The heat transfer equation for porous media is derived from the mixture rule on energies appearing in solid and fluid heat transfer equations (see Ref. 13). For undeformed immobile solids, Equation 4-14 simplifies into:

and for a fluid domain where pressure work and viscous dissipation are neglected, Equation 4-16 becomes:

The mixture rule applies by multiplying the first equation by the solid volume fraction, θp, multiplying the second one by the porosity, 1−θp, and summing resulting equations.

The theory for this hypothesis is detailed in the section Local Thermal Equilibrium below. Otherwise, the Local Thermal Non-Equilibrium section describes the theory for modeling heat transfer in porous media using two temperatures.