Effects of contact resistance on thermal conductivity of composite media with a periodic structure

The thermal conductivity of periodic composite media with spherical or cylindrical inclusions embedded in a homogeneous matrix is discussed. Using Green functions, the authors show that the Rayleigh identity can be generalized to deal with thermal properties of these systems. A new calculating method for effective conductivity of composite media is proposed. Useful formulae for effective thermal conductivity are derived, and meanings of contact resistance in engineering problems are explained.