Effective thermal conductivity of composites with a thermal contact resistance between the constituents: Nondilute case

The effective thermal conductivity of a particulate composite exhibiting a thermal contact resistance at interphase boundaries is considered. Two micromechanical models, the generalized self-consistent scheme, and the Mori–Tanaka theory Acta Metall. 21, 571 (1973) previously used in composite media with perfect interfaces, are generalized to allow for the phenomenon of thermal contact resistance between the constituents. Spherical inclusions are considered and their interaction is approximately taken into account, so that the presented treatment is valid at nondilute concentrations. Both methods, distinctly different in their approach, result in the same closed-form simple expression for the effective thermal conductivity.