Thermal conductivity of composites

Abstract

A general expression for the effective thermal conductivity of inhomogeneous media in terms of the Fourier components of the spatial variation of the conductivity is applied to composites consisting of inclusions in a continuous matrix. It is reformulated in terms of the mean square fluctuations of the conductivity. Specific cases treated are spherical inclusions and long cylinders, both random and with preferred directions. The results hold provided the difference in thermal conductivities is small or provided the concentration of inclusions is not too large. The theory fails if the thermal conductivity of the matrix is much smaller than that of the inclusions. The same considerations also apply to electrical conductivity.