Abstract
Heat transfer in a porous medium subjected to the effect of internal heat sources is considered. Macroscopic equations are obtained from the method of volume averaging. Both local equilibrium and non-local equilibrium conditions are considered. It is shown that homogeneous sources can simply be taken into account by introducing averaged values in the macroscopic equations. The heterogeneous source term corresponding to heat sources at the interface between the two phases requires a different treatment. The average source is distributed in the two macroscopic equations of the local non-equilibrium model through a distribution coefficient, which is given by a local "closure problem". This closure problem is solved numerically for different representative unit cells, and for different values of the thermal conductivity ratio and Peclet number. Numerical experiments are performed to test the theory, and results show a good agreement between theoretical and "experimental" predictions.
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