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Thermophysical Solid Models

Overview

The ‘Thermophysical models’ define how the energy, heat and physical properties of the solid are calculated. These variables are then determined based on the analysis type and the selected models.

The thermophysical model selection appears under ‘Model’ and then ‘Material’ sub-tree after the addition of a solid material.

Thermo-models-1

Adding a material with thermophysical model under ‘Model’.

For Conjugate Heat transfer analysis, 7 properties are required and must be defined. These setting are briefly described below.

Thermo-models-2

Parameters required for solid thermophysical models.

1. Type

The Thermo ‘Type’ of model describes how the flow thermal variables are calculated.

The available type on the SimScale platform for solid materials is the ‘heSolidThermo’.

i- heSolidThermo

The “heSolidThermo” Thermophysical model is for a solid with uniform homogeneous composition.

It uses the Energy equation and fundamental solid thermodynamic properties to determine the heat distribution. This model uses the ‘thermal conductivity’ , ‘specific heat capacity’ (at constant pressure) and the ‘density’ of the solid.

2. Mixture

The ‘Mixture’ specifies the solid mixture composition. Generally, a uniform homogeneous material is categorised as pure mixture, which represents a mixture with fixed composition. Currently only ‘pure Mixture’ can be selected under ‘Material’ and sub-option ‘Mixture’.

3. Specie

Under specie the composition of the constituent is specified. As currently, a single constituent is available, so parameter values for one constituent are required. The following values are required for the specie:

i- nMoles

This is the number of moles of the component. This parameter has a default value of 1 and generally is not required to be changed.

ii- molWeight

This is the molecular weight of the solid component in units of kg/kmol and is dependent on the molecular structure of the solid material.

4. Transport Model

The Transport model relates to the calculation of the transport variable . Here the user must specify \(\kappa\) and thermal diffusivity \(\alpha\) ( for energy and enthalpy equations). [1] Depending upon the problem, the following types of transport models are available:

i- constIso

The ‘const’ type will assume constant properties for the transport package. Here the ‘Thermal conductivity’ is constant in all coordinate directions in the solid.

ii- constAnIso

For ‘constAnIso’ type the user can define different ‘Thermal conductivity’ value for each of the specified coordinate directions. Here, the user must also define the coordinate system vectors.

iii- polynomial

The user may also enter a custom relation for calculation of dynamic viscosity \(\mu\) and thermal conductivity \(\kappa\) as a function of temperature \(T\) by a polynomial of order \(N\) (maximum order N = 7). The relation is then given as follows:

\[\mu = \sum_{i=0}^{N-1}a_{i}T^{i} \qquad [1]\]

5. Thermodynamic Models

The thermodynamic models are used to calculate the specific heat \(c_{p}\) (at constant pressure) for the solid, from which then the other properties are derived. The following methods are available for the evaluation of \(c_{p}\).

i- hConst

This options assumes a constant value for specific heat \(c_{p}\) and the heat of fusion \(H_{f}\). These values are specified by the user in standard S.I units.

ii- hPolynaomial

This option is available if a ‘polynomial’ Transport model is selected. Then the specific heat (\(c_{p}\)) is calculated as a function of temperature by a polynomial of order N as below.

\[c_p = \sum_{i=0}^{N-1}a_{i}T^{i} \qquad [1]\]

6. Equation of State

An equation of state is a thermodynamic relation describing the interconnection between various macroscopic properties of a solid. In OpenFoam solver, it describes the relation between density \(\rho\) of a solid and the pressure \(P\) and temperature \(T\). [1]

Based on the thermophysical model type, the following equations of state can be used :

i- rhoConst

In this case, the solid density \(\rho\) is kept constant and does not change by pressure \(P\) or temperature \(T\)

\[\rho = constant\]

7. Energy

Under ‘Energy’ there is only one option, ‘sensible Enthalpy’ that is available for the form of energy to be used in the solution. In this case, the equations have the form that does not include the heat of formation \(\Delta h_{f}\) as the solid material composition remains constant.