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

The effective conductivity of composite media with ellipsoidal inhomogeneit ies and highly conducting, interfaces is studied. At such interfaces the te mperature field is continuous, but the normal component of the heat flux un dergoes a discontinuity a which is proportional to the local surface Laplac ian of the temperature field. The dilute approximation for the case of elli psoidal inhomogeneities in such circumstances is derived. The derivation in volves the solution of an auxiliary problem of a single particle embedded i n an infinite medium and employs ellipsoidal harmonics. This solution is al so used to derive a mean-field approximation for Pion-dilute concentrations .