ThermoDiffusion Class Reference

Models thermo-diffusion (aka Soret effect, thermophoresis, etc.). More...

#include <ThermoDiffusion.h>

Inheritance diagram for ThermoDiffusion:

Public Member Functions
	ThermoDiffusion (const InputParameters &parameters)

Protected Member Functions
virtual Real	computeQpResidual ()
virtual Real	computeQpJacobian ()
virtual Real	computeQpOffDiagJacobian (unsigned int jvar)
	Computes contribution from grad( T ) / T^2 term. More...

Private Member Functions
RealGradient	thermoDiffusionVelocity () const

Private Attributes
const VariableValue &	_temperature
const VariableGradient &	_grad_temperature
const MaterialProperty< Real > &	_mass_diffusivity
const MaterialProperty< Real > &	_heat_of_transport
const Real	_gas_constant
const unsigned int	_temperature_index

Detailed Description

Models thermo-diffusion (aka Soret effect, thermophoresis, etc.).

The mass flux J due to the thermal gradient is:

J_thermal = - ( D C Qstar / ( R T^2 ) ) * grad( T )

where D is the mass diffusivity (same as for Fick's law), C is the concentration Qstar is the heat of transport, R is the gas constant, and T is the temperature. Note that that grad( T ) / T^2 == -grad( 1/T ), which is how the term appears in Onsager's symmetry (this kernel works just as well for that form).

Also note that coupled diffusion terms like ThermoDiffusion (and Nernst, Ettingshausen, Dufour effects) can cause non-physical stability issues if a regular diffusion term is not included. Thus, ThermoDiffusion should always appear with a Fick's Law kernel such as CoefDiffusion.

The only restriction on the units of C, Qstar, and R is that they should be consistent with each other and with C and T (could be mass ppm, mols/m^3, etc.).

This kernel applies to the concentration C, but the off-diagonal terms in the Jacobian that are due to temperature dependence are also available.

Definition at line 37 of file ThermoDiffusion.h.

Constructor & Destructor Documentation

ThermoDiffusion()

ThermoDiffusion::ThermoDiffusion

(

const InputParameters &

parameters

)

Definition at line 30 of file ThermoDiffusion.C.

  : Kernel(parameters),
    _temperature(coupledValue("temp")),
    _grad_temperature(coupledGradient("temp")),
    _mass_diffusivity(getMaterialProperty<Real>(getParam<std::string>("mass_diffusivity"))),
    _heat_of_transport(getMaterialProperty<Real>(getParam<std::string>("heat_of_transport"))),
    _gas_constant(getParam<Real>("gas_constant")),
    _temperature_index(coupled("temp"))
{
}

Member Function Documentation

computeQpJacobian()

Real ThermoDiffusion::computeQpJacobian ( )

protectedvirtual

Definition at line 63 of file ThermoDiffusion.C.

{
  return thermoDiffusionVelocity() * _phi[_j][_qp] * _grad_test[_i][_qp];
}

computeQpOffDiagJacobian()

Real ThermoDiffusion::computeQpOffDiagJacobian ( unsigned int  jvar )

protectedvirtual

Computes contribution from grad( T ) / T^2 term.

Definition at line 69 of file ThermoDiffusion.C.

{
  if (jvar == _temperature_index)
  {
    Real coeff = _mass_diffusivity[_qp] * _heat_of_transport[_qp] /
                 (_gas_constant * _temperature[_qp] * _temperature[_qp]);
    return coeff * _grad_test[_i][_qp] * _u[_qp] *
           (_grad_phi[_j][_qp] - 2 * _phi[_j][_qp] * _grad_temperature[_qp] / _temperature[_qp]);
  }
  return 0;
}

computeQpResidual()

Real ThermoDiffusion::computeQpResidual ( )

protectedvirtual

Definition at line 57 of file ThermoDiffusion.C.

{
  return thermoDiffusionVelocity() * _u[_qp] * _grad_test[_i][_qp];
}

thermoDiffusionVelocity()

RealGradient ThermoDiffusion::thermoDiffusionVelocity ( ) const

private

Definition at line 42 of file ThermoDiffusion.C.

{
  // The thermo-diffusion term looks like grad( v * C ) where v is like a diffusive
  // velocity. If the concentration C does not couple back into the heat equation,
  // then the one-way coupling of temperature means that thermo-diffusion of C
  // behaves like advection. Then v is the velocity:
  //
  //   v = D Qstar grad(T) / ( R T^2 )
  //
  Real coeff = _mass_diffusivity[_qp] * _heat_of_transport[_qp] /
               (_gas_constant * _temperature[_qp] * _temperature[_qp]);
  return coeff * _grad_temperature[_qp];
}

Referenced by computeQpJacobian(), and computeQpResidual().

Member Data Documentation

_gas_constant

const Real ThermoDiffusion::_gas_constant

private

Definition at line 59 of file ThermoDiffusion.h.

Referenced by computeQpOffDiagJacobian(), and thermoDiffusionVelocity().

_grad_temperature

const VariableGradient& ThermoDiffusion::_grad_temperature

private

Definition at line 56 of file ThermoDiffusion.h.

Referenced by computeQpOffDiagJacobian(), and thermoDiffusionVelocity().

_heat_of_transport

const MaterialProperty<Real>& ThermoDiffusion::_heat_of_transport

private

Definition at line 58 of file ThermoDiffusion.h.

Referenced by computeQpOffDiagJacobian(), and thermoDiffusionVelocity().

_mass_diffusivity

const MaterialProperty<Real>& ThermoDiffusion::_mass_diffusivity

private

Definition at line 57 of file ThermoDiffusion.h.

Referenced by computeQpOffDiagJacobian(), and thermoDiffusionVelocity().

_temperature

const VariableValue& ThermoDiffusion::_temperature

private

Definition at line 55 of file ThermoDiffusion.h.

Referenced by computeQpOffDiagJacobian(), and thermoDiffusionVelocity().

_temperature_index

const unsigned int ThermoDiffusion::_temperature_index

private

Definition at line 60 of file ThermoDiffusion.h.

Referenced by computeQpOffDiagJacobian().

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The documentation for this class was generated from the following files:

• misc/include/kernels/ThermoDiffusion.h
• misc/src/kernels/ThermoDiffusion.C