Bounds of Effective Thermal Conductivity of Short-Fiber Composites

Abstract

This paper presents bounds of effective thermal conductivities for mul ti-component unidirectional short-fiber composites, based upon an ap proach originally developed by the authors for composite effective elastic moduli. A perturbation expansion of the local temperature gradient is developed by using a Green's function tensor. The effective thermal con ductivity can be expressed in series form and the correlation functions of thermal conductivity have been evaluated up to the third order term. It also has been shown that the series expressions obtained by Kröner, and Zeller and Dederichs are approximations of the present solution. The pre sent solution also coincides with Beran's results for statistically isotropic materials, and provides tighter bounds than those of Hashin and Shtrik man, whose approach is equivalent to considering the correlation function up to the second order.