SideSetHeatTransferMaterial

This material constructs the necessary coefficients and properties for SideSetHeatTransferKernel.

Description

This is a interface material (boudary restricted material) specifically for application to SideSetHeatTransferKernel. Material properties generated:

- gap_conductance: $var element = document.getElementById("moose-equation-f1053766-7f44-423f-808e-e8ab0dc1c26f");katex.render("C_{\\mathrm{gap}} = k_{\\mathrm{gap}} / \\delta", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

- gap_Tbulk : $var element = document.getElementById("moose-equation-97858d5b-25b5-4169-9022-7e556d67f0bb");katex.render("T_{\\mathrm{bulk}}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

- gap_h_master : $var element = document.getElementById("moose-equation-5e2a20dd-1c72-4416-a4e7-3bb9e413b445");katex.render("h^{+}_{\\mathrm{gap}}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

- gap_h_neighbor : $var element = document.getElementById("moose-equation-c5175b5d-fc87-4459-9edc-a3e4196aa805");katex.render("h^{-}_{\\mathrm{gap}}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

- gap_emissivity_eff_master :

$var element = document.getElementById("moose-equation-f0a12194-db91-4088-b2fa-ac280b819140");katex.render(" \\epsilon^{+}_{\\mathrm{eff}} = \\sigma\\epsilon^{+}\\frac{1-\\rho^{-}}{1-\\rho^{+}\\rho^{-}}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

- gap_emissivity_eff_neighbor :

$var element = document.getElementById("moose-equation-14394609-cffe-4bcb-9a42-3961804d2e81");katex.render(" \\epsilon^{-}_{\\mathrm{eff}} = \\sigma\\epsilon^{-}\\frac{1-\\rho^{+}}{1-\\rho^{+}\\rho^{-}}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

$var element = document.getElementById("moose-equation-a0e58530-f41b-45fb-8c39-dab13dc6b4f1");katex.render("\\sigma", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the Stefan-Boltzmann constant defined as $var element = document.getElementById("moose-equation-38b34736-3933-4046-92d3-eda4e4b1faa1");katex.render("5.670374419\\times 10^{-8} \\ W/m^2/K^4", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ . The input variables that define these materials with their default values:

- conductivity: $var element = document.getElementById("moose-equation-f564cee0-b570-4796-a14f-b2c052f4d3d0");katex.render("k(\\vec{r},t)", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ default: 0

- conductivity_temperature_function: $var element = document.getElementById("moose-equation-97682a93-ff2c-4c21-a4ec-8ad1c9193bd6");katex.render("k_{\\mathrm{gap}}(\\vec{r},T)", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

- gap_temperature : $var element = document.getElementById("moose-equation-9341de6f-2b54-4566-8cfb-046304579898");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ for $var element = document.getElementById("moose-equation-74d767cd-d62b-44b4-b4e0-ec7e07c75bde");katex.render("k_{\\mathrm{gap}}(\\vec{r},T)", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

- gap_length : $var element = document.getElementById("moose-equation-bf1adbe1-6f2e-4bd3-93a8-36e1a67c8fd8");katex.render("\\delta", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ default: 1

- Tbulk : $var element = document.getElementById("moose-equation-bb25e957-4649-48b6-9e0d-ef25ae5d1d60");katex.render("T_{\\mathrm{bulk}}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ default: 300 K

- h_master : $var element = document.getElementById("moose-equation-064e4eb9-fdb0-402f-bfea-49187713cce6");katex.render("h^{+}_{\\mathrm{gap}}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ default: 0

- h_neighbor : $var element = document.getElementById("moose-equation-43dbf409-77e0-4009-87e0-15d9d13290cc");katex.render("h^{-}_{\\mathrm{gap}}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ default: 0

- emissivity_master : $var element = document.getElementById("moose-equation-725a6a95-68c6-4a17-9b27-45d3e7e76669");katex.render("\\epsilon^{+}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ default: 0

- emissivity_neighbor : $var element = document.getElementById("moose-equation-622a63a7-436d-4bad-b53b-0de103b75e20");katex.render("\\epsilon^{-}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ default: 0

- reflectivity_master : $var element = document.getElementById("moose-equation-62392f4a-cfba-4754-900e-b1872932406f");katex.render("\\rho^{+}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ default: $var element = document.getElementById("moose-equation-b71062f4-148f-49f4-930e-da4a8680d5ff");katex.render("1-\\epsilon^{+}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

- reflectivity_neighbor : $var element = document.getElementById("moose-equation-98ee4e0b-7107-4936-aad8-ece7ac3eb5fb");katex.render("\\rho^{-}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ default: $var element = document.getElementById("moose-equation-25dabadb-2b25-4ae5-a46d-c216ddde13eb");katex.render("1-\\epsilon^{-}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

Example Input File Syntax

Defining conductivity as a space-time dependent function:

[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
[]

/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
[]

Defining conductivity as a temperature dependent function:

[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
[]

/opt/civet/build_0/moose/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
[]

Input Parameters

Tbulk300Bulk temperature of gap in K.
Default:300
C++ Type:FunctionName
Options:
Description:Bulk temperature of gap in K.
blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
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
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Options:
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
conductivity0Heat conductivity in W/m/K.
Default:0
C++ Type:FunctionName
Options:
Description:Heat conductivity in W/m/K.
conductivity_temperature_functionHeat conductivity in W/m/K as a function of temperature.
C++ Type:FunctionName
Options:
Description:Heat conductivity in W/m/K as a function of temperature.
emissivity_master0Master face emissivity.
Default:0
C++ Type:FunctionName
Options:
Description:Master face emissivity.
emissivity_neighbor0Neighbor face emissivity.
Default:0
C++ Type:FunctionName
Options:
Description:Neighbor face emissivity.
gap_length1Total width of gap in m.
Default:1
C++ Type:FunctionName
Options:
Description:Total width of gap in m.
gap_temperatureCoupled Temperature of gap, used for computing temperature dependent conductivity.
C++ Type:std::vector
Options:
Description:Coupled Temperature of gap, used for computing temperature dependent conductivity.
h_master0Convective heat transfer coefficient (master face) in W/m^2/K.
Default:0
C++ Type:FunctionName
Options:
Description:Convective heat transfer coefficient (master face) in W/m^2/K.
h_neighbor0Convective heat transfer coefficient (neighbor face) in W/m^2/K.
Default:0
C++ Type:FunctionName
Options:
Description:Convective heat transfer coefficient (neighbor face) in W/m^2/K.
reflectivity_masterMaster face reflectivity, uses (1-emissivity) if not provided.
C++ Type:FunctionName
Options:
Description:Master face reflectivity, uses (1-emissivity) if not provided.
reflectivity_neighborNeighbor face reflectivity, uses (1-emissivity) if not provided.
C++ Type:FunctionName
Options:
Description:Neighbor face reflectivity, uses (1-emissivity) if not provided.

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
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
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

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector
Options:
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object

Outputs 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
[]

References

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