
[]

[Variables]
  # Defining a DFEM variable to handle gap discontinuity
  [T]
    order = FIRST
    family = MONOMIAL
  []
[]

[AuxVariables]
  # Auxvariable containing bulk temperature of gap
  [Tbulk]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300 # K
  []
[]

[Kernels]
  [diff]
    type = MatDiffusion
    variable = T
    diffusivity = conductivity
  []
  [source]
    type = BodyForce
    variable = T
    value = 1.0
  []
[]

[DGKernels]
  # DG kernel to represent diffusion accross element faces
  [./dg_diff]
    type = DGDiffusion
    variable = T
    epsilon = -1
    sigma = 6
    diff = conductivity
    # Ignoring gap side set because no diffusion accross there
    exclude_boundary = 'interface0'
  [../]
[]

[InterfaceKernels]
  active = 'gap'
  # Heat transfer kernel using Tbulk as material
  [gap]
    type = SideSetHeatTransferKernel
    variable = T
    neighbor_var = T
    boundary = 'interface0'
  []
  # Heat transfer kernel using Tbulk as auxvariable
  [gap_var]
    type = SideSetHeatTransferKernel
    variable = T
    neighbor_var = T
    boundary = 'interface0'
    Tbulk_var = Tbulk
  []
[]

[Functions]
  [bc_func]
    type = ConstantFunction
    value = 300
  []
  [exact]
    type = ParsedFunction
    value = '
            A := if(x < 1, -0.5, -0.25);
            B := if(x < 1, -0.293209850655001, 0.0545267662299068);
            C := if(x < 1, 300.206790149345, 300.19547323377);
            d := -1;
            A * (x+d) * (x+d) + B * (x+d) + C'
  []
[]

[BCs]
  [bc_left]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'left'
    variable = T
    diff = 'conductivity'
    epsilon = -1
    sigma = 6
    function = bc_func
  []
  [bc_right]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'right'
    variable = T
    diff = 'conductivity'
    epsilon = -1
    sigma = 6
    function = bc_func
  []
[]

[Materials]
  [k0]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 1.0
    block = 0
  []
  [k1]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 2.0
    block = 1
  []
  [gap_mat]
    type = SideSetHeatTransferMaterial
    boundary = 'interface0'
    conductivity = 1.5
    gap_length = 1.0
    h_master = 1
    h_neighbor = 1
    Tbulk = 300
    emissivity_master = 1
    emissivity_neighbor = 1
  []
[]

[Postprocessors]
  [error]
    type = ElementL2Error
    variable = T
    function = exact
  []
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

Input Parameters

neighbor_varThe variable on the other side of the interface.
C++ Type:std::vector
Options:
Description:The variable on the other side of the interface.
variableThe name of the variable that this boundary condition applies to
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this boundary condition applies to

Required Parameters

Tbulk_matgap_TbulkBulk temperature of gap as material
Default:gap_Tbulk
C++ Type:MaterialPropertyName
Options:
Description:Bulk temperature of gap as material
Tbulk_varBulk temperature of gap as variable
C++ Type:std::vector
Options:
Description:Bulk temperature of gap as variable
boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
conductancegap_conductanceConductivity of gap divided by effective gap width,conductance ignored if not provided
Default:gap_conductance
C++ Type:MaterialPropertyName
Options:
Description:Conductivity of gap divided by effective gap width,conductance ignored if not provided
diag_save_inThe name of auxiliary variables to save this Kernel'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 Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
diag_save_in_var_sideThis parameter must exist if diag_save_in variables are specified and must have the same length as diag_save_in. This vector specifies whether the corresponding aux_var should save-in jacobian contributions from the master ('m') or slave side ('s').
C++ Type:MultiMooseEnum
Options:m s
Description:This parameter must exist if diag_save_in variables are specified and must have the same length as diag_save_in. This vector specifies whether the corresponding aux_var should save-in jacobian contributions from the master ('m') or slave side ('s').
emissivity_eff_mastergap_emissivity_eff_masterEffective emmissivity of master face, radiation ignored if not provided. This value contains contributions from reflectivity, see SideSetHeatTransferMaterial for details.
Default:gap_emissivity_eff_master
C++ Type:MaterialPropertyName
Options:
Description:Effective emmissivity of master face, radiation ignored if not provided. This value contains contributions from reflectivity, see SideSetHeatTransferMaterial for details.
emissivity_eff_neighborgap_emissivity_eff_neighborEffective emmissivity of neighbor face, radiation ignored if not provided. This value contains contributions from reflectivity, see SideSetHeatTransferMaterial for details.
Default:gap_emissivity_eff_neighbor
C++ Type:MaterialPropertyName
Options:
Description:Effective emmissivity of neighbor face, radiation ignored if not provided. This value contains contributions from reflectivity, see SideSetHeatTransferMaterial for details.
h_mastergap_h_masterConvective heat transfer coefficient (master face), convection ignored if not provided
Default:gap_h_master
C++ Type:MaterialPropertyName
Options:
Description:Convective heat transfer coefficient (master face), convection ignored if not provided
h_neighborgap_h_neighborConvective heat transfer coefficient (neighbor face), convection ignored if not provided
Default:gap_h_neighbor
C++ Type:MaterialPropertyName
Options:
Description:Convective heat transfer coefficient (neighbor face), convection ignored if not provided
save_inThe name of auxiliary variables to save this Kernel'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 Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
save_in_var_sideThis parameter must exist if save_in variables are specified and must have the same length as save_in. This vector specifies whether the corresponding aux_var should save-in residual contributions from the master ('m') or slave side ('s').
C++ Type:MultiMooseEnum
Options:m s
Description:This parameter must exist if save_in variables are specified and must have the same length as save_in. This vector specifies whether the corresponding aux_var should save-in residual contributions from the master ('m') or slave side ('s').

Optional Parameters

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.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
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
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
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.

Advanced Parameters

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
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
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

Tagging Parameters

Input Files

modules/heat_conduction/test/tests/sideset_heat_transfer/cfem_gap.i
modules/heat_conduction/test/tests/sideset_heat_transfer/gap_thermal_1D.i
modules/heat_conduction/test/tests/sideset_heat_transfer/gap_thermal_ktemp_1D.i

modules/heat_conduction/test/tests/sideset_heat_transfer/cfem_gap.i

[Mesh]
  # Build 2-by-2 mesh
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    xmax = 2
    ny = 2
    ymax = 2
  []

  # Create blocs 0, 1, 2, 3
  [block_1]
    type = SubdomainBoundingBoxGenerator
    input = mesh
    block_id = 1
    bottom_left = '1 0 0'
    top_right = '2 1 0'
  []
  [block_2]
    type = SubdomainBoundingBoxGenerator
    input = block_1
    block_id = 2
    bottom_left = '0 1 0'
    top_right = '1 2 0'
  []
  [block_3]
    type = SubdomainBoundingBoxGenerator
    input = block_2
    block_id = 3
    bottom_left = '1 1 0'
    top_right = '2 2 0'
  []

  # Create inner sidesets
  [interface_01]
    type = SideSetsBetweenSubdomainsGenerator
    input = block_3
    master_block = 0
    paired_block = 1
    new_boundary = 'interface_01'
  []
  [interface_13]
    type = SideSetsBetweenSubdomainsGenerator
    input = interface_01
    master_block = 1
    paired_block = 3
    new_boundary = 'interface_13'
  []
  [interface_32]
    type = SideSetsBetweenSubdomainsGenerator
    input = interface_13
    master_block = 3
    paired_block = 2
    new_boundary = 'interface_32'
  []
  [interface_20]
    type = SideSetsBetweenSubdomainsGenerator
    input = interface_32
    master_block = 2
    paired_block = 0
    new_boundary = 'interface_20'
  []

  # Create outer boundaries
  [boundary_left_0]
    type = SideSetsAroundSubdomainGenerator
    input = interface_20
    block = 0
    normal = '-1 0 0'
    new_boundary = 'left_0'
  []
  [boundary_bot_0]
    type = SideSetsAroundSubdomainGenerator
    input = boundary_left_0
    block = 0
    normal = '0 -1 0'
    new_boundary = 'bot_0'
  []
  [boundary_bot_1]
    type = SideSetsAroundSubdomainGenerator
    input = boundary_bot_0
    block = 1
    normal = '0 -1 0'
    new_boundary = 'bot_1'
  []
  [boundary_right_1]
    type = SideSetsAroundSubdomainGenerator
    input = boundary_bot_1
    block = 1
    normal = '1 0 0'
    new_boundary = 'right_1'
  []
  [boundary_right_3]
    type = SideSetsAroundSubdomainGenerator
    input = boundary_right_1
    block = 3
    normal = '1 0 0'
    new_boundary = 'right_3'
  []
  [boundary_top_3]
    type = SideSetsAroundSubdomainGenerator
    input = boundary_right_3
    block = 3
    normal = '0 1 0'
    new_boundary = 'top_3'
  []
  [boundary_top_2]
    type = SideSetsAroundSubdomainGenerator
    input = boundary_top_3
    block = 2
    normal = '0 1 0'
    new_boundary = 'top_2'
  []
  [boundary_left_2]
    type = SideSetsAroundSubdomainGenerator
    input = boundary_top_2
    block = 2
    normal = '-1 0 0'
    new_boundary = 'left_2'
  []
  uniform_refine = 4
[]

[Variables]
  # Need to have variable for each block to allow discontinuity
  [T0]
    block = 0
  []
  [T1]
    block = 1
  []
  [T2]
    block = 2
  []
  [T3]
    block = 3
  []
[]

[Kernels]
  # Diffusion kernel for each block's variable
  [diff_0]
    type = MatDiffusion
    variable = T0
    diffusivity = conductivity
    block = 0
  []
  [diff_1]
    type = MatDiffusion
    variable = T1
    diffusivity = conductivity
    block = 1
  []
  [diff_2]
    type = MatDiffusion
    variable = T2
    diffusivity = conductivity
    block = 2
  []
  [diff_3]
    type = MatDiffusion
    variable = T3
    diffusivity = conductivity
    block = 3
  []

  # Source for two of the blocks
  [source_0]
    type = BodyForce
    variable = T0
    value = 5e5
    block = '0'
  []
  [source_3]
    type = BodyForce
    variable = T3
    value = 5e5
    block = '3'
  []
[]

[InterfaceKernels]
  # Side set kernel to represent heat transfer across blocks
  # Automatically uses the materials defined in SideSetHeatTransferMaterial
  [gap_01]
    type = SideSetHeatTransferKernel
    # This variable defined on a given block must match the master_block given when the side set was generated
    variable = T0
    # This variable defined on a given block must match the paired_block given when the side set was generated
    neighbor_var = T1
    boundary = 'interface_01'
  []
  [gap_13]
    type = SideSetHeatTransferKernel
    variable = T1
    neighbor_var = T3
    boundary = 'interface_13'
  []
  [gap_32]
    type = SideSetHeatTransferKernel
    variable = T3
    neighbor_var = T2
    boundary = 'interface_32'
  []
  [gap_20]
    type = SideSetHeatTransferKernel
    variable = T2
    neighbor_var = T0
    boundary = 'interface_20'
  []
[]

# Creating auxiliary variable to combine block restricted solutions
# Ignores discontinuity though
[AuxVariables]
  [T]
  []
[]

[AuxKernels]
  [temp_0]
    type = NormalizationAux
    variable = T
    source_variable = T0
    block = 0
  []
  [temp_1]
    type = NormalizationAux
    variable = T
    source_variable = T1
    block = 1
  []
  [temp_2]
    type = NormalizationAux
    variable = T
    source_variable = T2
    block = 2
  []
  [temp_3]
    type = NormalizationAux
    variable = T
    source_variable = T3
    block = 3
  []
[]

[BCs]
  # Boundary condition for each block's outer surface
  [bc_left_2]
    type = DirichletBC
    boundary = 'left_2'
    variable = T2
    value = 300.0
  []
  [bc_left_0]
    type = DirichletBC
    boundary = 'left_0'
    variable = T0
    value = 300.0
  []

  [bc_bot_0]
    type = DirichletBC
    boundary = 'bot_0'
    variable = T0
    value = 300.0
  []
  [bc_bot_1]
    type = DirichletBC
    boundary = 'bot_1'
    variable = T1
    value = 300.0
  []

  [./bc_top_2]
    type = ConvectiveFluxFunction # (Robin BC)
    variable = T2
    boundary = 'top_2'
    coefficient = 1e3 # W/K/m^2
    T_infinity = 600.0
  [../]
  [./bc_top_3]
    type = ConvectiveFluxFunction # (Robin BC)
    variable = T3
    boundary = 'top_3'
    coefficient = 1e3 # W/K/m^2
    T_infinity = 600.0
  [../]

  [./bc_right_3]
    type = ConvectiveFluxFunction # (Robin BC)
    variable = T3
    boundary = 'right_3'
    coefficient = 1e3 # W/K/m^2
    T_infinity = 600.0
  [../]
  [./bc_right_1]
    type = ConvectiveFluxFunction # (Robin BC)
    variable = T1
    boundary = 'right_1'
    coefficient = 1e3 # W/K/m^2
    T_infinity = 600.0
  [../]
[]

[Materials]
  [fuel]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 75
    block = '0 3'
  []
  [mod]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 7.5
    block = '1 2'
  []
  # Interface material used for SideSetHeatTransferKernel
  # Heat transfer meachnisms ignored if certain properties are not supplied
  [gap_mat]
    type = SideSetHeatTransferMaterial
    boundary = 'interface_01 interface_13 interface_32 interface_20'
    conductivity = 0.41
    gap_length = 0.002
    Tbulk = 750
    h_master = 3000
    h_neighbor = 3000
    emissivity_master = 0.85
    emissivity_neighbor = 0.85
  []
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-12
  l_tol = 1e-8
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  50'
[]

[Outputs]
  exodus = true
[]

modules/heat_conduction/test/tests/sideset_heat_transfer/gap_thermal_1D.i

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 2
    xmax = 2
  []
  [split]
    type = SubdomainBoundingBoxGenerator
    input = mesh
    block_id = 1
    bottom_left = '1 0 0'
    top_right = '2 0 0'
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = split
    master_block = 1
    paired_block = 0
    new_boundary = 'interface0'
  []
  uniform_refine = 4
[]

[Variables]
  # Defining a DFEM variable to handle gap discontinuity
  [T]
    order = FIRST
    family = MONOMIAL
  []
[]

[AuxVariables]
  # Auxvariable containing bulk temperature of gap
  [Tbulk]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300 # K
  []
[]

[Kernels]
  [diff]
    type = MatDiffusion
    variable = T
    diffusivity = conductivity
  []
  [source]
    type = BodyForce
    variable = T
    value = 1.0
  []
[]

[DGKernels]
  # DG kernel to represent diffusion accross element faces
  [./dg_diff]
    type = DGDiffusion
    variable = T
    epsilon = -1
    sigma = 6
    diff = conductivity
    # Ignoring gap side set because no diffusion accross there
    exclude_boundary = 'interface0'
  [../]
[]

[InterfaceKernels]
  active = 'gap'
  # Heat transfer kernel using Tbulk as material
  [gap]
    type = SideSetHeatTransferKernel
    variable = T
    neighbor_var = T
    boundary = 'interface0'
  []
  # Heat transfer kernel using Tbulk as auxvariable
  [gap_var]
    type = SideSetHeatTransferKernel
    variable = T
    neighbor_var = T
    boundary = 'interface0'
    Tbulk_var = Tbulk
  []
[]

[Functions]
  [bc_func]
    type = ConstantFunction
    value = 300
  []
  [exact]
    type = ParsedFunction
    value = '
            A := if(x < 1, -0.5, -0.25);
            B := if(x < 1, -0.293209850655001, 0.0545267662299068);
            C := if(x < 1, 300.206790149345, 300.19547323377);
            d := -1;
            A * (x+d) * (x+d) + B * (x+d) + C'
  []
[]

[BCs]
  [bc_left]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'left'
    variable = T
    diff = 'conductivity'
    epsilon = -1
    sigma = 6
    function = bc_func
  []
  [bc_right]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'right'
    variable = T
    diff = 'conductivity'
    epsilon = -1
    sigma = 6
    function = bc_func
  []
[]

[Materials]
  [k0]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 1.0
    block = 0
  []
  [k1]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 2.0
    block = 1
  []
  [gap_mat]
    type = SideSetHeatTransferMaterial
    boundary = 'interface0'
    conductivity = 1.5
    gap_length = 1.0
    h_master = 1
    h_neighbor = 1
    Tbulk = 300
    emissivity_master = 1
    emissivity_neighbor = 1
  []
[]

[Postprocessors]
  [error]
    type = ElementL2Error
    variable = T
    function = exact
  []
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

modules/heat_conduction/test/tests/sideset_heat_transfer/gap_thermal_ktemp_1D.i

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 2
    xmax = 2
  []
  [split]
    type = SubdomainBoundingBoxGenerator
    input = mesh
    block_id = 1
    bottom_left = '1 0 0'
    top_right = '2 0 0'
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = split
    master_block = 1
    paired_block = 0
    new_boundary = 'interface0'
  []
  uniform_refine = 4
[]

[Variables]
  [T]
    order = FIRST
    family = MONOMIAL
  []
[]

[AuxVariables]
  [Tbulk]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300 # K
  []
[]

[Kernels]
  [diff]
    type = MatDiffusion
    variable = T
    diffusivity = conductivity
  []
  [source]
    type = BodyForce
    variable = T
    value = 1.0
  []
[]

[DGKernels]
  [dg_diff]
    type = DGDiffusion
    variable = T
    epsilon = -1
    sigma = 6
    diff = conductivity
    exclude_boundary = 'interface0'
  []
[]

[InterfaceKernels]
  [gap_var]
    type = SideSetHeatTransferKernel
    variable = T
    neighbor_var = T
    boundary = 'interface0'
    Tbulk_var = Tbulk
  []
[]

[Functions]
  # Defining temperature dependent fucntion for conductivity across side set
  [kgap]
    type = ParsedFunction
    value = 't / 200'
  []
  [bc_func]
    type = ConstantFunction
    value = 300
  []
  [exact]
    type = ParsedFunction
    value = '
            A := if(x < 1, -0.5, -0.25);
            B := if(x < 1, -0.293209850655001, 0.0545267662299068);
            C := if(x < 1, 300.206790149345, 300.19547323377);
            d := -1;
            A * (x+d) * (x+d) + B * (x+d) + C'
  []
[]

[BCs]
  [bc_left]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'left'
    variable = T
    diff = 'conductivity'
    epsilon = -1
    sigma = 6
    function = bc_func
  []
  [bc_right]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'right'
    variable = T
    diff = 'conductivity'
    epsilon = -1
    sigma = 6
    function = bc_func
  []
[]

[Materials]
  [k0]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 1.0
    block = 0
  []
  [k1]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 2.0
    block = 1
  []
  [gap_mat]
    type = SideSetHeatTransferMaterial
    boundary = 'interface0'
    # Using temperature dependent function for gap conductivity
    conductivity_temperature_function = kgap
    # Variable to evaluate conductivity with
    gap_temperature = Tbulk
    gap_length = 1.0
    h_master = 1
    h_neighbor = 1
    emissivity_master = 1
    emissivity_neighbor = 1
  []
[]

[Postprocessors]
  [error]
    type = ElementL2Error
    variable = T
    function = exact
  []
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

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