A three-phase confocal elliptical cylinder model for predicting the thermal conductivity of composites

A three-phase confocal elliptical cylinder model accounting for variations in fiber section shapes and randomness in distribution and orientation is developed for predicting the thermal conductivity of fiber reinforced composites. The representative volume element consisting of a fiber and a matrix elliptical ring is embedded in an infinite homogenous composite. Using the conformal mapping technique and the Laurent series expansions approach, an analytical solution for the thermal conductivities of composites is obtained. A comparison with other micromechanics methods such as the dilute, self-consistent and Mori-Tanaka models shows that the present method provides convergent and reasonable results for a full range of variations in fiber section shapes, for a complete spectrum of the fiber volume fraction. Numerical results are presented to discuss the dependence of the effective conductivities of composites on the fiber conductivity and aspect radio. The present solutions are helpful to analysis and design of such composites.