GrayLambertNeumannBC

This BC imposes a heat flux density that is computed from the GrayLambertSurfaceRadiationBase userobject.

This boundary condition computes the heat flux density resulting from the radiative heat transfer between surfaces adjacent to this boundary. These surfaces must be diffuse, gray radiators (Lambert radiators). The heat flux is computed by the net radiation method described in Modest (2013). More information is available here.

There are two modes available for operating this boundary condition. The mode can be switched by the reconstruct_emission parameter. If set to false, the object queries the net radiation object (GrayLambertSurfaceRadiationBase or derived class) object for the net heat flux density on the surface. This heat flux density is applied as a constant for each participating sideset. If the sidesets are large and the flat heat flux densities on two adjacent sidesets sufficiently different, then the temperature will be non-smooth.

A smoother temperature distribution on the surface is usually obtained by noting that a large fraction of the spatial distribution of the heat flux stems from the temperature distribution and hence from the emission. The approximation made is that the emission is allowed to spatially vary, while the irradiation from other sidesets to the given sideset is assumed to be spatially flat. The heat flux at location $var element = document.getElementById("moose-equation-18629f66-0704-494c-b80a-596a5ed9dd35");katex.render("\\vec{x}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ on sideset $var element = document.getElementById("moose-equation-4d14327d-e4b5-4b2c-b092-d9ed9251ce83");katex.render("i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is computed by:

$var element = document.getElementById("moose-equation-60278cde-086e-4528-84bf-214dc1c8a392");katex.render(" \\dot{q}_i(\\vec{x}) = \\epsilon_i \\left( \\sigma T(\\vec{x})^4 - H_i\\right),", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

where $var element = document.getElementById("moose-equation-fa6bc3ed-5115-4752-aa83-d23b9c57a144");katex.render("\\sigma", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the Stefan-Boltzmann constat, $var element = document.getElementById("moose-equation-8a036f96-0fe0-498f-9751-605da5ec746c");katex.render("\\epsilon_i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ the emissivity of sideset $var element = document.getElementById("moose-equation-dae154b9-6edb-4873-8692-f3f35aacc252");katex.render("i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , and $var element = document.getElementById("moose-equation-7290e2ff-040a-45fa-81cd-a9a26bb594ec");katex.render("H_i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ the average irradiation into sideset $var element = document.getElementById("moose-equation-711fa01d-1dc7-4369-988c-435969cbcbeb");katex.render("i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ .

[Problem]
  kernel_coverage_check = false
[]

[Mesh]
  type = MeshGeneratorMesh

  [./cartesian]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1 1'
    ix = '2 2 2'
    dy = '5'
    iy = '10'
    subdomain_id = '1 2 3'
  [../]

  [./break_sides]
    type = BreakBoundaryOnSubdomainGenerator
    boundaries = 'bottom top'
    input = cartesian
  [../]

  [./left_interior]
    type = SideSetsBetweenSubdomainsGenerator
    master_block = 1
    paired_block = 2
    new_boundary = left_interior
    input = break_sides
  [../]

  [./right_interior]
    type = SideSetsBetweenSubdomainsGenerator
    master_block = 3
    paired_block = 2
    new_boundary = right_interior
    input = left_interior
  [../]
  [./rename]
    type = RenameBlockGenerator
    input = right_interior
    old_block_id = '1 2 3'
    new_block_id = '1 4 3'
  [../]
[]

[Variables]
  [./temperature]
    initial_condition = 300
    block = '1 3'
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temperature
    diffusion_coefficient = 1
    block = '1 3'
  [../]
[]

[UserObjects]
  [./cavity_radiation]
    type = ConstantViewFactorSurfaceRadiation
    boundary = 'left_interior right_interior bottom_to_2 top_to_2'
    temperature = temperature
    emissivity = '0.8 0.8 0.8 0.8'
    adiabatic_boundary = 'bottom_to_2 top_to_2'
    # these view factors are made up to exactly balance energy
    # transfer through the cavity
    view_factors = '0    0.8 0.1 0.1;
                    0.8  0   0.1 0.1;
                    0.45 0.45  0 0.1;
                    0.45 0.45 0.1  0'
    execute_on = 'INITIAL LINEAR TIMESTEP_END'
  [../]
[]

[BCs]
  [./bottom_left]
    type = DirichletBC
    preset = false
    variable = temperature
    boundary = bottom_to_1
    value = 1500
  [../]

  [./top_right]
    type = DirichletBC
    preset = false
    variable = temperature
    boundary = top_to_3
    value = 300
  [../]

  [./radiation]
    type = GrayLambertNeumannBC
    variable = temperature
    reconstruct_emission = false
    surface_radiation_object_name = cavity_radiation
    boundary = 'left_interior right_interior'
  [../]
[]

[Postprocessors]
  [./qdot_left]
    type = GrayLambertSurfaceRadiationPP
    boundary = left_interior
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_right]
    type = GrayLambertSurfaceRadiationPP
    boundary = right_interior
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_top]
    type = GrayLambertSurfaceRadiationPP
    boundary = top_to_2
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_bottom]
    type = GrayLambertSurfaceRadiationPP
    boundary = bottom_to_2
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

/opt/civet/build_0/moose/modules/heat_conduction/test/tests/gray_lambert_radiator/coupled_heat_conduction.i

[Problem]
  kernel_coverage_check = false
[]

[Mesh]
  type = MeshGeneratorMesh

  [./cartesian]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1 1'
    ix = '2 2 2'
    dy = '5'
    iy = '10'
    subdomain_id = '1 2 3'
  [../]

  [./break_sides]
    type = BreakBoundaryOnSubdomainGenerator
    boundaries = 'bottom top'
    input = cartesian
  [../]

  [./left_interior]
    type = SideSetsBetweenSubdomainsGenerator
    master_block = 1
    paired_block = 2
    new_boundary = left_interior
    input = break_sides
  [../]

  [./right_interior]
    type = SideSetsBetweenSubdomainsGenerator
    master_block = 3
    paired_block = 2
    new_boundary = right_interior
    input = left_interior
  [../]
  [./rename]
    type = RenameBlockGenerator
    input = right_interior
    old_block_id = '1 2 3'
    new_block_id = '1 4 3'
  [../]
[]

[Variables]
  [./temperature]
    initial_condition = 300
    block = '1 3'
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temperature
    diffusion_coefficient = 1
    block = '1 3'
  [../]
[]

[UserObjects]
  [./cavity_radiation]
    type = ConstantViewFactorSurfaceRadiation
    boundary = 'left_interior right_interior bottom_to_2 top_to_2'
    temperature = temperature
    emissivity = '0.8 0.8 0.8 0.8'
    adiabatic_boundary = 'bottom_to_2 top_to_2'
    # these view factors are made up to exactly balance energy
    # transfer through the cavity
    view_factors = '0    0.8 0.1 0.1;
                    0.8  0   0.1 0.1;
                    0.45 0.45  0 0.1;
                    0.45 0.45 0.1  0'
    execute_on = 'INITIAL LINEAR TIMESTEP_END'
  [../]
[]

[BCs]
  [./bottom_left]
    type = DirichletBC
    preset = false
    variable = temperature
    boundary = bottom_to_1
    value = 1500
  [../]

  [./top_right]
    type = DirichletBC
    preset = false
    variable = temperature
    boundary = top_to_3
    value = 300
  [../]

  [./radiation]
    type = GrayLambertNeumannBC
    variable = temperature
    reconstruct_emission = false
    surface_radiation_object_name = cavity_radiation
    boundary = 'left_interior right_interior'
  [../]
[]

[Postprocessors]
  [./qdot_left]
    type = GrayLambertSurfaceRadiationPP
    boundary = left_interior
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_right]
    type = GrayLambertSurfaceRadiationPP
    boundary = right_interior
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_top]
    type = GrayLambertSurfaceRadiationPP
    boundary = top_to_2
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_bottom]
    type = GrayLambertSurfaceRadiationPP
    boundary = bottom_to_2
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

Input Parameters

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
surface_radiation_object_nameName of the GrayLambertSurfaceRadiationBase UO
C++ Type:UserObjectName
Options:
Description:Name of the GrayLambertSurfaceRadiationBase UO
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

displacementsThe displacements
C++ Type:std::vector
Options:
Description:The displacements
reconstruct_emissionTrueFlag to apply constant heat flux on sideset or reconstruct emission by T^4 law.
Default:True
C++ Type:bool
Options:
Description:Flag to apply constant heat flux on sideset or reconstruct emission by T^4 law.

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

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/radiation_transfer_action/radiative_transfer_no_action.i
modules/heat_conduction/test/tests/gray_lambert_radiator/coupled_heat_conduction.i

modules/heat_conduction/test/tests/radiation_transfer_action/radiative_transfer_no_action.i

[Problem]
  kernel_coverage_check = false
[]

[Mesh]
  type = MeshGeneratorMesh

  [./cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1.3 1.9'
    ix = '3 3 3'
    dy = '2 1.2 0.9'
    iy = '3 3 3'
    subdomain_id = '0 1 0
                    4 5 2
                    0 3 0'
  [../]

  [./inner_bottom]
    type = SideSetsBetweenSubdomainsGenerator
    input = cmg
    master_block = 1
    paired_block = 5
    new_boundary = 'inner_bottom'
  [../]

  [./inner_left]
    type = SideSetsBetweenSubdomainsGenerator
    input = inner_bottom
    master_block = 4
    paired_block = 5
    new_boundary = 'inner_left'
  [../]

  [./inner_right]
    type = SideSetsBetweenSubdomainsGenerator
    input = inner_left
    master_block = 2
    paired_block = 5
    new_boundary = 'inner_right'
  [../]

  [./inner_top]
    type = SideSetsBetweenSubdomainsGenerator
    input = inner_right
    master_block = 3
    paired_block = 5
    new_boundary = 'inner_top'
  [../]

  [./rename]
    type = RenameBlockGenerator
    old_block_id = '1 2 3 4'
    new_block_id = '0 0 0 0'
    input = inner_top
  [../]

  [./split_inner_bottom]
    type = PatchSidesetGenerator
    sideset = 4
    n_patches = 2
    partitioner = centroid
    centroid_partitioner_direction = x
    input = rename
  [../]

  [./split_inner_left]
    type = PatchSidesetGenerator
    sideset = 5
    n_patches = 2
    partitioner = centroid
    centroid_partitioner_direction = y
    input = split_inner_bottom
  [../]

  [./split_inner_right]
    type = PatchSidesetGenerator
    sideset = 6
    n_patches = 2
    partitioner = centroid
    centroid_partitioner_direction = y
    input = split_inner_left
  [../]

  [./split_inner_top]
    type = PatchSidesetGenerator
    sideset = 7
    n_patches = 3
    partitioner = centroid
    centroid_partitioner_direction = x
    input = split_inner_right
  [../]
[]

[Variables]
  [./temperature]
    block = 0
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temperature
    block = 0
    diffusion_coefficient = 5
  [../]
[]

[UserObjects]
  [./gray_lambert]
    type = ViewFactorObjectSurfaceRadiation
    boundary = 'inner_bottom_0 inner_bottom_1
                inner_left_0 inner_left_1
                inner_right_0 inner_right_1
                inner_top_0 inner_top_1 inner_top_2'
    fixed_temperature_boundary = 'inner_bottom_0 inner_bottom_1'
    fixed_boundary_temperatures = '1200          1200'
    adiabatic_boundary = 'inner_top_0 inner_top_1 inner_top_2'
    emissivity = '0.9 0.9
                  0.8 0.8
                  0.4 0.4
                  1 1 1'
    temperature = temperature
    view_factor_object_name = view_factor
    execute_on = 'LINEAR TIMESTEP_END'
  [../]

  [./view_factor]
    type = UnobstructedPlanarViewFactor
    boundary = 'inner_bottom_0 inner_bottom_1
                inner_left_0 inner_left_1
                inner_right_0 inner_right_1
                inner_top_0 inner_top_1 inner_top_2'
    normalize_view_factor = true
    execute_on = 'INITIAL'
  [../]
[]

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

  [./right]
    type = DirichletBC
    variable = temperature
    boundary = right
    value = 300
  [../]

  [./radiation]
    type = GrayLambertNeumannBC
    variable = temperature
    surface_radiation_object_name = gray_lambert
    boundary = 'inner_bottom_0 inner_bottom_1
                inner_left_0 inner_left_1
                inner_right_0 inner_right_1
                inner_top_0 inner_top_1 inner_top_2'
  [../]
[]

[Postprocessors]
  [./average_T_inner_right]
    type = SideAverageValue
    variable = temperature
    boundary = inner_right
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

modules/heat_conduction/test/tests/gray_lambert_radiator/coupled_heat_conduction.i

[Problem]
  kernel_coverage_check = false
[]

[Mesh]
  type = MeshGeneratorMesh

  [./cartesian]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1 1'
    ix = '2 2 2'
    dy = '5'
    iy = '10'
    subdomain_id = '1 2 3'
  [../]

  [./break_sides]
    type = BreakBoundaryOnSubdomainGenerator
    boundaries = 'bottom top'
    input = cartesian
  [../]

  [./left_interior]
    type = SideSetsBetweenSubdomainsGenerator
    master_block = 1
    paired_block = 2
    new_boundary = left_interior
    input = break_sides
  [../]

  [./right_interior]
    type = SideSetsBetweenSubdomainsGenerator
    master_block = 3
    paired_block = 2
    new_boundary = right_interior
    input = left_interior
  [../]
  [./rename]
    type = RenameBlockGenerator
    input = right_interior
    old_block_id = '1 2 3'
    new_block_id = '1 4 3'
  [../]
[]


[Variables]
  [./temperature]
    initial_condition = 300
    block = '1 3'
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temperature
    diffusion_coefficient = 1
    block = '1 3'
  [../]
[]

[UserObjects]
  [./cavity_radiation]
    type = ConstantViewFactorSurfaceRadiation
    boundary = 'left_interior right_interior bottom_to_2 top_to_2'
    temperature = temperature
    emissivity = '0.8 0.8 0.8 0.8'
    adiabatic_boundary = 'bottom_to_2 top_to_2'
    # these view factors are made up to exactly balance energy
    # transfer through the cavity
    view_factors = '0    0.8 0.1 0.1;
                    0.8  0   0.1 0.1;
                    0.45 0.45  0 0.1;
                    0.45 0.45 0.1  0'
    execute_on = 'INITIAL LINEAR TIMESTEP_END'
  [../]
[]

[BCs]
  [./bottom_left]
    type = DirichletBC
    preset = false
    variable = temperature
    boundary = bottom_to_1
    value = 1500
  [../]

  [./top_right]
    type = DirichletBC
    preset = false
    variable = temperature
    boundary = top_to_3
    value = 300
  [../]

  [./radiation]
    type = GrayLambertNeumannBC
    variable = temperature
    reconstruct_emission = false
    surface_radiation_object_name = cavity_radiation
    boundary = 'left_interior right_interior'
  [../]
[]

[Postprocessors]
  [./qdot_left]
    type = GrayLambertSurfaceRadiationPP
    boundary = left_interior
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_right]
    type = GrayLambertSurfaceRadiationPP
    boundary = right_interior
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_top]
    type = GrayLambertSurfaceRadiationPP
    boundary = top_to_2
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_bottom]
    type = GrayLambertSurfaceRadiationPP
    boundary = bottom_to_2
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

M.F. Modest. Radiative Heat Transfer. Elsevier Science, 2013. ISBN 9780123869906. URL: https://books.google.com/books?id=J2KZq0e4lCIC.

@book{modest2013radiative,
    author = "Modest, M.F.",
    title = "Radiative Heat Transfer",
    isbn = "9780123869906",
    lccn = "2012474399",
    url = "https://books.google.com/books?id=J2KZq0e4lCIC",
    year = "2013",
    publisher = "Elsevier Science"
}

Input Parameters
Input Files

Application Usage

Physics and Syntax

Application Development

Framework Development

MOOSEDocs

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