Radiative and conductive heat transfer in porous media: Estimation of the effective thermal conductivity

The effective thermal conductivity κeff of porous media has been studied when both radiation and conduction is present. Expressions for κeff of a solid containing dispersed, equisized, disconnected spherical pores are derived within an extended effective medium theory. When no radiation is present, the results agree very well with exact results for an fcc lattice of spheres. The effective medium approach is also used to calculate the transverse effective thermal conductivity of a solid containing aligned, infinitely long, equisized, disconnected, cylindrical pores. When no radiation is present, the result is in excellent agreement with exact results for a hexagonal array of cylinders. In the direction parallel to the cylinder axes, the effective thermal conductivity is found exactly. An estimation of κeff for a system of random, overlapping, solid spheres in a gas matrix is presented.