Thermal Conductivities of Composite Materials

Abstract

A field solution for long wavelengths of the equation of heat conduction is obtained for a composite material with orthorhombic symmetry. This yields exact expressions for the three principal thermal conductivities. They are valid for any number of ortho rhombic constituents and even for continuously varying thermal conductivities within the elementary cell. For a lamellar composite, the average thermal conductivities of the material are expressed directly as integrals over the space-dependent thermal conductivi ties. For a filamentary composite, such explicit expressions are obtained only in the Wigner-Seitz approximation and only for a stepwise variation of the thermal conductivities within the ele mentary cell. In the same manner, the average thermal conduc tivity of a composite with cubic symmetry, e.g. isotropic spherical inclusions in a cubic lattice, is calculated. Analogies with previous results on diffusion coefficients and elastic shear moduli are discussed.