Effective thermal conductivity of micro-inhomogeneous media containing imperfectly bonded ellipsoidal inclusions

In this paper we consider the problem of thermal polarization of an ellipsoidal inclusion surrounded by a thin conducting layer. To calculate the effective thermal conductivity of a medium containing such inclusions we use the homogenization scheme named the effective field method. The application of this scheme allows one to take into account the texture of micro-inhomogeneous medium. We obtained the solution for a set of parallel and randomly oriented ellipsoidal inclusions with a thin layer with surface conductivity. Our calculations show that the effective thermal conductivity depends on the size of inclusions.