UO2ThermalMeso

Computes thermal conductivity and specific heat capacity of uranium dioxide fuel.

Description

UO2ThermalMeso computes the thermal conductivity of UO $var element = document.getElementById("moose-equation-0bb74ccc-b095-47d0-b454-fb6723b4b199");katex.render("_2", element, {displayMode:false,throwOnError:false});$ based on Fink (2000) and Lucuta et al. (1996), and mesoscale insights. The model builds on UO2Thermal. In particular, the model computes a modified correction due to porosity. The modified correction is given by $var element = document.getElementById("moose-equation-bff7c7d6-7584-418d-bc63-7c7808cf45c5");katex.render(" f_{por}' = \\kappa_{GB} \\kappa_{bulk} f_{por}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-08313b91-c3d1-4a5d-9b46-5d133a804b79");katex.render("f_{por}'", element, {displayMode:false,throwOnError:false});$ is the modified correction, $var element = document.getElementById("moose-equation-078ef09b-7ff9-48cf-839c-f27a71fa4435");katex.render("\\kappa_{GB}", element, {displayMode:false,throwOnError:false});$ is a correction for grain boundary porosity, $var element = document.getElementById("moose-equation-df60aa71-d1f6-47af-9a19-1bcec1a88086");katex.render("\\kappa_{bulk}", element, {displayMode:false,throwOnError:false});$ is a correction for bulk porosity, and $var element = document.getElementById("moose-equation-dfd8a27c-5064-4db6-9472-a3d2da128dcc");katex.render("f_{por}", element, {displayMode:false,throwOnError:false});$ is the correction from UO2Thermal. $var element = document.getElementById("moose-equation-13943988-c846-4884-b2f4-61af97b2f848");katex.render(" \\kappa_{GB} = \\frac{1.0}{1 + \\frac{k_0 R_k'}{2 r_g}}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-23240d72-1dd2-4ec7-997b-c3fe34e86c18");katex.render("r_g", element, {displayMode:false,throwOnError:false});$ is the grain radius and $var element = document.getElementById("moose-equation-005c4651-7361-441a-9b74-abf765441b3d");katex.render("k_0", element, {displayMode:false,throwOnError:false});$ is the unirradiated thermal conductivity of UO $var element = document.getElementById("moose-equation-67f1d2bc-0871-404e-a1cf-58b1d66ada88");katex.render("_2", element, {displayMode:false,throwOnError:false});$ . $var element = document.getElementById("moose-equation-fbf8cee5-8761-4c2c-89aa-4d53972980ee");katex.render(" R_k' = \\frac{A_{bub} + A_{GB}}{\\frac{A_{GB}}{R_{k0}} + \\frac{A_{bub}}{R_{bub}}}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-4f531aa3-3074-4559-b9c9-443dbfb4d17d");katex.render("A_{bub} = 2 d_{bub} c_{GB}", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-fc87b359-4266-4850-95c0-c72115c558db");katex.render("A_{GB} = d_{GB}(1-c_{GB})", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-a72dde8d-bf79-4638-aadc-5b480eb31d77");katex.render("R_{k0}", element, {displayMode:false,throwOnError:false});$ is the grain boundary thermal resistance, $var element = document.getElementById("moose-equation-70722434-ea58-41a8-910c-523fd05ff44a");katex.render("R_{bub}", element, {displayMode:false,throwOnError:false});$ is the bubble thermal resistance (defined as $var element = document.getElementById("moose-equation-5c0d8a47-360f-4b3a-830d-97b29e237dc0");katex.render("d_{bub}/k_{bub}", element, {displayMode:false,throwOnError:false});$ ), $var element = document.getElementById("moose-equation-e22ed961-cca1-43f9-9cef-13b26d1a2462");katex.render("d_{bub}", element, {displayMode:false,throwOnError:false});$ is the bubble diameter, $var element = document.getElementById("moose-equation-f84ce86e-4cf0-4cc7-89b0-1336e8999cf3");katex.render("c_{GB}", element, {displayMode:false,throwOnError:false});$ is the grain boundary coverage, $var element = document.getElementById("moose-equation-b7cb8d2a-d54c-4ca3-99f6-a4a6db913944");katex.render("d_{GB}", element, {displayMode:false,throwOnError:false});$ is the grain boundary representative length, and $var element = document.getElementById("moose-equation-b1065452-cfaf-4d38-9cb3-0c971a5b8932");katex.render("k_{bub}", element, {displayMode:false,throwOnError:false});$ is the thermal conductivity within the bubbles.

$var element = document.getElementById("moose-equation-abd59fe8-8031-4421-b6b3-c25f89b58f8f");katex.render(" \\kappa_{bulk} = \\frac{1 - p_{bulk}}{1 + 0.5 p_{bulk}}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-961fb12b-2111-4959-91a5-8f1eed75ef36");katex.render("p_{bulk}", element, {displayMode:false,throwOnError:false});$ is given by $var element = document.getElementById("moose-equation-68b50c3a-1f09-4d4b-9de5-54075625406c");katex.render(" p_{bulk} = (f_{grain} + f_{resolved}) \\frac{N_A}{N}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-4f98a78f-8fd2-4910-a041-a043f2513ed6");katex.render("f_{grain} + f_{resolved}", element, {displayMode:false,throwOnError:false});$ is the total fission gas in the grains, $var element = document.getElementById("moose-equation-9be12c15-c78e-4bcd-964b-819858069ca8");katex.render("N_A", element, {displayMode:false,throwOnError:false});$ is Avagadro's number, and $var element = document.getElementById("moose-equation-fdee52fc-ec3b-4a7d-978e-67a872c68826");katex.render("N = 4/l_c^3", element, {displayMode:false,throwOnError:false});$ with $var element = document.getElementById("moose-equation-12f3a126-f320-4dbc-983c-1d89909e76c0");katex.render("l_c", element, {displayMode:false,throwOnError:false});$ being the lattice constant for UO $var element = document.getElementById("moose-equation-6ba19c53-8cf2-40e3-8b13-efeb48fd76da");katex.render("_2", element, {displayMode:false,throwOnError:false});$ .

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [fuel_thermal]
    type = UO2ThermalMeso<<<{"description": "Computes thermal conductivity and specific heat capacity of uranium dioxide fuel.", "href": "UO2ThermalMeso.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 2
    temperature<<<{"description": "Coupled temperature"}>>> = T
    thermal_conductivity_model<<<{"description": "The thermal conductivity model."}>>> = FINK_LUCUTA
    burnup<<<{"description": "Coupled burnup"}>>> = burnup
    initial_porosity<<<{"description": "Initial porosity.  Must be between 0.0 and 1.0."}>>> = 0.015
    grain_radius<<<{"description": "fuel Grain radius in m"}>>> = 2.5e-6
  []
[]

Input Parameters

temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature
thermal_conductivity_modelFINK_LUCUTAThe thermal conductivity model.
Default:FINK_LUCUTA
C++ Type:MooseEnum
Options:FINK_LUCUTA, HALDEN, NFIR, MODIFIED_NFI, RONCHI, STAICU, TOPTAN
Controllable:No
Description:The thermal conductivity model.

Required Parameters

Gd_content0Weight fraction of gadolinium in fuel.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Weight fraction of gadolinium in fuel.
Lucuta_and_mesoTrueUse mesoscale model and Lucuta model
Default:True
C++ Type:bool
Controllable:No
Description:Use mesoscale model and Lucuta model
Rk01.13e-09GB thermal resistance, defaults to value for Sym. Tilt GB in UO2 from LANL MD.
Default:1.13e-09
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:GB thermal resistance, defaults to value for Sym. Tilt GB in UO2 from LANL MD.
axial_relocation_objectName of the AxialRelocationUserObject that determines whether the fuel has crumbled.
C++ Type:UserObjectName
Controllable:No
Description:Name of the AxialRelocationUserObject that determines whether the fuel has crumbled.
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
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
bubble_radius5e-07fuel Grain radius in m
Default:5e-07
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:fuel Grain radius in m
burnupCoupled burnup
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled burnup
burnup_functionBurnup function
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Burnup function
burnup_materialMaterial property name for burnup.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Material property name for burnup.
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
d_GB4e-09GB representative length in m, defaults to value for Rk0 = 1.13e-9 m^2 K/W
Default:4e-09
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:GB representative length in m, defaults to value for Rk0 = 1.13e-9 m^2 K/W
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_thermal_conductivityThe layered average thermal conductivity across the gas gap.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The layered average thermal conductivity across the gas gap.
grain_radius1e-05fuel Grain radius in m
Default:1e-05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:fuel Grain radius in m
hbs_porosity_correctionNONEThe porosity correction method for the thermal conductivity model in the high burnup structure.
Default:NONE
C++ Type:MooseEnum
Options:NONE, KAMPF, LEE, MAXWELLEUCKEN
Controllable:No
Description:The porosity correction method for the thermal conductivity model in the high burnup structure.
initial_porosity0.05Initial porosity. Must be between 0.0 and 1.0.
Default:0.05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial porosity. Must be between 0.0 and 1.0.
k_bub0.00565Thermal conductivity within the bubbles. Defaults to thermal conductivity of Xe.
Default:0.00565
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Thermal conductivity within the bubbles. Defaults to thermal conductivity of Xe.
model_hbs_formationFalseFlag on whether to take into account the volume fraction of high burnup structure that has formed on the thermal conductivity calculation.
Default:False
C++ Type:bool
Controllable:No
Description:Flag on whether to take into account the volume fraction of high burnup structure that has formed on the thermal conductivity calculation.
no_FGFalseNo irradiation effects on thermal conductivity
Default:False
C++ Type:bool
Controllable:No
Description:No irradiation effects on thermal conductivity
oxy_to_metal_ratio2Oxygen-to-metal ratio.
Default:2
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Oxygen-to-metal ratio.
porosityCoupled porosity
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled porosity
porosity_materialFalseWhether a material property for porosity is supplied.
Default:False
C++ Type:bool
Controllable:No
Description:Whether a material property for porosity is supplied.

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

Input Files

(test/tests/meso_thcond_test/onlymeso_thcond_test.i)
(test/tests/meso_thcond_test/meso_thcond_test.i)

References

J. K. Fink. Thermophysical properties of uranium dioxide. Journal of Nuclear Materials, 279(1):1–18, 2000.

@ARTICLE{fink00,
    author = "Fink, J. K.",
    title = "Thermophysical properties of uranium dioxide",
    journal = "Journal of Nuclear Materials",
    year = "2000",
    volume = "279",
    pages = "1-18",
    number = "1",
    issn = "0022-3115"
}

P.G. Lucuta, Hj. Matzke, and I.J. Hastings. A pragmatic approach to modelling thermal conductivity of irradiated UO$_2$ fuel: review and recommendations. Journal of Nuclear Materials, 232(2-3):166–180, 1996. URL: http://www.sciencedirect.com/science/article/pii/S0022311596004047, doi:10.1016/S0022-3115(96)00404-7.

@ARTICLE{Lucuta1996,
    author = "Lucuta, P.G. and Matzke, Hj. and Hastings, I.J.",
    title = "A pragmatic approach to modelling thermal conductivity of irradiated {UO}$\_2$ fuel: Review and recommendations",
    journal = "Journal of Nuclear Materials",
    year = "1996",
    volume = "232",
    pages = "166-180",
    number = "2-3",
    bdsk-url-1 = "http://www.sciencedirect.com/science/article/pii/S0022311596004047",
    bdsk-url-2 = "http://dx.doi.org/10.1016/S0022-3115(96)00404-7",
    doi = "10.1016/S0022-3115(96)00404-7",
    issn = "0022-3115",
    url = "http://www.sciencedirect.com/science/article/pii/S0022311596004047"
}

(test/tests/meso_thcond_test/meso_thcond_test.i)

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = pelletfine1_rz.e
  []
[]

[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300.0 # set initial T to ambient
  []
[]

[AuxVariables]
  [fission_rate]
    order = FIRST
    family = LAGRANGE
    block = 2
  []
  [burnup]
    order = FIRST
    family = LAGRANGE
    block = 2
  []
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []
  [heat_source]
    type = NeutronHeatSource
    variable = T
    block = 2
    energy_per_fission = 3.2e-11
    fission_rate = fission_rate
  []
[]

[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    block = 2
    value = 1.183e19 # corrected average power to 200 W/cm
  []
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 2
  []
  [burnup]
    type = ConstantAux
    variable = burnup
    value = 0.001
  []
[]

[BCs]
  [ConstantT]
    type = DirichletBC
    boundary = 10
    variable = T
    value = 500
  []
[]

[Materials]
  [GBcoverage]
    type = GenericConstantMaterial
    prop_names = 'GBCoverage fis_gas_grain fis_gas_reslvd'
    prop_values = '0.4 300.0 41.0'
    block = 2
  []
  [fuel_thermal]
    type = UO2ThermalMeso
    block = 2
    temperature = T
    thermal_conductivity_model = FINK_LUCUTA
    burnup = burnup
    initial_porosity = 0.015
    grain_radius = 2.5e-6
  []
  [density]
    type = ParsedMaterial
    block = 2
    property_name = density
    expression = 10431.0
  []
[]

[Problem]
[]

[Postprocessors]
  [MaxT]
    type = NodalExtremeValue
    variable = T
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'


  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart -mat_mffd_type'
  petsc_options_value = 'hypre boomeramg 101 ds'
  l_max_its = 60
  l_tol = 1e-4
  nl_max_its = 15
  nl_rel_tol = 1e-11
  nl_abs_tol = 1e-12
[]

[Outputs]
  file_base = out
  exodus = true
[]

(test/tests/meso_thcond_test/onlymeso_thcond_test.i)

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = pelletfine1_rz.e
  []
[]

[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300.0 # set initial T to ambient
  []
[]

[AuxVariables]
  [fission_rate]
    order = FIRST
    family = LAGRANGE
    block = 2
  []
  [burnup]
    order = FIRST
    family = LAGRANGE
    block = 2
  []
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []
  [heat_source]
    type = NeutronHeatSource
    variable = T
    block = 2
    energy_per_fission = 3.2e-11
    fission_rate = fission_rate
  []
[]

[Problem]
[]

[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    block = 2
    value = 1.183e19 # corrected average power to 200 W/cm
  []
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 2
  []
  [burnup]
    type = ConstantAux
    variable = burnup
    value = 0.001
  []
[]

[BCs]
  [ConstantT]
    type = DirichletBC
    boundary = 10
    variable = T
    value = 500
  []
[]

[Materials]
  [GBcoverage]
    # prop_values = '0.0 0.0'
    type = GenericConstantMaterial
    prop_names = 'GBCoverage fis_gas_grain fis_gas_reslvd'
    prop_values = '0.4 300.0 68.0'
    block = 2
  []
  [fuel_thermal]
    type = UO2ThermalMeso
    block = 2
    temperature = T
    thermal_conductivity_model = FINK_LUCUTA
    burnup = burnup
    initial_porosity = 0.015
    grain_radius = 2.5e-6
    Lucuta_and_meso = false
  []
  [density]
    type = ParsedMaterial
    block = 2
    property_name = density
    expression = 10431.0
  []
[]

[Postprocessors]
  [MaxT]
    type = NodalExtremeValue
    variable = T
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'


  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart -mat_mffd_type'
  petsc_options_value = 'hypre boomeramg 101 ds'
  l_max_its = 60
  l_tol = 1e-4
  nl_max_its = 15
  nl_rel_tol = 1e-11
  nl_abs_tol = 1e-12
[]

[Outputs]
  file_base = onlymeso
  exodus = true
[]

(test/tests/meso_thcond_test/meso_thcond_test.i)

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = pelletfine1_rz.e
  []
[]

[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300.0 # set initial T to ambient
  []
[]

[AuxVariables]
  [fission_rate]
    order = FIRST
    family = LAGRANGE
    block = 2
  []
  [burnup]
    order = FIRST
    family = LAGRANGE
    block = 2
  []
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []
  [heat_source]
    type = NeutronHeatSource
    variable = T
    block = 2
    energy_per_fission = 3.2e-11
    fission_rate = fission_rate
  []
[]

[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    block = 2
    value = 1.183e19 # corrected average power to 200 W/cm
  []
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 2
  []
  [burnup]
    type = ConstantAux
    variable = burnup
    value = 0.001
  []
[]

[BCs]
  [ConstantT]
    type = DirichletBC
    boundary = 10
    variable = T
    value = 500
  []
[]

[Materials]
  [GBcoverage]
    type = GenericConstantMaterial
    prop_names = 'GBCoverage fis_gas_grain fis_gas_reslvd'
    prop_values = '0.4 300.0 41.0'
    block = 2
  []
  [fuel_thermal]
    type = UO2ThermalMeso
    block = 2
    temperature = T
    thermal_conductivity_model = FINK_LUCUTA
    burnup = burnup
    initial_porosity = 0.015
    grain_radius = 2.5e-6
  []
  [density]
    type = ParsedMaterial
    block = 2
    property_name = density
    expression = 10431.0
  []
[]

[Problem]
[]

[Postprocessors]
  [MaxT]
    type = NodalExtremeValue
    variable = T
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'


  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart -mat_mffd_type'
  petsc_options_value = 'hypre boomeramg 101 ds'
  l_max_its = 60
  l_tol = 1e-4
  nl_max_its = 15
  nl_rel_tol = 1e-11
  nl_abs_tol = 1e-12
[]

[Outputs]
  file_base = out
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References