Effective thermal conductivity of porous media

Effective thermal conductivity of porous media is one of the most fundamental properties required for industrial applications of porous media. Its estimation, however, is not an easy task since tortuosity and thermal dispersion must be considered and modeled accordingly in a mathematical manner. In this chapter, a volume averaging theory for fluid saturated porous media is introduced to derive analytical expressions which take full account of such combined effects of tortuosity and thermal dispersion on the effective thermal conductivity. The derived expressions based on a unit cell model are quite general and valid for most of natural and manmade porous media, including packed beds, metal foams, wire screens and honeycomb structures. Moreover, metal frame core structures capable of carrying both mechanical and thermal loads are considered for promising candidates for thermal management applications. A general analytical approach is proposed to freely control the directional dependence of the thermal conductivity tensor in the metal frame core structure. The overlooked fundamental laws associated with the effective thermal conductivity, namely, the summation law and one-third the solidity law, are also discussed in connection with engineering applications of metal frame core structures.