B4CThermal

Compute B4C thermal conductivity and specific heat as functions of temperature, capture burnup, and porosity.

Description

This computes the thermal conductivity and specific heat of B4C. Due to the Grüneisen anharmonicity parameter ( $var element = document.getElementById("moose-equation-f54b21ee-fb16-42bb-8601-3c2388fb285f");katex.render("\\gamma", element, {displayMode:false,throwOnError:false});$ ) being dependent on specific heat, thermal conductivity is calculated after specific heat. The thermal conductivity also requires porosity and a capture burnup. Capture burnup, $var element = document.getElementById("moose-equation-982f698d-1608-4122-aa8f-4ad7a60f08e6");katex.render("x", element, {displayMode:false,throwOnError:false});$ , is the fraction of boron atoms that have captured a neutron making them unavailable to capture further neutrons compared to the initial total available boron atoms.

Add the prefix AD (e.g., ADB4CThermal) to use the AD version. Also, it is recommended to set Outputs parameter (e.g., Outputs = all) to visualize thermal properties as the models are dependent on many different inputs, and the behavior is unknown for every combination of inputs.

Thermal Conductivity

The implemented thermal conductivity model is model 3 from Qu et al. (2022). The implementation differs in that related material models available during multiphysics simulations use calculated values instead of assumed constants used in Qu et al. (2022).

The thermal conductivity (W/m-K), $var element = document.getElementById("moose-equation-410431f8-0c0e-4a5b-8f28-131352775e45");katex.render("k", element, {displayMode:false,throwOnError:false});$ , is

$var element = document.getElementById("moose-equation-3fb69e28-5dc3-462f-90a8-e6761dbeda3d");katex.render(" k = k_2 \\frac{1 - C \\phi_1}{1 - C \\phi_0},", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-1f055871-7ee8-4fc2-8eba-b7518ac3d57c");katex.render("C", element, {displayMode:false,throwOnError:false});$ is 3.6 assuming B4C is irradiated. $var element = document.getElementById("moose-equation-b71e7b11-3c0a-41da-9f07-fb0885cbd563");katex.render("\\phi", element, {displayMode:false,throwOnError:false});$ terms are related to initial porosity, $var element = document.getElementById("moose-equation-50aabfb6-3157-4c95-8c5c-bb311d90c6af");katex.render("\\phi_0", element, {displayMode:false,throwOnError:false});$ , and current porosity, $var element = document.getElementById("moose-equation-5579b6d2-42af-4add-8c91-a6a4a582b6b7");katex.render("\\phi_1", element, {displayMode:false,throwOnError:false});$ . The current porosity is provided by either an assumption (Qu et al., 2022) or by another material model during simulation. Either will need to be provided to this model. $var element = document.getElementById("moose-equation-49e076e9-09be-459c-831c-922878c68606");katex.render("k_2", element, {displayMode:false,throwOnError:false});$ is from model 2 defined as

$var element = document.getElementById("moose-equation-9c6c6446-c55b-4307-a3a1-8910d0017dab");katex.render(" k_2 = \\frac{k_1}{1.54 \\left( 1 - \\frac{k_1}{k_0} \\right) + 1},", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-fc6593af-4c2d-4839-b2cd-d5ceca6f4a59");katex.render("k_0", element, {displayMode:false,throwOnError:false});$ is a fit to experimental data (Qu et al., 2022) as

$var element = document.getElementById("moose-equation-3ef3238b-9655-42a5-ab6f-d7fcc9ec9dde");katex.render(" k_0 = \\left( 3.767 \\times 10^{-5} T + 2.429 \\times 10^{-2} \\right)^{-1},", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-d33b4db5-12f6-4296-9a29-152e913d45bc");katex.render("T", element, {displayMode:false,throwOnError:false});$ is temperature in Kelvin. $var element = document.getElementById("moose-equation-fadd4761-419b-4e0b-be93-feaf9bbb8e53");katex.render("k_1", element, {displayMode:false,throwOnError:false});$ is from model 1 defined as

$var element = document.getElementById("moose-equation-d3656543-6e6e-43d7-af3b-2a31d213aa39");katex.render(" k_1 = k_0 \\frac{\\omega_0}{\\omega_m} \\arctan\\left(\\frac{\\omega_m}{\\omega_0}\\right),", element, {displayMode:true,throwOnError:false});$

with

$var element = document.getElementById("moose-equation-93f2903d-471a-42c6-9073-45154ddbf712");katex.render(" \\left(\\frac{\\omega_0}{\\omega_m}\\right)^2 = \\frac{4 \\gamma^2 k_B N T}{3 \\pi \\mu \\Omega \\Gamma},", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-bae55c65-9c90-4c6e-9cda-fa29cda46718");katex.render("N = 5", element, {displayMode:false,throwOnError:false});$ as the number of atoms in a unit cell of B4C, $var element = document.getElementById("moose-equation-b50a409f-1cc3-464c-837a-2744b2d38859");katex.render("k_B", element, {displayMode:false,throwOnError:false});$ is the Boltzmann's constant, $var element = document.getElementById("moose-equation-71594e8a-3a32-4056-9b73-b07f3c1f4cc3");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ is the shear modulus assumed as a constant 200 GPa, $var element = document.getElementById("moose-equation-deaf10e6-0198-4d61-95a3-175859b88850");katex.render("\\Omega", element, {displayMode:false,throwOnError:false});$ is the average atomic volume of $var element = document.getElementById("moose-equation-8ff4e5a7-e047-4687-887f-95dccf18c27e");katex.render("7.282 \\times 10^{-30}", element, {displayMode:false,throwOnError:false});$ m $var element = document.getElementById("moose-equation-8cb05b44-3fa6-45ba-92e7-772494f774b0");katex.render("^3", element, {displayMode:false,throwOnError:false});$ , and the imperfection scattering parameter $var element = document.getElementById("moose-equation-822ff472-546a-4dfd-9967-367fbbc4d8df");katex.render("\\Gamma", element, {displayMode:false,throwOnError:false});$ is

$var element = document.getElementById("moose-equation-ccab07c1-8b50-41c9-9f6c-7fa428f02d82");katex.render(" \\Gamma = \\frac{4}{5} \\left(\\frac{M_B}{M_{uc}} \\right)^2 \\Gamma_B,", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-425216ee-3be2-4f70-8fa0-31acd5a03dc1");katex.render("M_B", element, {displayMode:false,throwOnError:false});$ is the atomic weight of the enriched boron and $var element = document.getElementById("moose-equation-c7469b28-a58a-4bf3-bcd8-975f47511a73");katex.render("M_{uc}", element, {displayMode:false,throwOnError:false});$ is the atomic weight of a unit cell of B4C. $var element = document.getElementById("moose-equation-4054a03f-02ab-4e6c-ba3e-21eb4aea294a");katex.render("\\Gamma_B", element, {displayMode:false,throwOnError:false});$ is

$var element = document.getElementById("moose-equation-e55dd01c-39eb-4e69-a121-2cd79dbaffc6");katex.render(" \\Gamma_B = x(1-x) \\left(\\left(\\frac{M_{Li}-M_B}{\\overline{M}}\\right)^2+\\psi \\left(\\frac{R_{Li}-R_B}{\\overline{R}}\\right)^2\\right),", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-baa8d358-be2b-44f3-8350-8c1280db52be");katex.render("M_{Li}", element, {displayMode:false,throwOnError:false});$ is the atomic weight of lithium produced from neutron capture, $var element = document.getElementById("moose-equation-bfc41519-60de-4ea1-9cf9-bef61e29aa23");katex.render("x", element, {displayMode:false,throwOnError:false});$ corresponds to a fractional burnup of total boron, $var element = document.getElementById("moose-equation-caa0d3ca-bb6d-4869-99b5-2f5f938df487");katex.render("\\overline{M} = x M_{Li} + (1-x) M_B", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-d95de95d-c95c-4981-b909-d0afc002378a");katex.render("R_{Li}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-b85b6a38-202b-421b-a587-5294f26eaabd");katex.render("R_B", element, {displayMode:false,throwOnError:false});$ are atomic radius for lithium and boron as $var element = document.getElementById("moose-equation-c8028bd9-66b0-41bc-a14c-b6d198e78fe3");katex.render("1.33 \\times 10^{-10}", element, {displayMode:false,throwOnError:false});$ m and $var element = document.getElementById("moose-equation-f037fe95-6319-4e27-a4b2-789ccd4618b4");katex.render("8.5 \\times 10^{-11}", element, {displayMode:false,throwOnError:false});$ m, respectively, $var element = document.getElementById("moose-equation-ecc794f5-2117-449a-a080-fa1bb9d2f960");katex.render("\\overline{R} = x R_{Li} + (1-x) R_B", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-eb6ec276-4205-4835-99ea-d4ffaa13e5c9");katex.render("\\psi", element, {displayMode:false,throwOnError:false});$ is

$var element = document.getElementById("moose-equation-05dad6f3-a924-4b14-858b-542ec1d4f2c1");katex.render(" \\psi = \\frac{2}{9} \\left(6.4 \\gamma \\frac{1+\\nu}{1-\\nu}\\right)^2,", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-2eace5fa-5fdd-4969-b574-69fef408e229");katex.render("\\nu", element, {displayMode:false,throwOnError:false});$ is Poisson's ratio of 0.18. $var element = document.getElementById("moose-equation-a3790dc8-206a-4b1a-9346-be306736b991");katex.render("\\gamma", element, {displayMode:false,throwOnError:false});$ is approximated as

$var element = document.getElementById("moose-equation-6a6a700c-9c92-41cb-a537-7bb6af0202b2");katex.render(" \\gamma = 3 \\frac{\\alpha_l K}{c_p \\rho_{th}},", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-f844dacf-a5f4-434d-b567-3724bf8628d1");katex.render("\\alpha_l", element, {displayMode:false,throwOnError:false});$ is the mean linear coefficient of thermal expansion, $var element = document.getElementById("moose-equation-1584087e-7186-4797-95b3-65779e4bec15");katex.render("K", element, {displayMode:false,throwOnError:false});$ is the bulk modulus set as a constant 245 GPa, $var element = document.getElementById("moose-equation-03fe9062-cb56-49c9-a40f-20d4f6bd0baf");katex.render("\\rho_{th}", element, {displayMode:false,throwOnError:false});$ is the theoretical density of B4C taken as 2389 kg/m $var element = document.getElementById("moose-equation-fc3f6120-18e6-40a6-9ebe-346623d66bca");katex.render("^3", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-364fea29-72f0-4910-ab8f-c4235fbd40b4");katex.render("c_p", element, {displayMode:false,throwOnError:false});$ is the specific heat.

Specific Heat

The specific heat (J/kg-K) is provided by a fit to experimental data (Thévenot, 1990) as

$var element = document.getElementById("moose-equation-8a793135-6de8-40ad-9120-73efb5497c64");katex.render(" c_p = \\left(22.99 + 0.0054 T - 1072000 T^{-2}\\right) \\frac{4184}{M_{B4C}},", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-c4adf8bd-b1d2-4df1-a874-4d3d0853b1f0");katex.render("M_{B4C}", element, {displayMode:false,throwOnError:false});$ is the atomic weight of B4C.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [new_mat]
    type = B4CThermal<<<{"description": "Compute B4C thermal conductivity and specific heat as functions of temperature, capture burnup, and porosity.", "href": "B4CThermal.html"}>>>
    temperature<<<{"description": "Coupled temperature"}>>> = temperature
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = all
  []
[]

Input Parameters

temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature

Required Parameters

base_nameOptional parameter that allows the user to define multiple material systems on the same block, i.e. for multiple phases
C++ Type:std::string
Controllable:No
Description:Optional parameter that allows the user to define multiple material systems on the same block, i.e. for multiple phases
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
boron_10_enrichment0.92Boron 10 atomic fraction.
Default:0.92
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Boron 10 atomic fraction.
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
capture_burnupcapture_burnupMaterial property name for burnup of boron captures.
Default:capture_burnup
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Material property name for burnup of boron captures.
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.
initial_density2269.55Initial density of B4C in kg/m^3.
Default:2269.55
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial density of B4C in kg/m^3.
mean_thermal_expansion_coefficient_name4.323e-06Material property name for mean linear thermal expansion coefficient.
Default:4.323e-06
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Material property name for mean linear thermal expansion coefficient.
poissons_ratio0.18Poisson's ratio of B4C.
Default:0.18
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Poisson's ratio of B4C.
porosityporosityPorosity material property name.
Default:porosity
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Porosity material property name.
theoretical_density2389Theorectical maximum density of B4C in kg/m^3.
Default:2389
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Theorectical maximum density of B4C in kg/m^3.

Optional 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_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
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

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

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

specific_heat_scale_factor1Optional scaling factor applied to the overall specific heat.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Optional scaling factor applied to the overall specific heat.
thermal_conductivity_scale_factor1Optional scaling factor applied to the overall thermal conductivity.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Optional scaling factor applied to the overall thermal conductivity.

Advanced: Scaling Factors Parameters

References

Zhixue Qu, Chuanjin Yu, Yitong Wei, Xiping Su, and Aibing Du. Thermal conductivity of boron carbide under fast neutron irradiation. Journal of Advanced Ceramics, 11:482–494, 3 2022. doi:10.1007/s40145-022-0572-8.

@article{Qu2022482,
    author = "Qu, Zhixue and Yu, Chuanjin and Wei, Yitong and Su, Xiping and Du, Aibing",
    title = "Thermal conductivity of boron carbide under fast neutron irradiation",
    doi = "10.1007/s40145-022-0572-8",
    journal = "Journal of Advanced Ceramics",
    month = "3",
    year = "2022",
    volume = "11",
    pages = "482-494"
}

Francois Thévenot. Boron carbide—a comprehensive review. Journal of the European Ceramic Society, 6(4):205–225, 1990. doi:10.1016/0955-2219(90)90048-K.

@article{THEVENOT1990205,
    author = "Thévenot, Francois",
    title = "Boron carbide—A comprehensive review",
    journal = "Journal of the European Ceramic Society",
    volume = "6",
    number = "4",
    pages = "205-225",
    year = "1990",
    issn = "0955-2219",
    doi = "10.1016/0955-2219(90)90048-K"
}

(test/tests/thermalB4C/exact.i)

# This test is used to compare hand calculations for B4C thermal conductivity and specific heat.

[Mesh]
  [geo]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 5
  []
[]

[Variables]
  [temperature]
    initial_condition = 400
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat]
    type = HeatConduction
    variable = temperature
  []
[]

[BCs]
  [left_right]
    type = DirichletBC
    boundary = 'left right'
    variable = temperature
    value = 600
  []
[]

[Materials]
  [mat_density]
    type = GenericConstantMaterial
    prop_names = 'density porosity capture_burnup'
    prop_values = '2269.55 0.05 0'
  []
  [new_mat]
    type = B4CThermal
    temperature = temperature
    outputs = all
  []
  [calc_cp]
    type = ParsedMaterial
    property_name = 'calc_cp'
    coupled_variables = 'temperature'
    expression = '(22.99 + 0.0054 * temperature - 1072000.0 * pow(temperature, -2)) / (52.38158589 / 1000.0) * 4.184'
    outputs = all
  []
  [calc_k]
    type = ParsedMaterial
    property_name = 'calc_k'
    material_property_names = 'porosity'
    coupled_variables = 'temperature'
    expression = 'k2 := 1.0 / (3.767e-5 * temperature + 2.429e-2); k2 * (1.0 - 3.6 * porosity) / (1.0 - 3.6 * 0.05)'
    outputs = all
  []
[]

[Postprocessors]
  [avg_T]
    type = ElementAverageValue
    variable = temperature
  []
  [k_avg]
    type = ElementAverageMaterialProperty
    mat_prop = 'thermal_conductivity'
  []
  [cp_avg]
    type = ElementAverageMaterialProperty
    mat_prop = 'specific_heat'
  []
  [exact_k]
    type = ElementAverageMaterialProperty
    mat_prop = 'calc_k'
  []
  [exact_cp]
    type = ElementAverageMaterialProperty
    mat_prop = 'calc_cp'
  []
[]

[Executioner]
  type = Transient
  dt = 2000
  num_steps = 10
[]

[Outputs]
  csv = true
[]

(test/tests/thermalB4C/exact.i)

# This test is used to compare hand calculations for B4C thermal conductivity and specific heat.

[Mesh]
  [geo]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 5
  []
[]

[Variables]
  [temperature]
    initial_condition = 400
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat]
    type = HeatConduction
    variable = temperature
  []
[]

[BCs]
  [left_right]
    type = DirichletBC
    boundary = 'left right'
    variable = temperature
    value = 600
  []
[]

[Materials]
  [mat_density]
    type = GenericConstantMaterial
    prop_names = 'density porosity capture_burnup'
    prop_values = '2269.55 0.05 0'
  []
  [new_mat]
    type = B4CThermal
    temperature = temperature
    outputs = all
  []
  [calc_cp]
    type = ParsedMaterial
    property_name = 'calc_cp'
    coupled_variables = 'temperature'
    expression = '(22.99 + 0.0054 * temperature - 1072000.0 * pow(temperature, -2)) / (52.38158589 / 1000.0) * 4.184'
    outputs = all
  []
  [calc_k]
    type = ParsedMaterial
    property_name = 'calc_k'
    material_property_names = 'porosity'
    coupled_variables = 'temperature'
    expression = 'k2 := 1.0 / (3.767e-5 * temperature + 2.429e-2); k2 * (1.0 - 3.6 * porosity) / (1.0 - 3.6 * 0.05)'
    outputs = all
  []
[]

[Postprocessors]
  [avg_T]
    type = ElementAverageValue
    variable = temperature
  []
  [k_avg]
    type = ElementAverageMaterialProperty
    mat_prop = 'thermal_conductivity'
  []
  [cp_avg]
    type = ElementAverageMaterialProperty
    mat_prop = 'specific_heat'
  []
  [exact_k]
    type = ElementAverageMaterialProperty
    mat_prop = 'calc_k'
  []
  [exact_cp]
    type = ElementAverageMaterialProperty
    mat_prop = 'calc_cp'
  []
[]

[Executioner]
  type = Transient
  dt = 2000
  num_steps = 10
[]

[Outputs]
  csv = true
[]

(test/tests/thermalB4C/ad_thermal.i)

# This test is used to compare hand calculations for B4C thermal conductivity and specific heat with more coupling.

[Mesh]
  [geo]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 5
  []
[]

[Variables]
  [temperature]
    initial_condition = 400
  []
[]

[Kernels]
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
  [heat]
    type = ADHeatConduction
    variable = temperature
  []
[]

[BCs]
  [left_right]
    type = ADDirichletBC
    boundary = 'left right'
    variable = temperature
    value = 800
  []
[]

[Materials]
  [mat_density]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = '2269.55'
  []
  [mat_porosity]
    type = ADPiecewiseLinearInterpolationMaterial
    property = porosity
    variable = temperature
    x = '300 500 1000'
    y = '0.05 0.065 0.09'
  []
  [mat_burnup]
    type = ADPiecewiseLinearInterpolationMaterial
    property = capture_burnup
    variable = temperature
    x = '300 500 1000'
    y = '0 0 1.5E-02'
    outputs = all
  []
  [new_mat]
    type = ADB4CThermal
    temperature = temperature
    outputs = all
  []
[]

[Postprocessors]
  [avg_T]
    type = ElementAverageValue
    variable = temperature
  []
  [k_avg]
    type = ADElementAverageMaterialProperty
    mat_prop = 'thermal_conductivity'
  []
  [cp_avg]
    type = ADElementAverageMaterialProperty
    mat_prop = 'specific_heat'
  []
  [avg_burnup]
    type = ADElementAverageMaterialProperty
    mat_prop = 'capture_burnup'
  []
  [avg_porosity]
    type = ADElementAverageMaterialProperty
    mat_prop = 'porosity'
  []
[]

[Executioner]
  type = Transient
  dt = 600
  num_steps = 10
[]

[Outputs]
  csv = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References