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 on sideset is computed by:

where is the Stefan-Boltzmann constant, the emissivity of sideset , and the average irradiation into sideset .

[Problem<<<{"href": "../../syntax/Problem/index.html"}>>>]
  kernel_coverage_check = false
[]

[Mesh<<<{"href": "../../syntax/Mesh/index.html"}>>>]
  type = MeshGeneratorMesh

  [./cartesian]
    type = CartesianMeshGenerator<<<{"description": "This CartesianMeshGenerator creates a non-uniform Cartesian mesh.", "href": "../meshgenerators/CartesianMeshGenerator.html"}>>>
    dim<<<{"description": "The dimension of the mesh to be generated"}>>> = 2
    dx<<<{"description": "Intervals in the X direction"}>>> = '1 1 1'
    ix<<<{"description": "Number of grids in all intervals in the X direction (default to all one)"}>>> = '2 2 2'
    dy<<<{"description": "Intervals in the Y direction (required when dim>1 otherwise ignored)"}>>> = '5'
    iy<<<{"description": "Number of grids in all intervals in the Y direction (default to all one)"}>>> = '10'
    subdomain_id<<<{"description": "Block IDs (default to all zero)"}>>> = '1 2 3'
  [../]

  [./break_sides]
    type = BreakBoundaryOnSubdomainGenerator<<<{"description": "Break boundaries based on the subdomains to which their sides are attached. Naming convention for the new boundaries will be the old boundary name plus \"_to_\" plus the subdomain name", "href": "../meshgenerators/BreakBoundaryOnSubdomainGenerator.html"}>>>
    boundaries<<<{"description": "Boundaries to be broken. Default means to break all boundaries"}>>> = 'bottom top'
    input<<<{"description": "The mesh we want to modify"}>>> = cartesian
  [../]

  [./left_interior]
    type = SideSetsBetweenSubdomainsGenerator<<<{"description": "MeshGenerator that creates a sideset composed of the nodes located between two or more subdomains.", "href": "../meshgenerators/SideSetsBetweenSubdomainsGenerator.html"}>>>
    primary_block<<<{"description": "The primary set of blocks for which to draw a sideset between"}>>> = 1
    paired_block<<<{"description": "The paired set of blocks for which to draw a sideset between"}>>> = 2
    new_boundary<<<{"description": "The list of boundary names to create on the supplied subdomain"}>>> = left_interior
    input<<<{"description": "The mesh we want to modify"}>>> = break_sides
  [../]

  [./right_interior]
    type = SideSetsBetweenSubdomainsGenerator<<<{"description": "MeshGenerator that creates a sideset composed of the nodes located between two or more subdomains.", "href": "../meshgenerators/SideSetsBetweenSubdomainsGenerator.html"}>>>
    primary_block<<<{"description": "The primary set of blocks for which to draw a sideset between"}>>> = 3
    paired_block<<<{"description": "The paired set of blocks for which to draw a sideset between"}>>> = 2
    new_boundary<<<{"description": "The list of boundary names to create on the supplied subdomain"}>>> = right_interior
    input<<<{"description": "The mesh we want to modify"}>>> = left_interior
  [../]
  [./rename]
    type = RenameBlockGenerator<<<{"description": "Changes the block IDs and/or block names for a given set of blocks defined by either block ID or block name. The changes are independent of ordering. The merging of blocks is supported.", "href": "../meshgenerators/RenameBlockGenerator.html"}>>>
    input<<<{"description": "The mesh we want to modify"}>>> = right_interior
    old_block<<<{"description": "Elements with these block ID(s)/name(s) will be given the new block information specified in 'new_block'"}>>> = '1 2 3'
    new_block<<<{"description": "The new block ID(s)/name(s) to be given by the elements defined in 'old_block'."}>>> = '1 4 3'
  [../]
[]

[Variables<<<{"href": "../../syntax/Variables/index.html"}>>>]
  [./temperature]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 300
    block = '1 3'
  [../]
[]

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [./heat_conduction]
    type = HeatConduction<<<{"description": "Diffusive heat conduction term $-\\nabla\\cdot(k\\nabla T)$ of the thermal energy conservation equation", "href": "../kernels/HeatConduction.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = temperature
    diffusion_coefficient<<<{"description": "Property name of the diffusion coefficient"}>>> = 1
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '1 3'
  [../]
[]

[UserObjects<<<{"href": "../../syntax/UserObjects/index.html"}>>>]
  [./cavity_radiation]
    type = ConstantViewFactorSurfaceRadiation<<<{"description": "ConstantViewFactorSurfaceRadiation computes radiative heat transfer between side sets and the view factors are provided in the input file", "href": "../userobjects/ConstantViewFactorSurfaceRadiation.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left_interior right_interior bottom_to_2 top_to_2'
    temperature<<<{"description": "The coupled temperature variable."}>>> = temperature
    emissivity<<<{"description": "Emissivities for each boundary."}>>> = '0.8 0.8 0.8 0.8'
    adiabatic_boundary<<<{"description": "The list of boundary IDs from the mesh that are adiabatic."}>>> = 'bottom_to_2 top_to_2'
    # these view factors are made up to exactly balance energy
    # transfer through the cavity
    view_factors<<<{"description": "The view factors from sideset i to sideset j."}>>> = '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<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'INITIAL LINEAR TIMESTEP_END'
  [../]
[]

[BCs<<<{"href": "../../syntax/BCs/index.html"}>>>]
  [./bottom_left]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "DirichletBC.html"}>>>
    preset<<<{"description": "Whether or not to preset the BC (apply the value before the solve begins)."}>>> = false
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = temperature
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = bottom_to_1
    value<<<{"description": "Value of the BC"}>>> = 1500
  [../]

  [./top_right]
    type = DirichletBC<<<{"description": "Imposes the essential boundary condition $u=g$, where $g$ is a constant, controllable value.", "href": "DirichletBC.html"}>>>
    preset<<<{"description": "Whether or not to preset the BC (apply the value before the solve begins)."}>>> = false
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = temperature
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = top_to_3
    value<<<{"description": "Value of the BC"}>>> = 300
  [../]

  [./radiation]
    type = GrayLambertNeumannBC<<<{"description": "This BC imposes a heat flux density that is computed from the GrayLambertSurfaceRadiationBase userobject.", "href": "GrayLambertNeumannBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = temperature
    reconstruct_emission<<<{"description": "Flag to apply constant heat flux on sideset or reconstruct emission by T^4 law."}>>> = false
    surface_radiation_object_name<<<{"description": "Name of the GrayLambertSurfaceRadiationBase UO"}>>> = cavity_radiation
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left_interior right_interior'
  [../]
[]

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [./qdot_left]
    type = GrayLambertSurfaceRadiationPP<<<{"description": "This postprocessor allows to extract radiosity, heat flux density, and temperature from the GrayLambertSurfaceRadiationBase object.", "href": "../postprocessors/GrayLambertSurfaceRadiationPP.html"}>>>
    boundary<<<{"description": "The boundary of interest."}>>> = left_interior
    surface_radiation_object_name<<<{"description": "Name of the GrayLambertSurfaceRadiationBase UO"}>>> = cavity_radiation
    return_type<<<{"description": "Requested return type: RADIOSITY | HEAT_FLUX_DENSITY | TEMPERATURE"}>>> = HEAT_FLUX_DENSITY
  [../]

  [./qdot_right]
    type = GrayLambertSurfaceRadiationPP<<<{"description": "This postprocessor allows to extract radiosity, heat flux density, and temperature from the GrayLambertSurfaceRadiationBase object.", "href": "../postprocessors/GrayLambertSurfaceRadiationPP.html"}>>>
    boundary<<<{"description": "The boundary of interest."}>>> = right_interior
    surface_radiation_object_name<<<{"description": "Name of the GrayLambertSurfaceRadiationBase UO"}>>> = cavity_radiation
    return_type<<<{"description": "Requested return type: RADIOSITY | HEAT_FLUX_DENSITY | TEMPERATURE"}>>> = HEAT_FLUX_DENSITY
  [../]

  [./qdot_top]
    type = GrayLambertSurfaceRadiationPP<<<{"description": "This postprocessor allows to extract radiosity, heat flux density, and temperature from the GrayLambertSurfaceRadiationBase object.", "href": "../postprocessors/GrayLambertSurfaceRadiationPP.html"}>>>
    boundary<<<{"description": "The boundary of interest."}>>> = top_to_2
    surface_radiation_object_name<<<{"description": "Name of the GrayLambertSurfaceRadiationBase UO"}>>> = cavity_radiation
    return_type<<<{"description": "Requested return type: RADIOSITY | HEAT_FLUX_DENSITY | TEMPERATURE"}>>> = HEAT_FLUX_DENSITY
  [../]

  [./qdot_bottom]
    type = GrayLambertSurfaceRadiationPP<<<{"description": "This postprocessor allows to extract radiosity, heat flux density, and temperature from the GrayLambertSurfaceRadiationBase object.", "href": "../postprocessors/GrayLambertSurfaceRadiationPP.html"}>>>
    boundary<<<{"description": "The boundary of interest."}>>> = bottom_to_2
    surface_radiation_object_name<<<{"description": "Name of the GrayLambertSurfaceRadiationBase UO"}>>> = cavity_radiation
    return_type<<<{"description": "Requested return type: RADIOSITY | HEAT_FLUX_DENSITY | TEMPERATURE"}>>> = HEAT_FLUX_DENSITY
  [../]
[]

[Executioner<<<{"href": "../../syntax/Executioner/index.html"}>>>]
  type = Steady
[]

[Outputs<<<{"href": "../../syntax/Outputs/index.html"}>>>]
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = true
[]