Effective conductivity of dispersions of spheres with a superconducting interface

We consider the problem of exactly determining the effective thermal conductivity, sigma(eff), of a composite material consisting of periodic or random arrays of spheres which possess superconducting interfaces. This requires the solution of the local temperature field in which there is a jump in the normal component of the heat flux across the sphere-matrix interface. The strength of this interface is characterized by a dimensionless parameter C greater than or equal to 0 such that C = 0 corresponds to the usual perfect interface case. An approximate formula for the effective conductivity, sigma(eff), compares favourably with our results for a wide range of sphere volume fractions, phase conductivity ratios, and values of the interfacial strength C.