GapConductance

Material to compute an effective gap conductance based on the thermal conductivity of the gap and diffusive approximation to the radiative heat transfer.

This material is automatically created by the ThermalContactAction when the gap conductance has not been specified by the user. It captures both conduction across the gap and radiation. This material takes care of computing both the conductance and the derivative of conductance with regards to temperature.

Radiative term

Gap conductance due to radiation is based on the diffusion approximation. Between surface $var element = document.getElementById("moose-equation-b68ba8e6-b02f-41e9-8e94-b64057b52dc5");katex.render("1", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-d138a656-d7dd-4887-82fc-783c9ad1e223");katex.render("2", element, {displayMode:false,throwOnError:false});$ , we define the heat flux as:

var element = document.getElementById("moose-equation-c13dd8c4-52fb-42ea-9da4-da5532772ce9");katex.render("q_{12} = \\sigma*Fe*(T_1^4 - T_2^4) ~ h_r(T_1 - T_2)", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-eee6e9e2-05f5-432d-824d-0b793d13a166");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ is the Stefan-Boltzmann constant, $var element = document.getElementById("moose-equation-6b8f70b3-16f2-4c2e-8ac8-d9b32b6d3b67");katex.render("Fe", element, {displayMode:false,throwOnError:false});$ is an emissivity function, $var element = document.getElementById("moose-equation-578565f4-228f-47be-8fde-8f424f938fb5");katex.render("T_1", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-3ae8c8ea-c79a-4c72-b20d-c76c87b9d715");katex.render("T_2", element, {displayMode:false,throwOnError:false});$ are the temperatures of the two surfaces, and $var element = document.getElementById("moose-equation-ab4757e0-c799-47e3-8169-ccda20e42ee1");katex.render("h_r", element, {displayMode:false,throwOnError:false});$ is the radiant gap conductance. Solving for $var element = document.getElementById("moose-equation-a7b9ae57-d6dd-49f2-a153-d977c28428ba");katex.render("h_r", element, {displayMode:false,throwOnError:false});$ ,

var element = document.getElementById("moose-equation-6cf5a45a-784f-4c77-9857-5994b9c86b5f");katex.render("h_r = \\sigma*Fe*(T_1^4 - T_2^4) / (T_1 - T_2)", element, {displayMode:true,throwOnError:false});

which can be factored to give:

var element = document.getElementById("moose-equation-b62f92e1-9206-4084-8a9c-03ad915826de");katex.render("h_r = \\sigma*Fe*(T_1^2 + T_2^2) * (T_1 + T_2)", element, {displayMode:true,throwOnError:false});

Assuming the gap is between infinite parallel planes, the emissivity function is given by:

var element = document.getElementById("moose-equation-cdd11fad-61fd-4482-91c2-ed157a9dcf21");katex.render("Fe = 1 / (1/e_1 + 1/e_2 - 1)", element, {displayMode:true,throwOnError:false});

For cylinders and spheres, see (Incropera et al., 2002). $var element = document.getElementById("moose-equation-92b9f13b-1d98-4080-9f04-2a4c4a7d29ec");katex.render("r_1", element, {displayMode:false,throwOnError:false});$ is the radius of surface 1, the primary surface, and $var element = document.getElementById("moose-equation-c9cca504-b678-4f5c-8590-7bc741fd586c");katex.render("r_2", element, {displayMode:false,throwOnError:false});$ the radius of the secondary surface. For cylinders:

var element = document.getElementById("moose-equation-c942f04d-6284-4225-af92-10f764831c8f");katex.render("Fe = 1 / (1/e_1 + (1/e_2 - 1) * (r_1/r_2))", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-9248b7cf-4580-4cf0-a539-89bfd6f19b80");katex.render("q_{21} = -q_{12} * (r_1/r_2)", element, {displayMode:true,throwOnError:false});

For spheres:

var element = document.getElementById("moose-equation-0e949918-ba15-4c49-9624-fb8c3769d632");katex.render("Fe = 1 / (1/e_1 + (1/e_2 - 1) * (r_1/r_2)^2)", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-8f1ab62c-0d36-447c-bd4d-8b1750d4bc42");katex.render("q_{21} = -q_{12} * (r_1/r_2)^2", element, {displayMode:true,throwOnError:false});

Input Parameters

variableTemperature variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Temperature variable

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object 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
Controllable:No
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.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
gap_tempTemperature on the other side of the gap
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Temperature on the other side of the gap
sphere_originOrigin for sphere geometry
C++ Type:libMesh::VectorValue<double>
Unit:(no unit assumed)
Controllable:No
Description:Origin for sphere geometry
stefan_boltzmann5.67037e-08The Stefan-Boltzmann constant
Default:5.67037e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The Stefan-Boltzmann constant

Optional Parameters

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

Material Property Retrieval Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshTrueWhether 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:True
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

cylinder_axis_point_1Start point for line defining cylindrical axis
C++ Type:libMesh::VectorValue<double>
Unit:(no unit assumed)
Controllable:No
Description:Start point for line defining cylindrical axis
cylinder_axis_point_2End point for line defining cylindrical axis
C++ Type:libMesh::VectorValue<double>
Unit:(no unit assumed)
Controllable:No
Description:End point for line defining cylindrical axis
gap_geometry_typeGap calculation type.
C++ Type:MooseEnum
Options:PLATE, CYLINDER, SPHERE
Controllable:No
Description:Gap calculation type.

Gap Geometry Parameters

emissivity_primary1The emissivity of the primary surface
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The emissivity of the primary surface
emissivity_secondary1The emissivity of the secondary surface
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The emissivity of the secondary surface

Radiative Heat Transfer Parameters

gap_conductivity1The thermal conductivity of the gap material
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The thermal conductivity of the gap material
gap_conductivity_functionThermal conductivity of the gap material as a function. Multiplied by gap_conductivity.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Thermal conductivity of the gap material as a function. Multiplied by gap_conductivity.
gap_conductivity_function_variableVariable to be used in the gap_conductivity_function in place of time
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Variable to be used in the gap_conductivity_function in place of time

Gap Conductivity Parameters

gap_distanceDistance across the gap
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Distance across the gap
max_gap1e+06A maximum gap (denominator) size
Default:1e+06
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:A maximum gap (denominator) size
min_gap1e-06A minimum gap (denominator) size
Default:1e-06
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:A minimum gap (denominator) size
min_gap_order0Order of the Taylor expansion below min_gap
Default:0
C++ Type:unsigned int
Controllable:No
Description:Order of the Taylor expansion below min_gap

Gap Size Parameters

orderFIRSTThe finite element order
Default:FIRST
C++ Type:MooseEnum
Options:CONSTANT, FIRST, SECOND, THIRD, FOURTH
Controllable:No
Description:The finite element order
quadratureFalseWhether or not to do quadrature point based gap heat transfer. If this is true then gap_distance and gap_temp should NOT be provided (and will be ignored); however, paired_boundary and variable are then required.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not to do quadrature point based gap heat transfer. If this is true then gap_distance and gap_temp should NOT be provided (and will be ignored); however, paired_boundary and variable are then required.

Integration Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

paired_boundaryThe boundary to be penetrated
C++ Type:BoundaryName
Controllable:No
Description:The boundary to be penetrated

Gap Surface Definition Parameters

warningsFalseWhether to output warning messages concerning nodes not being found
Default:False
C++ Type:bool
Controllable:No
Description:Whether to output warning messages concerning nodes not being found

Diagnostics And Debug Parameters

References

Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine, and others. Fundamentals of Heat and Mass Transfer. Wiley New York, sixth edition, 2002.

@book{incropera2002,
    author = "Incropera, Frank P. and DeWitt, David P. and Bergman, Theodore L. and Lavine, Adrienne S. and others",
    title = "Fundamentals of Heat and Mass Transfer",
    edition = "Sixth",
    year = "2002",
    publisher = "Wiley New York"
}

Radiative term
Input Parameters
References