Two-equation model for a diffusive process in porous media using the volume averaging method with an unsteady-state closure

For the diffusive transport through a two-phase material, a two-equation model must be used when the contrast between the thermal properties of the medium becomes so high that local equilibrium cannot be achieved. Using the volume averaging approach an unsteady-state closure is investigated, which leads to expression of a phase exchange term and conductive terms as temporal convolutions. Two application examples are studied, layered material and cylindrical particles embedded in a continuous phase. The results of the one-equation model, the two-equation models with a steady-state closure and an unsteady-state closure are compared. Surprisingly, in most cases, the steady-state closure gives satisfactory results.