The overall thermal conductivity in an isotropic porous medium containing cavities of various shapes is studied in this work. The cavity shapes under consideration include spherical and cylindrical pores, prelate and oblate spheroids, and cylindrical cavities with rectangular cross sections. The unique feature lies in the derivation of the scaling rules governing the overall thermal conductivity in porous media containing various shapes of internal cavities. The temperature distribution around the representative cavity surface, the central quantity in the present differential formulation, is obtained by the boundary element method employing the exterior formulation.
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