U10MoThermal

Computes thermal properties of low enriched uranium-molybdenum alloy.

Description

Low enriched uranium alloyed with 10 wt% (nominally) molybdenum is referred to as U-10Mo.

Thermal Conductivity

Thermal conductivity $var element = document.getElementById("moose-equation-b2a56f0b-4ced-40ac-a6f7-f70cdc5d978c");katex.render("k", element, {displayMode:false,throwOnError:false});$ (W/m-K) of U-10Mo, modeled in U10MoThermal is from Burkes et al. (2010) and Rabin et al. (2020). Three options are available.

Burkes uses $var element = document.getElementById("moose-equation-e80ded0d-9a55-4616-9c08-5a970aa8302e");katex.render("F_P", element, {displayMode:false,throwOnError:false});$ as a porosity correction given in Eq. (1), where it is assumed that $var element = document.getElementById("moose-equation-b12a4f90-0c08-4015-ac7e-9fd996121a97");katex.render("\\beta = 2.5", element, {displayMode:false,throwOnError:false});$ : $(1)var element = document.getElementById("moose-equation-e7c6096f-c177-49e9-9ae6-f979a979ec62");katex.render(" \\begin{aligned} k & = (0.606 + 0.0351 T) \\times F_p \\\\ F_p & = \\frac{(1-p)}{(1 + \\beta p)} \\\\ \\end{aligned}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-bd7252eb-165b-48bd-b91c-c4caae8e9b61");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature in K and $var element = document.getElementById("moose-equation-ecad0a79-5d24-4b20-b4e6-3c646d8ef3fd");katex.render("p", element, {displayMode:false,throwOnError:false});$ is the porosity.
USHPRR uses a set of linear relationships, each one for a given temperature with a linear dependence on fission density. For details, see p. 144 in Rabin et al. (2020).
USHPRRFit, uses a smoothed fit of the set of linear relationships in the USHPRR option. This preserves the character of the USHPRR equations while providing a smooth fit that provides better derivative information.

Specific Heat Capacity

Specific heat $var element = document.getElementById("moose-equation-c7db169f-8e4d-4f55-8206-fb5d79442da9");katex.render("c_P", element, {displayMode:false,throwOnError:false});$ (J/kg-K) of U-10Mo is from Burkes et al. (2010) and Rabin et al. (2020).

For the Burkes option: $var element = document.getElementById("moose-equation-1e08cb2f-577b-4450-9167-8b0d14913907");katex.render(" c_P = 113 + 0.0705 T", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-eb68828e-3033-4707-9440-0456190ad205");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature in K.
USHPRR uses a set of linear relationships, each one for a given temperature with a linear dependence on fission density. For details, see p. 129 in Rabin et al. (2020).
USHPRRFit, uses a smoothed fit of the set of linear relationships in the USHPRR option. This preserves the character of the USHPRR equations while providing a smooth fit that provides better derivative information.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [fuel_U10Mo]
    type = U10MoThermal<<<{"description": "Computes thermal properties of low enriched uranium-molybdenum alloy.", "href": "U10MoThermal.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
    temperature<<<{"description": "Coupled temperature"}>>> = T
    porosity<<<{"description": "Coupled Porosity"}>>> = por
  []
[]

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [U10Mo]
    type = U10MoThermal<<<{"description": "Computes thermal properties of low enriched uranium-molybdenum alloy.", "href": "U10MoThermal.html"}>>>
    temperature<<<{"description": "Coupled temperature"}>>> = temperature
    thermal_conductivity_model<<<{"description": "The model to use for thermal conductivity: Burkes USHPRR USHPRRFit table"}>>> = USHPRR
    specific_heat_model<<<{"description": "The model to use for specific heat: Burkes USHPRR USHPRRFit table"}>>> = USHPRR
  []
[]

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [U10Mo]
    type = U10MoThermal<<<{"description": "Computes thermal properties of low enriched uranium-molybdenum alloy.", "href": "U10MoThermal.html"}>>>
    temperature<<<{"description": "Coupled temperature"}>>> = temperature
    thermal_conductivity_model<<<{"description": "The model to use for thermal conductivity: Burkes USHPRR USHPRRFit table"}>>> = USHPRRFit
    specific_heat_model<<<{"description": "The model to use for specific heat: Burkes USHPRR USHPRRFit table"}>>> = USHPRRFit
  []
[]

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
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
cp_data0 5.5e+27 293.15 323.15 348.15 373.15 423.15 473.15 523.15 573.15 623.15 293.15 323.15 348.15 373.15 423.15 473.15 523.15 573.15 623.15 134 136 138 139 143 146 150 153 157 192.064 197.815 202.531 207.937 216.161 221.075 233.969 244.058 249.664 Specific heat data points.
Default:0 5.5e+27 293.15 323.15 348.15 373.15 423.15 473.15 523.15 573.15 623.15 293.15 323.15 348.15 373.15 423.15 473.15 523.15 573.15 623.15 134 136 138 139 143 146 150 153 157 192.064 197.815 202.531 207.937 216.161 221.075 233.969 244.058 249.664
C++ Type:std::vector<std::vector<double>>
Unit:(no unit assumed)
Controllable:No
Description:Specific heat data points.
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_porosity0The initial porosity
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The initial porosity
k_data0 5.5e+27 293.15 323.15 348.15 373.15 423.15 473.15 523.15 573.15 623.15 293.15 323.15 348.15 373.15 423.15 473.15 523.15 573.15 623.15 12.1 13.4 14.5 15.6 17.8 20 22 23.9 25.5 7.2644 7.702 8.076 8.4632 9.1199 9.4125 10.0931 10.7093 11.4107 Thermal conductivity data points.
Default:0 5.5e+27 293.15 323.15 348.15 373.15 423.15 473.15 523.15 573.15 623.15 293.15 323.15 348.15 373.15 423.15 473.15 523.15 573.15 623.15 12.1 13.4 14.5 15.6 17.8 20 22 23.9 25.5 7.2644 7.702 8.076 8.4632 9.1199 9.4125 10.0931 10.7093 11.4107
C++ Type:std::vector<std::vector<double>>
Unit:(no unit assumed)
Controllable:No
Description:Thermal conductivity data points.
porosityCoupled Porosity
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled Porosity
specific_heat_modelBurkesThe model to use for specific heat: Burkes USHPRR USHPRRFit table
Default:Burkes
C++ Type:MooseEnum
Options:Burkes, USHPRR, USHPRRFit, table
Controllable:No
Description:The model to use for specific heat: Burkes USHPRR USHPRRFit table
thermal_conductivity_modelBurkesThe model to use for thermal conductivity: Burkes USHPRR USHPRRFit table
Default:Burkes
C++ Type:MooseEnum
Options:Burkes, USHPRR, USHPRRFit, table
Controllable:No
Description:The model to use for thermal conductivity: Burkes USHPRR USHPRRFit table

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/thermalU10Mo/thermalU10MoTable.i)
(test/tests/thermalU10Mo/thermalU10MoUSHPRRFit.i)
(test/tests/thermalU10Mo/thermalU10Mo_P.i)
(examples/plate_fuel/plate_fuel_hypre.i)
(test/tests/thermalU10Mo/thermalU10MoUSHPRR.i)

References

D. E. Burkes, C. A. Papesch, A. P. Maddison, T. Hartmann, and F. J. Rice. Thermo-physical properties of DU-10 wt.% Mo alloys. Journal of Nuclear Materials, 403(1–3):160–166, 2010. doi:10.1016/j.jnucmat.2010.06.018.

@article{burkes2010,
    author = "Burkes, D. E. and Papesch, C. A. and Maddison, A. P. and Hartmann, T. and Rice, F. J.",
    title = "Thermo-physical properties of {DU}-10 wt.\\% {Mo} alloys",
    journal = "Journal of Nuclear Materials",
    pages = "160--166",
    year = "2010",
    volume = "403",
    number = "1--3",
    doi = "10.1016/j.jnucmat.2010.06.018"
}

B. Rabin, M. Meyer, J. Cole, I. Glagolenko, W. Jones, J-F. Jue, D. Keiser Jr, C. Miller, G. Moore, H. Ozaltun, F. Rice, A. Robinson, J. Smith, D. Wachs, W. Williams, N. Woolstenhulme, G. Hofman, and Y. Kim. Preliminary report on U-Mo monolithic fuel for research reactors. Technical Report INL EXT-17-40975, Idaho National Laboratory, 4 2020.

@techreport{EXT-17-40975R4,
    author = "Rabin, B. and Meyer, M. and Cole, J. and Glagolenko, I. and Jones, W. and Jue, J-F. and Jr, D. Keiser and Miller, C. and Moore, G. and Ozaltun, H. and Rice, F. and Robinson, A. and Smith, J. and Wachs, D. and Williams, W. and Woolstenhulme, N. and Hofman, G. and Kim, Y.",
    title = "Preliminary Report on {U-Mo} Monolithic Fuel for Research Reactors",
    institution = "Idaho National Laboratory",
    number = "INL EXT-17-40975",
    month = "4",
    year = "2020"
}

(test/tests/thermalU10Mo/thermalU10Mo_P.i)

# The mesh is a 1x1x1 cube (single element).
# The temperature is ramped on all faces of the cube from 300 K to 1200K
# and the porosity is ramped on all faces, using a diffusion approximation,
# from 0 to .5 over 100 Ms.
#
# Thermal conductivity and specific heat are computed using the U10Mo
# thermal model.
#
# The thermal conductivity and specific heat computed by BISON for the
# temperatures shown below and compared with analytical solution.
#
# The results are as follows:
#                         Thermal Conductivity             Specific Heat
#                      -------------------------       ---------------------
#                      Analytical      BISON        Analytical      BISON
#  Temp(K)  Porosity    (W/m-K)       (W/m-K)        J/(kgK)       J/(kgK)
#  300        0         11.136        11.136         134.15        134.15
#  600        0.15      13.394        13.394         155.3         155.3
#  900        0.3       12.878        12.878         176.45        176.45
#  1200       0.5       9.4947        9.4947         197.6         197.6

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1x1x1cube.e
  []
[]

[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300     # set initial T to 300 K
  []
  [por]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.0
  []
[]

[AuxVariables]
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [cp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []
  [por]
    type = Diffusion
    variable = por
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = T
  []
[]


[AuxKernels]
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 1
    execute_on = 'initial linear'
  []
  [cp]
    type = MaterialRealAux
    variable = cp
    property = specific_heat
    block = 1
    execute_on = 'initial linear'
  []
[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 30e6 60e6 100.e6'
    y = '300 600 900 1200'
  []
  [por_ramp]
    type = PiecewiseLinear
    x = '0.0 100.e6'
    y = '0 .5'
  []
[]

[BCs]
   [VariableT]
     type = FunctionDirichletBC
     boundary = 2      # All cube faces
     variable = T
     function = temp_ramp
   []
   [VariablePOR]
     type = FunctionDirichletBC
     boundary = 2      # All cube faces
     variable = por
     function = por_ramp
   []
[]

[Materials]
  [fuel_U10Mo]
    type = U10MoThermal
    block = 1
    temperature = T
    porosity = por
  []
  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 1200.0
  []
[]

[Executioner]

   type = Transient

   solve_type = PJFNK

   petsc_options = '-snes_ksp_ew'
   petsc_options_iname = '-ksp_gmres_restart'
   petsc_options_value = '101'

   line_search = 'none'

   l_max_its = 100
   nl_max_its = 100
   nl_rel_tol = 1e-4
   nl_abs_tol = 1e-6
   l_tol = 1e-5
   start_time = 0.0
   num_steps = 100
   dt = 1.0e6
[]

[Postprocessors]
   [ave_temp_interior]
     # average temperature
     type = SideAverageValue
     boundary = 2
     variable = T
     execute_on = 'initial timestep_end'
   []
   [avg_th_cond]
     type = ElementAverageValue
     block = 1
     variable = th_cond
     execute_on = 'initial timestep_end'
   []
   [avg_cp]
     type = ElementAverageValue
     block = 1
     variable = cp
     execute_on = 'initial timestep_end'
   []
   [average_fuel_T]
     type = ElementAverageValue
     block = 1
     variable = T
     execute_on = 'initial timestep_end'
   []
   [avg_por]
     # average porosity
     type = ElementAverageValue
     block = 1
     variable = por
     execute_on = timestep_end
   []
 []

[Outputs]
  exodus = true
[]

(test/tests/thermalU10Mo/thermalU10MoUSHPRR.i)

#
# This test checks thermal conductivity and specific heat correlations for U10Mo
# based on correlations from the USHPRR program.
#
# The mesh involveds separate 1D elements, one for each fission density to be tested.
#
[Mesh]
  [b0]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 1
    xmin = 0
    xmax = 1
  []
  [all]
    type = CombinerGenerator
    inputs = b0
    positions = '0 0   0
                 0 0.5  0
                 0 1    0
                 0 1.5  0
                 0 2    0
                 0 2.5  0
                 0 3    0
                 0 3.5  0
                 0 4    0
                 0 4.5  0
                 0 5    0
                 0 5.25 0
                 0 5.5  0'
  []
  [final]
    type = SubdomainPerElementGenerator
    input = all
    subdomain_ids = '0 1 2 3 4 5 6 7 8 9 10 11 12'
  []
[]

[Variables]
  [temperature]
    initial_condition = 293.15
  []
[]

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

[Functions]
  [fission_density]
    type = ParsedFunction
    expression = '1e27*y'
  []
  [temperature]
    type = ParsedFunction
    expression = '293.15 + t'
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'left right'
    function = temperature
  []
[]

[Materials]
  [fission_density]
    type = GenericFunctionMaterial
    prop_names = fission_density
    prop_values = fission_density
  []
  [U10Mo]
    type = U10MoThermal
    temperature = temperature
    thermal_conductivity_model = USHPRR
    specific_heat_model = USHPRR
  []
[]

[Executioner]
  type = Transient
  line_search = 'none'
  end_time = 330
  dt = 33
  [Quadrature]
    order = CONSTANT
  []
[]

[Postprocessors]
  [temperature]
    type = ElementAverageValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [k_00]
    type = ElementIntegralMaterialProperty
    block = 0
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_01]
    type = ElementIntegralMaterialProperty
    block = 1
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_02]
    type = ElementIntegralMaterialProperty
    block = 2
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_03]
    type = ElementIntegralMaterialProperty
    block = 3
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_04]
    type = ElementIntegralMaterialProperty
    block = 4
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_05]
    type = ElementIntegralMaterialProperty
    block = 5
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_06]
    type = ElementIntegralMaterialProperty
    block = 6
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_07]
    type = ElementIntegralMaterialProperty
    block = 7
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_08]
    type = ElementIntegralMaterialProperty
    block = 8
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_09]
    type = ElementIntegralMaterialProperty
    block = 9
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_10]
    type = ElementIntegralMaterialProperty
    block = 10
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_11]
    type = ElementIntegralMaterialProperty
    block = 11
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_12]
    type = ElementIntegralMaterialProperty
    block = 12
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []

  [cp_00]
    type = ElementIntegralMaterialProperty
    block = 0
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_01]
    type = ElementIntegralMaterialProperty
    block = 1
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_02]
    type = ElementIntegralMaterialProperty
    block = 2
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_03]
    type = ElementIntegralMaterialProperty
    block = 3
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_04]
    type = ElementIntegralMaterialProperty
    block = 4
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_05]
    type = ElementIntegralMaterialProperty
    block = 5
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_06]
    type = ElementIntegralMaterialProperty
    block = 6
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_07]
    type = ElementIntegralMaterialProperty
    block = 7
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_08]
    type = ElementIntegralMaterialProperty
    block = 8
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_09]
    type = ElementIntegralMaterialProperty
    block = 9
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_10]
    type = ElementIntegralMaterialProperty
    block = 10
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_11]
    type = ElementIntegralMaterialProperty
    block = 11
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_12]
    type = ElementIntegralMaterialProperty
    block = 12
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
[]

(test/tests/thermalU10Mo/thermalU10MoUSHPRRFit.i)

#
# This test checks thermal conductivity and specific heat correlations for U10Mo
# based on correlations from the USHPRR program.
#
# The mesh involveds separate 1D elements, one for each temperature to be tested.
#
[Mesh]
  [b0]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 1
    xmin = 0
    xmax = 1
  []
  [all]
    type = CombinerGenerator
    inputs = b0
    positions = '0 0   0
                 0 0.5  0
                 0 1    0
                 0 1.5  0
                 0 2    0
                 0 2.5  0
                 0 3    0
                 0 3.5  0
                 0 4    0
                 0 4.5  0
                 0 5    0
                 0 5.25 0
                 0 5.5  0'
  []
  [final]
    type = SubdomainPerElementGenerator
    input = all
    subdomain_ids = '0 1 2 3 4 5 6 7 8 9 10 11 12'
  []
[]

[Variables]
  [temperature]
    initial_condition = 293.15
  []
[]

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

[Functions]
  [fission_density]
    type = ParsedFunction
    expression = '1e27*y'
  []
  [temperature]
    type = ParsedFunction
    expression = '293.15 + t'
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'left right'
    function = temperature
  []
[]

[Materials]
  [fission_density]
    type = GenericFunctionMaterial
    prop_names = fission_density
    prop_values = fission_density
  []
  [U10Mo]
    type = U10MoThermal
    temperature = temperature
    thermal_conductivity_model = USHPRRFit
    specific_heat_model = USHPRRFit
  []
[]

[Executioner]
  type = Transient
  line_search = 'none'
  end_time = 330
  dt = 33
  [Quadrature]
    order = CONSTANT
  []
[]

[Postprocessors]
  [temperature]
    type = ElementAverageValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [k_00]
    type = ElementIntegralMaterialProperty
    block = 0
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_01]
    type = ElementIntegralMaterialProperty
    block = 1
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_02]
    type = ElementIntegralMaterialProperty
    block = 2
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_03]
    type = ElementIntegralMaterialProperty
    block = 3
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_04]
    type = ElementIntegralMaterialProperty
    block = 4
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_05]
    type = ElementIntegralMaterialProperty
    block = 5
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_06]
    type = ElementIntegralMaterialProperty
    block = 6
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_07]
    type = ElementIntegralMaterialProperty
    block = 7
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_08]
    type = ElementIntegralMaterialProperty
    block = 8
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_09]
    type = ElementIntegralMaterialProperty
    block = 9
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_10]
    type = ElementIntegralMaterialProperty
    block = 10
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_11]
    type = ElementIntegralMaterialProperty
    block = 11
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_12]
    type = ElementIntegralMaterialProperty
    block = 12
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []

  [cp_00]
    type = ElementIntegralMaterialProperty
    block = 0
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_01]
    type = ElementIntegralMaterialProperty
    block = 1
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_02]
    type = ElementIntegralMaterialProperty
    block = 2
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_03]
    type = ElementIntegralMaterialProperty
    block = 3
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_04]
    type = ElementIntegralMaterialProperty
    block = 4
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_05]
    type = ElementIntegralMaterialProperty
    block = 5
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_06]
    type = ElementIntegralMaterialProperty
    block = 6
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_07]
    type = ElementIntegralMaterialProperty
    block = 7
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_08]
    type = ElementIntegralMaterialProperty
    block = 8
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_09]
    type = ElementIntegralMaterialProperty
    block = 9
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_10]
    type = ElementIntegralMaterialProperty
    block = 10
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_11]
    type = ElementIntegralMaterialProperty
    block = 11
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_12]
    type = ElementIntegralMaterialProperty
    block = 12
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
[]

(test/tests/thermalU10Mo/thermalU10MoTable.i)

#
# This test checks thermal conductivity and specific heat correlations for U10Mo
# based on correlations from the USHPRR program.
#
# The mesh involveds separate 1D elements, one for each fission density to be tested.
#
[Mesh]
  [b0]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 1
    xmin = 0
    xmax = 1
  []
  [all]
    type = CombinerGenerator
    inputs = b0
    positions = '0 0   0
                 0 0.5  0
                 0 1    0
                 0 1.5  0
                 0 2    0
                 0 2.5  0
                 0 3    0
                 0 3.5  0
                 0 4    0
                 0 4.5  0
                 0 5    0
                 0 5.25 0
                 0 5.5  0'
  []
  [final]
    type = SubdomainPerElementGenerator
    input = all
    subdomain_ids = '0 1 2 3 4 5 6 7 8 9 10 11 12'
  []
[]

[Variables]
  [temperature]
    initial_condition = 199
  []
[]

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

[Functions]
  [fission_density]
    type = ParsedFunction
    expression = '1e27*y'
  []
  [temperature]
    type = ParsedFunction
    expression = '199 + t'
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'left right'
    function = temperature
  []
[]

[Materials]
  [fission_density]
    type = GenericFunctionMaterial
    prop_names = fission_density
    prop_values = fission_density
  []
  [U10Mo]
    type = U10MoThermal
    temperature = temperature
    thermal_conductivity_model = table
    specific_heat_model = table
    k_data = '0 1e27 5.5e27;
              200 202 203 204 205 206 207 208;
              200 202 203 204 205 206 207 208;
              200 202 203 204 205 206 207 208;
                1   3   4   5   6   7   8   9;
                3   5   6   7   8   9  10  11;
                3   5   6   7   8   9  10  11'
    cp_data = '0 1e27 5.5e27;
               200 202 203 204 205 206 207 208;
               200 202 203 204 205 206 207 208;
               200 202 203 204 205 206 207 208;
                10  30  40  50  60  70  80  90;
                30  50  60  70  80  90 100 110;
               120 140 150 160 170 180 190 200'
  []
[]

[Executioner]
  type = Transient
  line_search = 'none'
  end_time = 10
  dt = 1
  [Quadrature]
    order = CONSTANT
  []
[]

[Postprocessors]
  [_temperature]
    type = ElementAverageValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [k_00]
    type = ElementIntegralMaterialProperty
    block = 0
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_01]
    type = ElementIntegralMaterialProperty
    block = 1
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_02]
    type = ElementIntegralMaterialProperty
    block = 2
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_03]
    type = ElementIntegralMaterialProperty
    block = 3
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_04]
    type = ElementIntegralMaterialProperty
    block = 4
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_05]
    type = ElementIntegralMaterialProperty
    block = 5
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_06]
    type = ElementIntegralMaterialProperty
    block = 6
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_07]
    type = ElementIntegralMaterialProperty
    block = 7
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_08]
    type = ElementIntegralMaterialProperty
    block = 8
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_09]
    type = ElementIntegralMaterialProperty
    block = 9
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_10]
    type = ElementIntegralMaterialProperty
    block = 10
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_11]
    type = ElementIntegralMaterialProperty
    block = 11
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_12]
    type = ElementIntegralMaterialProperty
    block = 12
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []

  [cp_00]
    type = ElementIntegralMaterialProperty
    block = 0
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_01]
    type = ElementIntegralMaterialProperty
    block = 1
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_02]
    type = ElementIntegralMaterialProperty
    block = 2
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_03]
    type = ElementIntegralMaterialProperty
    block = 3
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_04]
    type = ElementIntegralMaterialProperty
    block = 4
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_05]
    type = ElementIntegralMaterialProperty
    block = 5
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_06]
    type = ElementIntegralMaterialProperty
    block = 6
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_07]
    type = ElementIntegralMaterialProperty
    block = 7
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_08]
    type = ElementIntegralMaterialProperty
    block = 8
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_09]
    type = ElementIntegralMaterialProperty
    block = 9
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_10]
    type = ElementIntegralMaterialProperty
    block = 10
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_11]
    type = ElementIntegralMaterialProperty
    block = 11
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_12]
    type = ElementIntegralMaterialProperty
    block = 12
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
[]

(test/tests/thermalU10Mo/thermalU10MoUSHPRRFit.i)

#
# This test checks thermal conductivity and specific heat correlations for U10Mo
# based on correlations from the USHPRR program.
#
# The mesh involveds separate 1D elements, one for each temperature to be tested.
#
[Mesh]
  [b0]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 1
    xmin = 0
    xmax = 1
  []
  [all]
    type = CombinerGenerator
    inputs = b0
    positions = '0 0   0
                 0 0.5  0
                 0 1    0
                 0 1.5  0
                 0 2    0
                 0 2.5  0
                 0 3    0
                 0 3.5  0
                 0 4    0
                 0 4.5  0
                 0 5    0
                 0 5.25 0
                 0 5.5  0'
  []
  [final]
    type = SubdomainPerElementGenerator
    input = all
    subdomain_ids = '0 1 2 3 4 5 6 7 8 9 10 11 12'
  []
[]

[Variables]
  [temperature]
    initial_condition = 293.15
  []
[]

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

[Functions]
  [fission_density]
    type = ParsedFunction
    expression = '1e27*y'
  []
  [temperature]
    type = ParsedFunction
    expression = '293.15 + t'
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'left right'
    function = temperature
  []
[]

[Materials]
  [fission_density]
    type = GenericFunctionMaterial
    prop_names = fission_density
    prop_values = fission_density
  []
  [U10Mo]
    type = U10MoThermal
    temperature = temperature
    thermal_conductivity_model = USHPRRFit
    specific_heat_model = USHPRRFit
  []
[]

[Executioner]
  type = Transient
  line_search = 'none'
  end_time = 330
  dt = 33
  [Quadrature]
    order = CONSTANT
  []
[]

[Postprocessors]
  [temperature]
    type = ElementAverageValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [k_00]
    type = ElementIntegralMaterialProperty
    block = 0
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_01]
    type = ElementIntegralMaterialProperty
    block = 1
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_02]
    type = ElementIntegralMaterialProperty
    block = 2
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_03]
    type = ElementIntegralMaterialProperty
    block = 3
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_04]
    type = ElementIntegralMaterialProperty
    block = 4
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_05]
    type = ElementIntegralMaterialProperty
    block = 5
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_06]
    type = ElementIntegralMaterialProperty
    block = 6
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_07]
    type = ElementIntegralMaterialProperty
    block = 7
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_08]
    type = ElementIntegralMaterialProperty
    block = 8
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_09]
    type = ElementIntegralMaterialProperty
    block = 9
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_10]
    type = ElementIntegralMaterialProperty
    block = 10
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_11]
    type = ElementIntegralMaterialProperty
    block = 11
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_12]
    type = ElementIntegralMaterialProperty
    block = 12
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []

  [cp_00]
    type = ElementIntegralMaterialProperty
    block = 0
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_01]
    type = ElementIntegralMaterialProperty
    block = 1
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_02]
    type = ElementIntegralMaterialProperty
    block = 2
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_03]
    type = ElementIntegralMaterialProperty
    block = 3
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_04]
    type = ElementIntegralMaterialProperty
    block = 4
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_05]
    type = ElementIntegralMaterialProperty
    block = 5
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_06]
    type = ElementIntegralMaterialProperty
    block = 6
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_07]
    type = ElementIntegralMaterialProperty
    block = 7
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_08]
    type = ElementIntegralMaterialProperty
    block = 8
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_09]
    type = ElementIntegralMaterialProperty
    block = 9
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_10]
    type = ElementIntegralMaterialProperty
    block = 10
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_11]
    type = ElementIntegralMaterialProperty
    block = 11
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_12]
    type = ElementIntegralMaterialProperty
    block = 12
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
[]

(test/tests/thermalU10Mo/thermalU10Mo_P.i)

# The mesh is a 1x1x1 cube (single element).
# The temperature is ramped on all faces of the cube from 300 K to 1200K
# and the porosity is ramped on all faces, using a diffusion approximation,
# from 0 to .5 over 100 Ms.
#
# Thermal conductivity and specific heat are computed using the U10Mo
# thermal model.
#
# The thermal conductivity and specific heat computed by BISON for the
# temperatures shown below and compared with analytical solution.
#
# The results are as follows:
#                         Thermal Conductivity             Specific Heat
#                      -------------------------       ---------------------
#                      Analytical      BISON        Analytical      BISON
#  Temp(K)  Porosity    (W/m-K)       (W/m-K)        J/(kgK)       J/(kgK)
#  300        0         11.136        11.136         134.15        134.15
#  600        0.15      13.394        13.394         155.3         155.3
#  900        0.3       12.878        12.878         176.45        176.45
#  1200       0.5       9.4947        9.4947         197.6         197.6

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1x1x1cube.e
  []
[]

[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300     # set initial T to 300 K
  []
  [por]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.0
  []
[]

[AuxVariables]
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [cp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []
  [por]
    type = Diffusion
    variable = por
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = T
  []
[]


[AuxKernels]
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 1
    execute_on = 'initial linear'
  []
  [cp]
    type = MaterialRealAux
    variable = cp
    property = specific_heat
    block = 1
    execute_on = 'initial linear'
  []
[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 30e6 60e6 100.e6'
    y = '300 600 900 1200'
  []
  [por_ramp]
    type = PiecewiseLinear
    x = '0.0 100.e6'
    y = '0 .5'
  []
[]

[BCs]
   [VariableT]
     type = FunctionDirichletBC
     boundary = 2      # All cube faces
     variable = T
     function = temp_ramp
   []
   [VariablePOR]
     type = FunctionDirichletBC
     boundary = 2      # All cube faces
     variable = por
     function = por_ramp
   []
[]

[Materials]
  [fuel_U10Mo]
    type = U10MoThermal
    block = 1
    temperature = T
    porosity = por
  []
  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 1200.0
  []
[]

[Executioner]

   type = Transient

   solve_type = PJFNK

   petsc_options = '-snes_ksp_ew'
   petsc_options_iname = '-ksp_gmres_restart'
   petsc_options_value = '101'

   line_search = 'none'

   l_max_its = 100
   nl_max_its = 100
   nl_rel_tol = 1e-4
   nl_abs_tol = 1e-6
   l_tol = 1e-5
   start_time = 0.0
   num_steps = 100
   dt = 1.0e6
[]

[Postprocessors]
   [ave_temp_interior]
     # average temperature
     type = SideAverageValue
     boundary = 2
     variable = T
     execute_on = 'initial timestep_end'
   []
   [avg_th_cond]
     type = ElementAverageValue
     block = 1
     variable = th_cond
     execute_on = 'initial timestep_end'
   []
   [avg_cp]
     type = ElementAverageValue
     block = 1
     variable = cp
     execute_on = 'initial timestep_end'
   []
   [average_fuel_T]
     type = ElementAverageValue
     block = 1
     variable = T
     execute_on = 'initial timestep_end'
   []
   [avg_por]
     # average porosity
     type = ElementAverageValue
     block = 1
     variable = por
     execute_on = timestep_end
   []
 []

[Outputs]
  exodus = true
[]

(examples/plate_fuel/plate_fuel_hypre.i)

#
# Plate fuel example problem.
#

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = false
[]

[Mesh]
  coord_type = XYZ
  [plate]
    type = PlateMeshGenerator
    fuel_dimensions = '82.550e-3 19.050e-3 0.216e-3'
    liner_thickness = 0.025e-3
    cladding_thicknesses = '9.4615e-3 9.4615e-3 3.175e-3 3.175e-3 0.489e-3 0.489e-3'
    number_fuel_elements = '25 15 3'
    number_cladding_elements = '4 4 3 3 4 4'
    ### For a more refined mesh (40 processors):
    # number_fuel_elements = '108 30 5'
    # number_cladding_elements = '15 15 5 5 8 8'
    ###
    number_liner_elements = 1
  []
  [translate_to_origin]
    type = TransformGenerator
    input = plate
    transform = translate_min_origin
  []
  [add_nodesets]
    type = ExtraNodesetGenerator
    input = translate_to_origin
    coord = '0 0 0; 0.101473 0 0; 0.101473 0.0254 0'
    new_boundary = 'left_bottom_back right_bottom_back right_top_back'
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = ref
  extra_tag_vectors = ref
  group_variables = 'disp_x disp_y disp_z'
[]

[Functions]
  [fission_density_fcn] # fis/m3
    type = PiecewiseLinear
    data_file = 'average_fission_density.csv'
    scale_factor = 1e27
    format = columns
  []
  [fluence_fcn] # n/m2
    type = PiecewiseLinear
    data_file = 'FLUENCE.csv'
    scale_factor = 1
    format = columns
  []
  [power_density]
    type = PiecewiseLinear
    data_file = 'POWER_DENSITY.csv' # W/cm3 to W/m3
    scale_factor = 1e6
    format = columns
  []
  [L2AR]
    type = ParsedFunction
    # fissprof_l2ar is the distribution from the L2AR tab: L2AR_ABAQUS at cell R64
    symbol_names = 'x_offset y_offset'
    symbol_values = '9.4615e-3 3.175e-3'
    expression = 'x0 := x-x_offset;
             y0 := y-y_offset;
             (4.669e-10*x0^5 - 8.657e-8*x0^4 + 5.877e-6*x0^3 - 0.0001962*x0^2 + 0.004373*x0 + 0.9446) * (5.047e-7*y0^6 - 2.974e-05*y0^5 + 0.0006881*y0^4 - 0.007883*y0^3 + 0.04726*y0^2 - 0.1458*y0 + 1.152)'
  []
  [power_history]
    type = CompositeFunction
    functions = 'power_density L2AR'
  []
[]

[Variables]
  [temperature]
    initial_condition = 294
  []
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat_source]
    type = HeatSource
    block = fuel
    function = power_history
    variable = temperature
    extra_vector_tags = 'ref'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  strain = FINITE
  temperature = temperature
  generate_output = 'stress_xx stress_yy stress_zz vonmises_stress
                     hydrostatic_stress elastic_strain_xx elastic_strain_yy
                     elastic_strain_zz strain_xx strain_yy strain_zz'
  [fuel_mechanics]
    block = fuel
    eigenstrain_names = 'fuel_thermal_strain'
    extra_vector_tags = 'ref'
  []
  [clad_mechanics]
    block = cladding
    eigenstrain_names = 'clad_thermal_strain'
    extra_vector_tags = ref
  []
  [liner_mechanics]
    block = liner
    eigenstrain_names = 'liner_thermal_strain'
    extra_vector_tags = ref
  []
[]

[BCs]
  [conv_BC_front]
    type = ConvectiveHeatFluxBC
    variable = temperature
    boundary = front
    T_infinity = 'tfilm_outer' # film temperature
    heat_transfer_coefficient = 'htc_outer'
    heat_transfer_coefficient_dT = 'dhtc_dT_outer'
  []
  [conv_BC_back]
    type = ConvectiveHeatFluxBC
    variable = temperature
    boundary = back
    T_infinity = 'tfilm_inner' # film temperature
    heat_transfer_coefficient = 'htc_inner'
    heat_transfer_coefficient_dT = 'dhtc_dT_inner'
  []
  [disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'left_bottom_back'
    value = 0.0
  []
  [disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'left_bottom_back right_bottom_back'
    value = 0.0
  []
  [disp_z]
    type = DirichletBC
    variable = disp_z
    boundary = 'left_bottom_back right_bottom_back right_top_back'
    value = 0.0
  []
[]

[Materials]
  [fission_density]
    type = GenericFunctionMaterial
    prop_names = fission_density
    prop_values = fission_density_fcn
  []
  [fluence]
    type = GenericFunctionMaterial
    prop_names = fast_neutron_fluence
    prop_values = fluence_fcn
    outputs = all
  []
  [tfilm_inner]
    type = ParsedMaterial
    property_name = tfilm_inner
    coupled_variables = temperature
    expression = '325.15'
  []
  [htc_inner]
    type = ParsedMaterial
    property_name = htc_inner
    coupled_variables = 'temperature'
    expression = '-3.3647*temperature^2 + 2744.5*temperature - 454016.0'
  []
  [dhtc_dT_inner]
    type = ParsedMaterial
    property_name = dhtc_dT_inner
    coupled_variables = 'temperature'
    expression = '-6.7294*temperature + 2744.5'
  []
  [tfilm_outer]
    type = ParsedMaterial
    property_name = tfilm_outer
    coupled_variables = temperature
    expression = '325.15'
  []
  [htc_outer]
    type = ParsedMaterial
    property_name = htc_outer
    coupled_variables = 'temperature'
    expression = '-2.8992*temperature^2 + 2354.8*temperature - 387945.0'
  []
  [dhtc_dT_outer]
    type = ParsedMaterial
    property_name = dhtc_dT_outer
    coupled_variables = 'temperature'
    expression = '-5.7984*temperature + 2354.8'
  []
  # fuel properties
  [fuel_thermal]
    type = U10MoThermal
    block = fuel
    temperature = temperature
    thermal_conductivity_model = USHPRR
    specific_heat_model = USHPRR
  []
  [fuel_elasticity]
    type = U10MoElasticityTensor
    block = fuel
    temperature = temperature
  []
  [fuel_thermal_expansion]
    type = U10MoThermalExpansionEigenstrain
    block = fuel
    temperature = temperature
    eigenstrain_name = fuel_thermal_strain
    stress_free_temperature = 298
    model_option = Rest
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  #  [fuel_swelling]
  #    type = U10MoVolumetricSwellingEigenstrain
  #    eigenstrain_name = fuel_swelling_strain
  #    fission_rate = 0
  #  []
  [fuel_density]
    type = ParsedMaterial
    block = fuel
    property_name = density
    coupled_variables = 'temperature'
    expression = '-0.884*temperature + 17391.0'
    outputs = exodus
  []
  # liner properties
  [liner_thermal]
    type = ZrThermal
    block = liner
    temperature = temperature
    thermal_conductivity_model = USHPRR
    specific_heat_model = USHPRR
  []
  [liner_elasticity]
    type = ZrElasticityTensor
    block = liner
    temperature = temperature
  []
  [liner_stress]
    type = ComputeFiniteStrainElasticStress
    block = liner
  []
  [liner_thermal_expansion]
    type = ZrThermalExpansionEigenstrain
    block = liner
    temperature = temperature
    eigenstrain_name = liner_thermal_strain
    stress_free_temperature = 293.0
    model_option = ASM
  []
  [liner_density]
    type = StrainAdjustedDensity
    block = liner
    strain_free_density = 6499.0 # 6.499e-9 ton/mm3
    outputs = exodus
  []
  # cladding properties
  [clad_thermal]
    type = Al6061Thermal
    temperature = temperature
    block = cladding
    thermal_conductivity_model = T6
    specific_heat_model = ASM
  []
  [clad_elasticity]
    type = Al6061ElasticityTensor
    block = cladding
    temperature = temperature
    fast_neutron_fluence = 0
    youngs_modulus_model = Kaufman
  []
  [clad_thermal_expansion]
    type = Al6061ThermalExpansionEigenstrain
    stress_free_temperature = 293.15
    temperature = temperature
    eigenstrain_name = clad_thermal_strain
    block = cladding
  []
  [clad_stress]
    type = ComputeFiniteStrainElasticStress
    block = cladding
  []
  [clad_density]
    type = ParsedMaterial
    block = cladding
    property_name = density
    coupled_variables = 'temperature'
    expression = '-0.0003*temperature^2 + 0.0966*temperature + 2690.4'
    outputs = exodus
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = 'Newton'

  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'
  #petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  #petsc_options_value = 'lu superlu_dist'

  line_search = 'none'

  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-8
  nl_max_its = 50

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  end_time = 4586400
  num_steps = 2500

  dtmax = 86400

  [Predictor]
    type = SimplePredictor
    scale = 1
  []

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1800
    optimal_iterations = 12
    iteration_window = 2
    growth_factor = 2
    cutback_factor = .5
    timestep_limiting_function = power_density
    force_step_every_function_point = true
  []
[]

[Postprocessors]
  [average_fuel_T]
    type = ElementAverageValue
    block = fuel
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [fuelVolume]
    type = InternalVolume
    boundary = fuel_all
  []
  [totalVolume]
    type = InternalVolume
    boundary = all
  []
  [power_history]
    type = FunctionValuePostprocessor
    function = power_history
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  perf_graph = true
  csv = true
  exodus = true
[]

(test/tests/thermalU10Mo/thermalU10MoUSHPRR.i)

#
# This test checks thermal conductivity and specific heat correlations for U10Mo
# based on correlations from the USHPRR program.
#
# The mesh involveds separate 1D elements, one for each fission density to be tested.
#
[Mesh]
  [b0]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 1
    xmin = 0
    xmax = 1
  []
  [all]
    type = CombinerGenerator
    inputs = b0
    positions = '0 0   0
                 0 0.5  0
                 0 1    0
                 0 1.5  0
                 0 2    0
                 0 2.5  0
                 0 3    0
                 0 3.5  0
                 0 4    0
                 0 4.5  0
                 0 5    0
                 0 5.25 0
                 0 5.5  0'
  []
  [final]
    type = SubdomainPerElementGenerator
    input = all
    subdomain_ids = '0 1 2 3 4 5 6 7 8 9 10 11 12'
  []
[]

[Variables]
  [temperature]
    initial_condition = 293.15
  []
[]

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

[Functions]
  [fission_density]
    type = ParsedFunction
    expression = '1e27*y'
  []
  [temperature]
    type = ParsedFunction
    expression = '293.15 + t'
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'left right'
    function = temperature
  []
[]

[Materials]
  [fission_density]
    type = GenericFunctionMaterial
    prop_names = fission_density
    prop_values = fission_density
  []
  [U10Mo]
    type = U10MoThermal
    temperature = temperature
    thermal_conductivity_model = USHPRR
    specific_heat_model = USHPRR
  []
[]

[Executioner]
  type = Transient
  line_search = 'none'
  end_time = 330
  dt = 33
  [Quadrature]
    order = CONSTANT
  []
[]

[Postprocessors]
  [temperature]
    type = ElementAverageValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [k_00]
    type = ElementIntegralMaterialProperty
    block = 0
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_01]
    type = ElementIntegralMaterialProperty
    block = 1
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_02]
    type = ElementIntegralMaterialProperty
    block = 2
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_03]
    type = ElementIntegralMaterialProperty
    block = 3
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_04]
    type = ElementIntegralMaterialProperty
    block = 4
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_05]
    type = ElementIntegralMaterialProperty
    block = 5
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_06]
    type = ElementIntegralMaterialProperty
    block = 6
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_07]
    type = ElementIntegralMaterialProperty
    block = 7
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_08]
    type = ElementIntegralMaterialProperty
    block = 8
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_09]
    type = ElementIntegralMaterialProperty
    block = 9
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_10]
    type = ElementIntegralMaterialProperty
    block = 10
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_11]
    type = ElementIntegralMaterialProperty
    block = 11
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_12]
    type = ElementIntegralMaterialProperty
    block = 12
    mat_prop = thermal_conductivity
    execute_on = 'initial timestep_end'
  []

  [cp_00]
    type = ElementIntegralMaterialProperty
    block = 0
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_01]
    type = ElementIntegralMaterialProperty
    block = 1
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_02]
    type = ElementIntegralMaterialProperty
    block = 2
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_03]
    type = ElementIntegralMaterialProperty
    block = 3
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_04]
    type = ElementIntegralMaterialProperty
    block = 4
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_05]
    type = ElementIntegralMaterialProperty
    block = 5
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_06]
    type = ElementIntegralMaterialProperty
    block = 6
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_07]
    type = ElementIntegralMaterialProperty
    block = 7
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_08]
    type = ElementIntegralMaterialProperty
    block = 8
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_09]
    type = ElementIntegralMaterialProperty
    block = 9
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_10]
    type = ElementIntegralMaterialProperty
    block = 10
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_11]
    type = ElementIntegralMaterialProperty
    block = 11
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
  [cp_12]
    type = ElementIntegralMaterialProperty
    block = 12
    mat_prop = specific_heat
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References