Effective Permeability of a Layered Porous Cavity

The feasibility of using a lumped system approach in the heat transfer analysis of a layered porous cavity is numerically investigated in this paper. Two layered cavities are considered; in one case the sublayers are perpendicular to the imposed temperature gradient while in the other case they are parallel to the imposed temperature gradient. Numerical calculations have covered a wide range of parameters (i.e., $10⩽Ra1⩽1000,$$0.01⩽K1/K2⩽100,$ and $L1/LH1/H=0.25,$ 0.5 and 0.75). The results are presented in term of the effective Rayleigh number which is defined based on the effective permeability. Two averaging techniques are used for the evaluation of the effective permeability; one is arithmetic average and the other is harmonic average. The results show that the lumped system approach can provide a fairly accurate prediction in heat transfer if the permeability is correctly characterized. Also found is that the effective permeability of a layered porous cavity is strongly dependent on the orientation of sublayers and the primary heat flow direction.