The effective conductivity of composites with imperfect thermal contact at constituent interfaces

This paper is an investigation of the effective conductivities of composite media in which a thermal boundary resistance exists at constituent interfaces. The fundamental concepts in the theory of composite media in the context of thermal conduction are reconsidered in the presence of a temperature discontinuity between the constituents. The well-known procedures for defining and computing effective moduli are generalized to include the above mentioned interface effects. The developed procedure is applied to derive the effective conductivities of a composite with embedded spheroidal inclusions at a dilute concentration ratio. The method of solution of the auxiliary problem is based on the use of spheroidal harmonics in prolate and oblate configurations.