ThermoDiffusion

Description

ThermoDiffusion implements thermodiffusion (also called thermophoresis, thermomigration, or the Soret effect), or the movement of species due a temperature gradient. The mass flux $var element = document.getElementById("moose-equation-6cd0218f-081b-402a-a832-995fabca8289");katex.render("J", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is given as

$var element = document.getElementById("moose-equation-283e0352-c013-4063-b226-16137c10341e");katex.render("\\mathbf{J}=-S\\nabla T", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-9a5d685d-cbc2-4137-8895-107be299917f");katex.render("S", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is Soret diffusion coefficient, which is typically a combination of the species concentration, temperature, and other material parameters. $var element = document.getElementById("moose-equation-0007fa84-e568-4eca-bb12-a7e5debda873");katex.render("S", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is kept agnostic in this formulation and ultimately needs to be formulated in a separate material property definition.

Input Parameters

tempCoupled temperature
C++ Type:std::vector<VariableName>
Controllable:No
Description:Coupled temperature
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
displacementsThe displacements
C++ Type:std::vector<VariableName>
Controllable:No
Description:The displacements
gas_constant8.31446Gas constant
Default:8.31446
C++ Type:double
Controllable:No
Description:Gas constant
heat_of_transportheat_of_transportProperty name for the heat of transport.
Default:heat_of_transport
C++ Type:std::string
Controllable:No
Description:Property name for the heat of transport.
mass_diffusivitymass_diffusivityProperty name for the diffusivity.
Default:mass_diffusivity
C++ Type:std::string
Controllable:No
Description:Property name for the diffusivity.
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
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.

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging 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.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Controllable:No
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
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
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Controllable:No
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
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

Input Files

(modules/misc/test/tests/kernels/thermo_diffusion/thermo_diffusion.i)

References

No citations exist within this document.

(modules/misc/test/tests/kernels/thermo_diffusion/thermo_diffusion.i)

# Steady-state test for the ThermoDiffusion kernel.
#
# This test applies a constant temperature gradient to drive thermo-diffusion
# in the variable u. At steady state, the thermo-diffusion is balanced by
# diffusion due to Fick's Law, so the total flux is
#
#   J = -D ( grad(u) - ( Qstar u / R ) grad(1/T) )
#
# If there are no fluxes at the boundaries, then there is no background flux and
# these two terms must balance each other everywhere:
#
#   grad(u) = ( Qstar u / R ) grad(1/T)
#
# The dx can be eliminated to give
#
#   d(ln u) / d(1/T) = Qstar / R
#
# This can be solved to give the profile for u as a function of temperature:
#
#   u = A exp( Qstar / R T )
#
# Here, we are using simple heat conduction with Dirichlet boundaries on 0 <= x <= 1
# to give a linear profile for temperature: T = x + 1. We also need to apply one
# boundary condition on u, which is u(x=0) = 1. These conditions give:
#
#   u = exp( -(Qstar/R) (x/(x+1)) )
#
# This analytical result is tracked by the aux variable "correct_u".

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
[]

[Variables]
  [./u]
    initial_condition = 1
  [../]
  [./temp]
    initial_condition = 1
  [../]
[]

[Kernels]
  [./soret]
    type = ThermoDiffusion
    variable = u
    temp = temp
    gas_constant = 1
  [../]
  [./diffC]
    type = Diffusion
    variable = u
  [../]

  # Heat diffusion gives a linear temperature profile to drive the Soret diffusion.
  [./diffT]
    type = Diffusion
    variable = temp
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    preset = false
    boundary = left
    value = 1
  [../]

  [./leftt]
    type = DirichletBC
    variable = temp
    preset = false
    boundary = left
    value = 1
  [../]
  [./rightt]
    type = DirichletBC
    variable = temp
    preset = false
    boundary = right
    value = 2
  [../]
[]

[Materials]
  [./fake_material]
     type = GenericConstantMaterial
     block = 0
     prop_names = 'mass_diffusivity heat_of_transport'
     prop_values = '1 1'
  [../]
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [./error]
    type = NodalL2Error
    variable = u
    function = 'exp(-x/(x+1))'
  [../]
[]

[Outputs]
  execute_on = FINAL
  exodus = true
[]

Description
Input Parameters
Input Files
References