On the effective conductivity of composites with ellipsoidal inhomogeneities and highly conducting interfaces

Abstract

The effective conductivity of composite media with ellipsoidal inhomogeneities and highly conducting interfaces is studied. At such interfaces the temperature field is continuous, but the normal component of the heat flux undergoes a discontinuity which is proportional to the local surface Laplacian of the temperature field. The dilute approximation for the case of ellipsoidal inhomogeneities in such circumstances is derived. The derivation involves the solution of an auxiliary problem of a single particle embedded in an infinite medium and employs ellipsoidal harmonics. This solution is also used to derive a mean–field approximation for non–dilute concentrations.