This class deals with Thermal Transport Equation. More...

#include <thermal_transport_equation.h>

Inheritance diagram for FuelCellShop::Equation::ThermalTransportEquation< dim >:

Collaboration diagram for FuelCellShop::Equation::ThermalTransportEquation< dim >:

Public Member Functions
Constructors, destructor, and initalization
	ThermalTransportEquation (FuelCell::SystemManagement &system_management, boost::shared_ptr< FuelCell::ApplicationCore::ApplicationData > data=boost::shared_ptr< FuelCell::ApplicationCore::ApplicationData >())
	Constructor. More...

virtual	~ThermalTransportEquation ()
	Destructor. More...

virtual void	declare_parameters (ParameterHandler &param) const
	Declare parameters. More...

virtual void	initialize (ParameterHandler &param)
	Initialize parameters. More...

Local CG FEM based assemblers
virtual void	assemble_cell_matrix (FuelCell::ApplicationCore::MatrixVector &cell_matrices, const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local cell matrix. More...

virtual void	assemble_cell_residual (FuelCell::ApplicationCore::FEVector &cell_residual, const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local cell residual. More...

virtual void	assemble_bdry_matrix (FuelCell::ApplicationCore::MatrixVector &bdry_matrices, const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local boundary matrix. More...

virtual void	assemble_bdry_residual (FuelCell::ApplicationCore::FEVector &bdry_residual, const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local boundary residual. More...

Accessors and info
virtual void	print_equation_info () const
	This function prints out the equations info. More...

bool	get_electron_ohmic_heat_gdl () const
	Inline method to get whether the electronic ohmic heating in Gas diffusion layer is `ON` or `OFF` (electron_ohmic_heat_gdl). More...

bool	get_electron_ohmic_heat_mpl () const
	Inline method to get whether the electronic ohmic heating in Microporous layer is `ON` or `OFF` (electron_ohmic_heat_mpl). More...

bool	get_electron_ohmic_heat_cl () const
	Inline method to get whether the electronic ohmic heating in Catalyst layer is `ON` or `OFF` (electron_ohmic_heat_cl). More...

bool	get_proton_ohmic_heat_cl () const
	Inline method to get whether the protonic ohmic heating in Catalyst layer is `ON` or `OFF` (proton_ohmic_heat_cl). More...

bool	get_proton_ohmic_heat_ml () const
	Inline method to get whether the protonic ohmic heating in Membrane layer is `ON` or `OFF` (proton_ohmic_heat_ml). More...

Public Member Functions inherited from FuelCellShop::Equation::EquationBase< dim >
const couplings_map &	get_internal_cell_couplings () const
	This function returns `internal_cell_couplings` of a derived equation class. More...

const couplings_map &	get_internal_flux_couplings () const
	This function returns `internal_flux_couplings` (DG FEM only) of a derived equation class. More...

const component_materialID_value_map &	get_component_materialID_value () const
	This function returns `component_materialID_value` of a derived equation class. More...

const component_boundaryID_value_map &	get_component_boundaryID_value () const
	This function returns `component_boundaryID_value` of a derived equation class. More...

const std::vector< BoundaryType > &	get_boundary_types () const
	This function returns `boundary_types` of a derived equation class. More...

const std::vector< std::vector < BoundaryType > > &	get_multi_boundary_types () const
	This function returns `multi_boundary_types` of a derived equation class. More...

const std::vector< OutputType > &	get_output_types () const
	This function returns `output_types` of a derived equation class. More...

const std::vector< std::vector < OutputType > > &	get_multi_output_types () const
	This function returns `multi_output_types` of a derived equation class. More...

const std::string &	get_equation_name () const
	This function returns `equation_name` of a derived equation class. More...

const std::vector< unsigned int > &	get_matrix_block_indices () const
	This function returns `matrix_block_indices` of a derived equation class. More...

const std::vector< unsigned int > &	get_residual_indices () const
	This function returns `residual_indices` of a derived equation class. More...

Protected Member Functions
Local CG FEM based assemblers - make_ functions
virtual void	make_assemblers_generic_constant_data ()
	This function computes Local CG FEM based assemblers - constant data (generic). More...

virtual void	make_assemblers_cell_constant_data (const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info)
	This function computes Local CG FEM based assemblers - constant data (cell) and allocates the memory for `shape` `functions`, `shape` `function` `gradients`, and JxW_cell in Local CG FEM based assemblers - variable data (cell) . More...

virtual void	make_assemblers_bdry_constant_data (const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info)
	This function computes Local CG FEM based assemblers - constant data (boundary) and allocates the memory for `shape` `functions`, normal_vectors, and JxW_bdry in Local CG FEM based assemblers - variable data (boundary) . More...

virtual void	make_assemblers_cell_variable_data (const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	This function computes Local CG FEM based assemblers - variable data (cell) . More...

virtual void	make_assemblers_bdry_variable_data (const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	This function computes Local CG FEM based assemblers - variable data (boundary) . More...

template<typename porelayer >
void	gas_enthalpy_transport_assemblers_cell_data (const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, porelayer *const layer)
	This function computes Enthalpy transport assemblers - variable data (cell) corresponding to enthalpy transport via Fickian diffusion. More...

template<typename polymer >
void	lambda_enthalpy_transport_assemblers_cell_data (const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, const polymer *const layer)
	This function computes Enthalpy transport assemblers - variable data (cell) corresponding to enthalpy transport associated with lambda transport. More...

Other make_ functions
virtual void	make_internal_cell_couplings ()
	This function fills out `internal_cell_couplings`. More...

Protected Member Functions inherited from FuelCellShop::Equation::EquationBase< dim >
	EquationBase (FuelCell::SystemManagement &sys_management, boost::shared_ptr< FuelCell::ApplicationCore::ApplicationData > data=boost::shared_ptr< FuelCell::ApplicationCore::ApplicationData >())
	Constructor. More...

virtual	~EquationBase ()
	Destructor. More...

virtual void	set_parameters (const std::vector< std::string > &name_dvar, const std::vector< double > &value_dvar, ParameterHandler &param)
	Set parameters using the parameter file, in order to run parametric/optimization studies. More...

void	select_cell_assemblers (const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	This routine is used to select the make_assembly routines that need to be called inside assemble_cell_matrix to compute. More...

virtual void	make_internal_flux_couplings ()
	This function fills out `internal_flux_couplings` (DG FEM only) of a derived equation class. More...

virtual void	make_component_materialID_value ()
	This function fills out `component_materialID_value` of a derived equation class. More...

virtual void	make_component_boundaryID_value ()
	This function fills out `component_boundaryID_value` of a derived equation class. More...

virtual void	make_boundary_types ()
	This function fills out `boundary_types` of a derived equation class. More...

virtual void	make_multi_boundary_types ()
	This function fills out `multi_boundary_types` of a derived equation class. More...

virtual void	make_output_types ()
	This function fills out `output_types` of a derived equation class. More...

virtual void	make_multi_output_types ()
	This function fills out `multi_output_types` of a derived equation class. More...

virtual void	make_matrix_block_indices ()
	This function is only needed to provide the last argument to dealII_to_appframe. More...

virtual void	make_residual_indices ()
	This function is only needed to provide the last argument to dealII_to_appframe. More...

virtual void	assemble_cell_Jacobian_matrix (FuelCell::ApplicationCore::MatrixVector &cell_matrices, const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble the local Jacobian Matrix for Non-Linear problems. More...

virtual void	assemble_bdry_Jacobian_matrix (FuelCell::ApplicationCore::MatrixVector &bdry_matrices, const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local Jacobian boundary matrix for Non-Linear problems. More...

virtual void	assemble_cell_linear_matrix (FuelCell::ApplicationCore::MatrixVector &cell_matrices, const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble the local cell matrix for Linear problems. More...

virtual void	assemble_cell_residual_rhs (FuelCell::ApplicationCore::FEVector &cell_residual, const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local cell RHS for nonlinear problems. More...

virtual void	assemble_cell_linear_rhs (FuelCell::ApplicationCore::FEVector &cell_residual, const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local cell RHS for Linear problems. More...

virtual void	assemble_bdry_linear_matrix (FuelCell::ApplicationCore::MatrixVector &bdry_matrices, const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local boundary matrix for linear problems. More...

virtual void	assemble_bdry_linear_rhs (FuelCell::ApplicationCore::FEVector &bdry_residual, const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local boundary RHS for linear problems. More...

void	standard_to_block_wise (FullMatrix< double > &target) const
	This function changes the order of dealii::FullMatrix<double> `target` from standard to block-wise. More...

void	standard_to_block_wise (Vector< double > &target) const
	This function changes the order of dealii::Vector<double> `target` from standard to block-wise. More...

void	dealII_to_appframe (FuelCell::ApplicationCore::MatrixVector &dst, const FullMatrix< double > &src, const std::vector< unsigned int > &matrix_block_indices) const
	This function converts the standard ordered structure dealii::FullMatrix<double> `src` into the block-wise ordered structure FuelCell::ApplicationCore::MatrixVector `dst`. More...

void	dealII_to_appframe (FuelCell::ApplicationCore::FEVector &dst, const Vector< double > &src, const std::vector< unsigned int > &residual_indices) const
	This function converts the standard ordered structure dealii::Vector<double> `src` into the block-wise ordered structure FuelCell::ApplicationCore::FEVector `dst`. More...

bool	belongs_to_boundary (const unsigned int &tria_boundary_id, const unsigned int &param_boundary_id) const
	This function returns `true` if a boundary indicator of an external face on the triangulation coincides with a boundary indicator defined in the parameters file of a derived equation class. More...

void	print_caller_name (const std::string &caller_name) const
	This function is used to print out the name of another function that has been declared in the scope of this class, but not yet been implemented. More...

Protected Attributes
bool	cell_residual_counter
	Counter set to TRUE when `cell_residual` is being assembled. More...

bool	bdry_residual_counter
	Counter set to TRUE when `bdry_residual` is being assembled. More...

unsigned int	last_iter_cell
	Variable used to store the index in cell_info->global_data of the previous Newton solution The solution at the previous iteration is used to compute cell_matrix and cell_residual. More...

unsigned int	last_iter_bdry
	Variable used to store the index in bdry_info->global_data of the previous Newton solution The solution at the previous iteration is used to compute bdry_matrix and bdry_residual. More...

Boolean flags
bool	electron_ohmic_heat_gdl
	This boolean data member indicates that the electronic ohmic heating in Gas diffusion layer is `ON` or `OFF`. More...

bool	electron_ohmic_heat_mpl
	This boolean data member indicates that the electronic ohmic heating in Microporous layer is `ON` or `OFF`. More...

bool	electron_ohmic_heat_cl
	This boolean data member indicates that the electronic ohmic heating in Catalyst layer is `ON` or `OFF`. More...

bool	proton_ohmic_heat_cl
	This boolean data member indicates that the protonic ohmic heating in Catalyst layer is `ON` or `OFF`. More...

bool	proton_ohmic_heat_ml
	This boolean data member indicates that the protonic ohmic heating in Membrane layer is `ON` or `OFF`. More...

bool	enthalpy_fickian_transport
	This boolean data member indicates that the enthalpy transport via Fickian diffusion is `ON` or `OFF`. More...

bool	enthalpy_lambda_transport
	This boolean data member indicates that the enthalpy transport associated with lambda (sorbed water) transport is `ON` or `OFF`. More...

bool	flag_thermoosmosis
	This flag indicates that lambda transport due to thermo-osmotic diffusion is `ON` or `OFF`. More...

Boundary conditions
std::map< unsigned int, double >	const_heat_flux_map
	`std::map<` `unsigned` `int`, `double` > container for details regarding Constant Heat Flux boundaries. More...

std::map< unsigned int, std::vector< double > >	conv_heat_flux_map
	Container for details regarding Convective Heat Flux boundaries. More...

Generic Constant Data
VariableInfo	t_rev
	VariableInfo structure corresponding to base variable of this equation class, `"temperature_of_REV"`. More...

VariableInfo	phi_s
	VariableInfo structure corresponding to `"electronic_electrical_potential"`. More...

VariableInfo	phi_m
	VariableInfo structure corresponding to `"protonic_electrical_potential"`. More...

VariableInfo	lambda
	VariableInfo structure corresponding to `"membrane_water_content"`. More...

VariableInfo	s_liquid_water
	VariableInfo structure corresponding to `"liquid_water_saturation"`. More...

VariableInfo	p_liquid_water

std::map< std::string, VariableInfo >	xi_map
	Map of VariableInfo structures of various gaseous species, whose diffusion is being considered in the application. More...

Local CG FEM based assemblers - variable data (cell)
std::vector< Tensor< 2, dim > >	keff_cell
	Effective thermal conductivity, [`W/(cm-k` )], at all quadrature points of the cell. More...

std::vector< Tensor< 2, dim > >	dkeff_dT_cell
	Derivative of effective thermal conductivity w.r.t `"temperature_of_REV"`, at all quadrature points of the cell. More...

Tensor< 2, dim >	sigmaSeff_cell
	Effective electronic conductivity, [`S/cm`], of the cell. More...

std::vector< double >	sigmaMeff_cell
	Effective protonic conductivity, [`S/cm`], at all quadrature points of the cell. More...

std::vector< double >	dsigmaMeff_dT_cell
	Derivative of effective protonic conductivity w.r.t `"temperature_of_REV"`, at all quadrature points in the cell. More...

std::vector< double >	dsigmaMeff_dlambda_cell
	Derivative of effective protonic conductivity w.r.t `"membrane_water_content"`, at all quadrature points in the cell. More...

std::vector< std::vector < double > >	phi_T_cell
	$\mathbf{T}$ shape functions. More...

std::vector< std::vector < Tensor< 1, dim > > >	grad_phi_T_cell
	$\mathbf{T}$ shape function gradients. More...

std::vector< std::vector < Tensor< 1, dim > > >	grad_phi_phiS_cell
	$\mathbf{\phi_s}$ shape function gradients. More...

std::vector< std::vector < Tensor< 1, dim > > >	grad_phi_phiM_cell
	$\mathbf{\phi_m}$ shape function gradients. More...

std::vector< std::vector < double > >	phi_lambda_cell
	$\mathbf{\lambda}$ shape functions. More...

std::vector< std::vector < Tensor< 1, dim > > >	grad_phi_lambda_cell
	$\mathbf{\lambda}$ shape function gradients. More...

std::vector< std::vector < double > >	phi_s_cell
	$\mathbf{s}$ shape functions. More...

std::vector< std::vector < double > >	phi_p_cell

std::vector< Tensor< 1, dim > >	grad_phiM_cell_old
	Gradient of `"protonic_electrical_potential"` at a previous Newton iteration, at all quadrature points in the cell. More...

std::vector< Tensor< 1, dim > >	grad_phiS_cell_old
	Gradient of `"electronic_electrical_potential"` at a previous Newton iteration, at all quadrature points in the cell. More...

std::vector< Tensor< 1, dim > >	grad_lambda_cell_old
	Gradient of `"membrane_water_content"` at a previous Newton iteration, at all quadrature points in the cell. More...

Enthalpy transport assemblers - variable data (cell)
std::map< std::string, std::vector< Tensor< 2, dim > > >	conc_Deff_dHdT_map
	`Value` in the map represents $\left( c_T \cdot \hat{D}_{i,eff} \cdot \frac{\partial \bar{H}_i}{\partial T} \right) ~$ [`W/(cm-K)`], at previous iteration step at all quadrature points in the cell; corresponding to string `Key` representing for e.g "oxygen_molar_fraction". More...

std::map< std::string, std::vector< Tensor< 2, dim > > >	dT_concDeffdHdT_map
	`Value` in the map represents $\frac{\partial \left( c_T \cdot \hat{D}_{i,eff} \cdot \frac{\partial \bar{H}_i}{\partial T} \right) }{\partial T} ~$ [`W/(cm-K^2)`], at previous iteration step at all quadrature points in the cell; corresponding to string `Key` representing for e.g "oxygen_molar_fraction". More...

std::map< std::string, std::vector< Tensor< 2, dim > > >	ds_concDeffdHdT_map
	`Value` in the map represents $\frac{\partial \left( c_T \cdot \hat{D}_{i,eff} \cdot \frac{\partial \bar{H}_i}{\partial T} \right) }{\partial s} ~$ [`W/(cm-K)`], at previous iteration step at all quadrature points in the cell; corresponding to string `Key` representing for e.g "oxygen_molar_fraction". More...

std::map< std::string, std::vector< Tensor< 2, dim > > >	dp_concDeffdHdT_map

std::map< std::string, std::vector< std::vector < Tensor< 1, dim > > > >	grad_phi_xi_map
	Map of $\mathbf{x_i}$ shape function gradients. More...

std::vector< double >	electroosmotic_dhdT
	$\left(\frac{n_d \sigma_{m,eff}}{F} \right) \frac{\partial \bar{H}_{\lambda}}{\partial T}$ , at all quadrature points in the cell. More...

std::vector< double >	delectroosmotic_dhdT_dlambda
	$\frac{ \partial \left[ \left(\frac{n_d \sigma_{m,eff}}{F} \right) \frac{\partial \bar{H}_{\lambda}}{\partial T} \right]}{\partial \lambda}$ , at all quadrature points in the cell. More...

std::vector< double >	delectroosmotic_dhdT_dT
	$\frac{ \partial \left[ \left(\frac{n_d \sigma_{m,eff}}{F} \right) \frac{\partial \bar{H}_{\lambda}}{\partial T} \right]}{\partial T}$ , at all quadrature points in the cell. More...

std::vector< double >	backdiff_dhdT
	$\left(\frac{\rho_{dry}}{EW} \right) D_{\lambda ,eff} \frac{\partial \bar{H}_{\lambda}}{\partial T}$ , at all quadrature points in the cell. More...

std::vector< double >	dbackdiff_dhdT_dlambda
	$\frac{ \partial \left[ \left(\frac{\rho_{dry}}{EW} \right) D_{\lambda ,eff} \frac{\partial \bar{H}_{\lambda}}{\partial T} \right]}{\partial \lambda}$ , at all quadrature points in the cell. More...

std::vector< double >	dbackdiff_dhdT_dT
	$\frac{ \partial \left[ \left(\frac{\rho_{dry}}{EW} \right) D_{\lambda ,eff} \frac{\partial \bar{H}_{\lambda}}{\partial T} \right]}{\partial T}$ , at all quadrature points in the cell. More...

std::vector< double >	thermoosmotic_dhdT
	$\left(\frac{D_{T,eff}}{M_{water}} \right) \frac{\partial \bar{H}_{\lambda}}{\partial T}$ , at all quadrature points in the cell. More...

std::vector< double >	dthermoosmotic_dhdT_dT
	$\frac{ \partial \left[ \left(\frac{D_{T,eff}}{M_{water}} \right) \frac{\partial \bar{H}_{\lambda}}{\partial T} \right]}{\partial T}$ , at all quadrature points in the cell. More...

Local CG FEM based assemblers - variable data (boundary)
std::vector< Tensor< 2, dim > >	dkeff_dT_bdry
	Derivative of effective thermal conductivity w.r.t `"temperature_of_REV"`, at all quadrature points of the boundary. More...

std::vector< std::vector < double > >	phi_T_bdry
	$\mathbf{T}$ shape functions. More...

Protected Attributes inherited from FuelCellShop::Equation::EquationBase< dim >
unsigned int	dofs_per_cell
	Number of degrees of freedom per cell. More...

unsigned int	n_q_points_cell
	Number of quadrature points per cell. More...

unsigned int	n_q_points_bdry
	Number of quadrature points per boundary. More...

DoFHandler< dim > ::active_cell_iterator	cell
	Currently active DoFHandler<dim> active cell iterator. More...

DoFHandler< dim > ::active_face_iterator	bdry
	Currently active DoFHandler<dim> active boundary iterator. More...

std::vector< double >	JxW_cell
	Jacobian of mapping by Weight in the quadrature points of a cell. More...

std::vector< double >	JxW_bdry
	Jacobian of mapping by Weight in the quadrature points of a boundary. More...

std::vector< Point< dim > >	normal_vectors
	Normal vectors in the quadrature points of a boundary. More...

std::vector< std::vector < Point< dim > > >	tangential_vectors
	Tangential vectors in the quadrature points of a boundary. More...

FuelCell::SystemManagement *	system_management
	Pointer to the external YourApplication<dim>::system_management object. More...

couplings_map	internal_cell_couplings
	This object contains the info on how the equations and solution variables of a derived equation class are coupled. More...

couplings_map	internal_flux_couplings
	This object contains the info on how the "X" and "Y" of a derived equation class are coupled (DG FEM only). More...

component_materialID_value_map	component_materialID_value
	This object reflects the following structure (see FuelCell::InitialAndBoundaryData namespace docs): More...

component_boundaryID_value_map	component_boundaryID_value
	This object reflects the following structure (see FuelCell::InitialAndBoundaryData namespace docs): More...

std::vector< BoundaryType >	boundary_types
	The list of boundary types of a derived equation class. More...

std::vector< std::vector < BoundaryType > >	multi_boundary_types
	The list of multiple boundary types of a derived equation class. More...

std::vector< OutputType >	output_types
	The list of output types of a derived equation class. More...

std::vector< std::vector < OutputType > >	multi_output_types
	The list of multiple output types of a derived equation class. More...

std::string	equation_name
	The name of a derived equation class. More...

std::string	name_base_variable
	Const std::string member storing name of the base solution variable corresponding to the equation represented by this class. More...

std::vector< unsigned int >	matrix_block_indices
	The system matrix block indices (a derived equation class) drawn from the global structure (a derived equation class + other active equation classes included into the computation). More...

std::vector< unsigned int >	residual_indices
	The residual indices (a derived equation class) drawn from the global structure (a derived equation class + other active equation classes included into the computation). More...

std::vector< bool >	counter
	This vector contains the collection of internal "counters" used by the derived equation classes. More...

EquationFlags	assemble_flags
	This vector contains a collection of internal flags to tell derived equation classes what needs to be re-computed. More...

boost::shared_ptr < FuelCell::ApplicationCore::ApplicationData >	data
	Data object for the application data to be passed to the equation classes. More...

std::string	solution_vector_name
	The name of the solution vector in FEVectors. More...

std::string	residual_vector_name
	The name of the residual vector name in FEVectors. More...

Additional Inherited Members
Public Attributes inherited from FuelCellShop::Equation::EquationBase< dim >
bool	variable_initial_data
	`true`, if variable initial data is prescribed on a part of the domain. More...

bool	variable_boundary_data
	`true`, if variable Dirichlet boundary conditions are prescribed on a part of the boundary. More...

Detailed Description

template<int dim>
class FuelCellShop::Equation::ThermalTransportEquation< dim >

This class deals with Thermal Transport Equation.

This equation solves a steady-state, heat transfer equation (Fourier's law of conduction), alongwith enthalpy transport due to species diffusion in multi-component mixtures. Heat transfer via convection is generally very little (roughly 6 orders of magnitude smaller) as compared to conductive heat transport in a PEMFC, hence neglected here. Also currently, Fick's law of diffusion is being considered to account for enthalpy transport due to inter-diffusion amongst species.

It is solved with respect to $\mathbf{T}$ (temperature_of_REV)

where, $\mathbf{T}$ is in Kelvins.

This equation can be written as:

$\qquad -\mathbf{\nabla} \cdot \left( \hat{k}_{eff} \cdot \mathbf{\nabla} T \right) + \mathbf{\nabla} \cdot \left( \bar{H}_i \vec{J}_i \right) = \mathbf{S_{thermal}} \quad \in \quad \Omega$

where

$\qquad \mathbf{S_{thermal}} = \begin{cases} \hat{\sigma}_{s,eff} \cdot \left( \mathbf{\nabla} \phi_s \otimes \mathbf{\nabla} \phi_s \right) \quad - \quad \text{Electronic ohmic heating in all layers except Membrane layer} \\ ~ \\ \hat{\sigma}_{m,eff} \cdot \left( \mathbf{\nabla} \phi_m \otimes \mathbf{\nabla} \phi_m \right) \quad - \quad \text{Protonic ohmic heating in Catalyst layers and Membrane layer} \end{cases}$

$\hat{k}_{eff}$ is Thermal conductivity tensor [W/(cm-K)], which can be a function of other variables, e.g. (Temperature).
$\hat{\sigma}_{s,eff}$ is Electronic conductivity tensor [S/cm].
$\hat{\sigma}_{m,eff}$ is Protonic conductivity tensor [S/cm].
$\mathbf{S_{thermal}}$ is in [W/(cm^3)].
$\bar{H}_i$ is molar enthalpy [J/(mol)] of the diffusing specie "i".
is molar diffusion flux [mol/(cm^2-s)] of the diffusing specie "i", for gaseous species it is given as: , where:
- $\hat{D}_{i,eff}$ is effective diffusivity tensor [cm^2/s] of the diffusing gas "i".
- is total concentration [mol/cm^3] of all the gaseous species involved in the cell.
- is molar fraction of the diffusing gas "i".
Diffusing specie "i" can also be sorbed water, $\lambda$ .

To be well-posed, these equations are equipped with the appropriate boundary conditions. Dirichlet boundary conditions can be mentioned in the subsection "Boundary data". However, some other boundary types require additional information, which can also be provided by the parameter file. We consider several types of boundary conditions:

Constant Heat Flux: A constant heat flux, [W/cm^2] is provided at a boundary. This value is provided using parameter file. If the value is positive, it implies that heat flux is leaving out of the boundary, otherwise negative implies entering into the boundary.

$\qquad -\mathbf{n} \cdot \left( \hat{k}_{eff} \cdot \mathbf{\nabla} T \right) = C$

These are specified in the parameter file under subsection "Boundary conditions", as a list of comma-separated map-like values.

e.g.

set Constant Heat Flux Boundary Conditions = 1: 34.5 , 4: -23.5

where, boundary_id "1" has constant heat flux value of 34.5 [W/cm^2] (coming out of the boundary) and boundary_id "4" has constant heat flux value of -23.5 [W/cm^2] (going into the boundary).

Convective Heat Flux: Convective heat flux based boundary condition is applied at the boundary. It requires heat transfer coefficient, [W/(cm^2-K )] and ambient temperature, $T_{\infty}$ [K] at the boundary.

$\qquad -\mathbf{n} \cdot \left( \hat{k}_{eff} \cdot \mathbf{\nabla} T \right) = h(T - T_{\infty})$

These are specified in the parameter file under subsection "Boundary conditions", as a list of comma-separated map-like values.

e.g.

set Convective Heat Flux Boundary Conditions = 1: 1.5;340, 3: 0.4;230

where, boundary_id "1" has convective heat transfer coefficient of 1.5 [W/(cm^2-K )] and ambient temperature of 340 [K]; and boundary_id "3" has convective heat transfer coefficient of 0.4 [K] and ambient temperature of 230 [K]. Please note that ";" is necessary to provide both of the required parameters, viz., $ h $ and $T_{\infty}$ at a particular boundary.

No Heat Flux (Insulated) / Symmetric: A particular case of Neumann boundary condition.

$\qquad -\mathbf{n} \cdot \left( \hat{k}_{eff} \cdot \mathbf{\nabla} T \right) = 0$

Remarks

Ohmic heating source terms (electronic and protonic) can be turned ON or OFF, using flags defined under subsection "Boolean flags in the parameter file.
In order to have electronic ohmic heating source term, $\phi_s$ [Volts ], should be one of the solution variables, otherwise this class will throw an exception. Similarly, for protonic ohmic heating, $\phi_m$ [ Volts ], should be one of the solution variables.
Enthalpy tranport due to Fickian diffusion of species is defaulted to OFF. It can be turned ON by setting following paramter entry to TRUE, under subsection "Boolean flags :
set Enthalpy transport due to fickian diffusion of gases = true
Please note that while considering enthalpy transport due to fickian diffusion, it is very necessary to set the solvent gas for a particular layer as the last entry in the input vector to FuelCellShop::Layer::PorousLayer::set_gases method, in the initialization section of the application.
Enthalpy transport due to transport of sorbed water is defaulted to OFF. It can be turned ON by setting following parameter entry to TRUE, under subsection "Boolean flags :
set Enthalpy transport associated with lambda transport = true
Please note that while considering enthalpy transport due to lambda transport, it is very necessary to include membrane_water_content, $\lambda$ as one of the solution variables in the application.
Lambda transport accounts for diffusion, electro-osmosis if protonic_electrical_potential, $\phi_m$ is one of the solution variables and thermo-osmosis if it is set to TRUE in parameter entry for Membrane Water Content Transport Equation.
There is no provision to specify boundary indicators for No Heat Flux or Symmetric boundary conditions, as FEM formulation automatically implies a particular boundary is one of these cases, by default.
This class currently works with the following layer classes:
- FuelCellShop::Layer::GasDiffusionLayer<dim>
- FuelCellShop::Layer::MicroPorousLayer<dim>
- FuelCellShop::Layer::CatalystLayer<dim>
- FuelCellShop::Layer::MembraneLayer<dim>

We solve the whole problem by linearizing the governing equation at each Newton iteration with subsequent CG FEM discretization in space.

Usage Details:

* // Creating Equation object (in Application Header file)
* FuelCellShop::Equation::ThermalTransportEquation<dim> thermal_transport;
*
* // Declare parameters in application
* thermal_transport.declare_parameters(param);
*
* // Initialize in application
* thermal_transport.initialize(param);
*
* // Create a temporary vector in the application for storing couplings_map from all the equation used in the application.
* std::vector<couplings_map> tmp;
* ... // other equations
* tmp.push_back( thermal_transport.get_internal_cell_couplings() );
*
* // Look at ReactionSourceTerms class here, if source terms due to electrochemical reaction are to be considered.
* // Making cell couplings using SystemManagement object created in the application
* system_management.make_cell_couplings(tmp);
*
* // cell_matrix in application
* // Do a check against layer and it should match with the layers currently working for this equation class.
* // for eg: CGDL is FuelCellShop::Layer::DesignFibrousGDL<dim> object.
* thermal_transport.assemble_cell_matrix(cell_matrices, cell_info, &CGDL);
*
* // cell_residual in application
* thermal_transport.assemble_cell_residual(cell_vector, cell_info, &CGDL);
*
* // For bdry_matrices and bdry_vector; check for the layer present at that boundary. For eg: CGDL
* thermal_transport.assemble_bdry_matrix(bdry_matrices, bdry_info, &CGDL);
* thermal_transport.assemble_bdry_residual(bdry_vector, bdry_info, &CGDL);
* 

Note: This class doesn't assemble for reaction heat source terms; that is taken care off by ReactionSourceTerms class. Please read the documentation of ReactionSourceTerms class, for additional methods to be implemented in the application.

Warning: If heat source terms due to reaction are being considered, it's very important to use ReactionSourceTerms::adjust_internal_cell_couplings method, before using FuelCell::SystemManagement::make_cell_couplings at the application level.

Author: Madhur Bhaiya, 2013

Constructor & Destructor Documentation

template<int dim>

FuelCellShop::Equation::ThermalTransportEquation< dim >::ThermalTransportEquation	(	FuelCell::SystemManagement &	system_management,
		boost::shared_ptr< FuelCell::ApplicationCore::ApplicationData >	data = `boost::shared_ptr< FuelCell::ApplicationCore::ApplicationData >()`
	)

Constructor.

template<int dim>

virtual FuelCellShop::Equation::ThermalTransportEquation< dim >::~ThermalTransportEquation ( )

virtual

Destructor.

Member Function Documentation

template<int dim>

virtual void FuelCellShop::Equation::ThermalTransportEquation< dim >::assemble_bdry_matrix	(	FuelCell::ApplicationCore::MatrixVector &	bdry_matrices,
		const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &	bdry_info,
		FuelCellShop::Layer::BaseLayer< dim > *const	layer
	)

virtual

Assemble local boundary matrix.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::ThermalTransportEquation< dim >::assemble_bdry_residual	(	FuelCell::ApplicationCore::FEVector &	bdry_residual,
		const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &	bdry_info,
		FuelCellShop::Layer::BaseLayer< dim > *const	layer
	)

virtual

Assemble local boundary residual.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::ThermalTransportEquation< dim >::assemble_cell_matrix	(	FuelCell::ApplicationCore::MatrixVector &	cell_matrices,
		const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &	cell_info,
		FuelCellShop::Layer::BaseLayer< dim > *const	layer
	)

virtual

Assemble local cell matrix.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::ThermalTransportEquation< dim >::assemble_cell_residual	(	FuelCell::ApplicationCore::FEVector &	cell_residual,
		const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &	cell_info,
		FuelCellShop::Layer::BaseLayer< dim > *const	layer
	)

virtual

Assemble local cell residual.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::ThermalTransportEquation< dim >::declare_parameters ( ParameterHandler & param ) const

virtual

Declare parameters.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

template<typename porelayer >

void FuelCellShop::Equation::ThermalTransportEquation< dim >::gas_enthalpy_transport_assemblers_cell_data	(	const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &	cell_info,
		porelayer *const	layer
	)

protected

This function computes Enthalpy transport assemblers - variable data (cell) corresponding to enthalpy transport via Fickian diffusion.

template<int dim>

bool FuelCellShop::Equation::ThermalTransportEquation< dim >::get_electron_ohmic_heat_cl ( ) const

inline

Inline method to get whether the electronic ohmic heating in Catalyst layer is ON or OFF (electron_ohmic_heat_cl).