Thermal Properties¶

In this section of material properties, the user specifies the parameters of models for Fourier heat conduction and thermally-induced density changes (by volume expansion) and parameters controlling the onset of phase changes. Properties governing energy transport by convection, radiation and diffusion are specified elsewhere.

Heat Flux Model¶

Heat Flux Model = USER

Description / Usage¶

NOT TESTED. Use this optional card to specify a user-defined model for the conductive heat flux. The routine “usr_heat_flux” in file user_mp.c must appropriately define the heat flux/temperature gradient model. The single input parameter has only one possible value:

USER

the user-defined model for the conductive heat flux.

If this card is missing or has a different keyword, the Fourier conductive heat flux model will be used.

Examples¶

Following is the only permissible specification for the card:

Heat Flux Model = USER

Technical Discussion¶

No Discussion.

References¶

No References.

Conductivity¶

Conductivity = {model_name} {float_list} [E/LtT]

Description / Usage¶

This card is used to specify the model for thermal conductivity. Definitions of the input parameters are as follows:

{model_name}	Name of the model for thermal conductivity; this parameter can have the value CONSTANT or USER.
{float_list}	One or more floating point numbers (<float1> through <floatn>) whose values are determined by the selection for {model_name}. These are identified in the discussion of each model below.

Thus,

CONSTANT <float>

a constant thermal conductivity model, {float_list} is a single value:

<float1> - Standard value of k

USER <float1>… <floatn>

a user-defined model. With the USER option the appropriate modifications to the routine “usr_thermal_conductivity” in the user_mp.c file must be undertaken. The {float_list} can be of arbitrary length and is used to parameterize the model. These parameters are made available in the subroutine via <float1> through <floatn>.

TABLE <integer1> <character_string1> {LINEAR | BILINEAR} [integer2] [FILE = filenm]

Please see discussion at the beginning of the material properties chapter 5 for input description and options. Most often character_string1 will be TEMPERATURE or maybe MASS_FRACTION.

Examples¶

Following is a sample card:

Conductivity = USER 1. 1. 1. 1. 1.

Technical Discussion¶

No Discussion.

References¶

No References.

Heat Capacity¶

Heat Capacity = {model_name} {float_list} [E/MT]

Description / Usage¶

This required card is used to specify the model for the heat capacity. Definitions of the input parameters are as follows:

{model_name}	Name of the model for the heat capacity. This parameter can have one of the following values: ONSTANT, USER, or ENTHALPY.
{float_list}	One or more floating point numbers (<float1> through <floatn>) whose values are determined by the selection for {model_name}. These are identified in the discussion of each model below.

Thus,

CONSTANT <float>	This option specifies a constant heat capacity. The {float_list} has a single value: <float1> - Heat capacity
USER <float1>…	the heat capacity will be a user-defined model. This user-defined model must be incorporated by modifying the routine “usr_heat_capacity” in the file user_mp.c. The model parameters are entered in the {float_list} as <float1> through <floatn> and passed to the routine as an array.
ENTHALPY <float1>	a model of heat capacity that uses the latent heat of fusion parameter. The model goes as follows: Here the {float_list} requires two values, where: <float1> - Base heat capacity in the solid state, cp <float2> - Latent heat of fusion Hf The liquidus temperature Tl and the solidus temperature Ts are taken from the material file. This model is currently available for single species only, and is used for rapid melting problems in alloys.
TABLE <integer1> <character_string1> {LINEAR \| BILINEAR} [integer2] [FILE = filenm]	Please see discussion at the beginning of the material properties chapter 5 for input description and options. Most often character_string1 will be TEMPERATURE or maybe MASS_FRACTION.

Examples¶

Following is a sample card:

Heat Capacity = CONSTANT 1.

Technical Discussion¶

When the ENTHALPY option is used, the liquidus (Tl) and solidus (Ts) temperatures must be added through the Liquidus Temperature and Solidus Temperature cards.

References¶

No References.

Volume Expansion¶

Volume Expansion = CONSTANT <float> [1/T]

Description / Usage¶

This card is used to specify the model for the coefficient of volume expansion in the energy equation. This property is required for the BOUSS option on the Navier-Stokes Source card. Definitions of the input parameters are as follows:

CONSTANT

Name of the model for a constant volume-expansion coefficient.

<float> - the value of the volume expansion coefficient.

Examples¶

The following is a sample input card:

Volume Expansion = CONSTANT 1.

Technical Discussion¶

Warning: Please be careful that the Species Volume Expansion card is set appropriately. If the BOUSS or BOUSSINESQ model is turned on on the Navier- Stokes Source card, then both thermal and species volume expansion effects are included if the coefficients are nonzero. .

References¶

No References.

Reference Temperature¶

Reference Temperature = CONSTANT <float> [T]

Description / Usage¶

This card is used to specify the model for the reference temperature, which is required by the BOUSS option on the Navier-Stokes Source card and by the BINGHAM option on the Liquid Constitutive Equation card. Definitions of the input parameters are as follows:

CONSTANT

Name of the model for a constant reference temperature.

<float> - the value of the reference temperature.

Examples¶

The following is a sample input card:

Reference Temperature = CONSTANT 1.

Technical Discussion¶

No Discussion.

References¶

No References.

Liquidus Temperature¶

Liquidus Temperature = CONSTANT <float> [T]

Description / Usage¶

This card is used to specify the model for the liquidus temperature. Definitions of the input parameters are as follows:

CONSTANT

Name of the model for the liquidus temperature.

<float> - the value of the liquidus, Tl .

Examples¶

Following is a sample card:

Liquidus Temperature = CONSTANT 1.

Technical Discussion¶

This card is required when using the ENTHALPY option on the Heat Capacity card.

References¶

No References.

Solidus Temperature¶

Solidus Temperature = CONSTANT <float> [T]

Description / Usage¶

This card is used to specify the model for the solidus temperature. Definitions of the input parameters are as follows:

CONSTANT

Name of the model for the solidus temperature.

<float> - the value of the solidus, Ts .

Examples¶

The following is a sample card:

Solidus Temperature = CONSTANT 1.

Technical Discussion¶

This card is required when using the ENTHALPY option on the Heat Capacity card.

References¶

No References.

Energy Weight Function¶

Energy Weight Function = {GALERKIN | SUPG} <float>

Description / Usage¶

This card specifies the weight function to be used on the weighted residual of the energy equations. For high Peclet number cases, you may want to use a Petrov- Galerkin formulation rather than a Galerkin formulation. Definitions of the input parameters are as follows:

GALERKIN

Name of the model for the weight functions for a full Galerkin formulation. This is the default when this card is absent.

<float> - the value of the weight function, a number between 0. and 1.; a value of 0. corresponds to GALERKIN.

SUPG

Name of the model for the weight functions for a streamwise upwinded Petrov-Galerkin formulation.

<float> - the value of the weight function, a number between 0. and 1.; a value of 1. corresponds to a full SUPG.

Examples¶

The following is a sample input card:

Energy Weight Function = GALERKIN 0.0

Technical Discussion¶

The SUPG weighting is applied only to the advective term in the Energy conservation equation and Jacobian assembly.

References¶

No References.