Theory for the Local Thermal Non-Equilibrium Interface
The detailed theory leading to the equations of local thermal non-equilibrium heat transfer in porous media is presented above in Theory for Heat Transfer in Porous Media. This part only recalls the main results and describes how Local Thermal Non-Equilibrium multiphysics coupling feature implements them.
The local thermal non-equilibrium hypothesis describes heat transfer in a porous medium using two temperature fields to solve: Tf for the fluid phase and Ts for the porous matrix. These should satisfy the following couple of partial differential equations:
(4-123)
(4-124)
Recall the Fourier’s law of conduction adapted to the local thermal non-equilibrium hypothesis:
and the quantities used in this problem:
•
θp is the solid volume fraction (SI unit: 1)
•
ρs and ρf are the solid and fluid densities (SI unit: kg/m3)
•
Cp, s and Cp, f are the solid and fluid heat capacities at constant pressure (SI unit: J/(kg·K))
•
qs and qf are the solid and fluid conductive heat fluxes (SI unit: W/m2)
•
ks and kf are the solid and fluid thermal conductivities (SI unit: W/(m·K))
•
qsf is the interstitial convective heat transfer coefficient (SI unit: W/(m3·K))
•
Qs and Qf are the solid and fluid heat sources (SI unit: W/m3)
•
up is the porous velocity vector (SI unit: m/s)
Predefined Multiphysics Interface
The Local Thermal Non-Equilibrium Interface is a predefined coupling between The Heat Transfer in Solids Interface and The Heat Transfer in Fluids Interface. These two interfaces solve for Equation 4-123 and Equation 4-124, respectively, but without the heat exchange term ±qsf(Tf − Ts).
The Local Thermal Non-Equilibrium multiphysics coupling feature combines two actions in order to couple the two aforementioned physics interfaces. It first multiplies each energy equation by its volume fraction: θp and (1 − θp) for solid and fluid phases, respectively. Then it adds the heat exchange term ±qsf(Tf − Ts) in both equations.
Volumetric and Surface Thermal Conditions
As shown in Equation 4-123 and Equation 4-124, the volumetric heat sources θpQs and (1 − θp)Qf are applied to the energy equations. The Heat Source features of each physics interface though specifies Qs and Qf. Special care is therefore needed when defining a heat source for the whole porous medium. You would have to ensure that the heat source densities, Qs and Qf, are both equal to the heat rate density that was intended to the porous medium.