THERMAL-CONDUCTIVITY OF POLYDISPERSE COMPOSITES WITH PERIODIC MICROSTRUCTURES

A method is developed to treat the effective thermal conductivity of p eriodic composites whose inclusions are of different sizes or of diffe rent thermal conductivities. Based on the Green's function formalism, the effects of induced heat sources on inclusion boundaries are explic itly taken into account, and a set of Rayleigh identities are establis hed. Hence the temperature distribution in a polydisperse composite an d its effective thermal conductivity can be evaluated with very high a ccuracy. The method is applied to two-dimensional polydisperse systems with cylindrical inclusions as well as to three-dimensional ones with spherical inclusions. Illustrative calculations of the effective ther mal conductivity are presented for both isotropic and anisotropic syst ems. The application of the method is further exemplified by an analyt ical formula for the effective thermal conductivity of a composite whi ch possesses a square symmetry and contains two different kinds of inc lusions. The numerical calculations have been carried out for two-dime nsional systems.