Local Thermal Non-Equilibrium
Use the Local Thermal Non-Equilibrium multiphysics coupling () to account for heat transfer in porous domains where the solid and fluid temperatures are not in equilibrium. This is achieved by coupling the heat equations in the solid and fluid subdomains through a transfer term proportional to the temperature difference between the fluid and the solid. The corresponding heat equations in the solid and in the fluid subdomains read
with the following material properties:
•
θp is the solid volume fraction.
•
ρs and ρf are the solid and fluid densities.
•
Cp, s and Cp, f are the solid and fluid heat capacities at constant pressure.
•
ks and kf are the solid and fluid thermal conductivities.
•
qsf is the interstitial convective heat transfer coefficient.
•
us and uf are the solid and fluid velocity vectors.
The fluid velocity is deduced from a porous velocity up, coming, for example, from the Darcy’s law or the Brinkman equations, according to:
See also Local Thermal Non-Equilibrium in Theory for Heat Transfer in Porous Media.
Settings
The Label is the default multiphysics coupling feature name.
The Name is used primarily as a scope prefix for variables defined by the coupling node. Refer to such variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different coupling nodes or physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.
The default Name (for the first multiphysics coupling feature in the model) is ltne1.
Coupled Interfaces
This section defines the physics involved in the Local Thermal Non-Equilibrium multiphysics coupling.
Select the Heat transfer in solids interface associated to the solid temperature dependent variable. Select the Heat transfer in fluids interface associated to the fluid temperature-dependent variable.
Local Thermal Non-Equilibrium Settings
Enter a Solid volume fraction θp (dimensionless). The default value is 0.5.
Select an Interstitial convective heat transfer coefficient: Spherical pellet bed, General configuration, or User defined (the default).
Spherical Pellet Bed
In this particular configuration, the interstitial convective heat transfer coefficient can be directly expressed as a function of the average pellet radius rp and the fluid-to-solid Nusselt number for which the fluid dynamic viscosity μ is needed.
Enter a value for the Average pellet radius rp (SI unit: m). Default value is 5e-4 m.
The default Dynamic viscosity μ (SI unit: Pa·s) is used From material. In the list, choose User defined to enter another value or expression. When the dynamic viscosity is set in the Heat Transfer in Fluids interface, it also appears in the list.
The Heat Transfer in Fluids interface defines the dynamic viscosity if either Moist air is selected as Fluid type in the Thermodynamics, Fluid section, or the Equivalent conductivity for convection check box is selected in the Equivalent Conductivity for Convection section.
General Configuration
The interstitial convective heat transfer coefficient is expressed as the product of the specific surface area asf and the interstitial heat transfer coefficient hsf.
Enter a value for the Specific surface area asf (SI unit: 1/m).
Enter a value for the Interstitial heat transfer coefficient hsf (SI unit: W/(m2·K)).
User Defined
Enter a custom value for qsf (SI unit: W/(m3·K)).
Location in User Interface
Context menus
 Multiphysics>Local Thermal Non-Equilibrium
when the Heat Transfer in Solids interface with Solid feature is added together with the Heat Transfer in Fluids interface with Heat Transfer in Fluids feature.