Effective thermal conductivity of two-phase composites containing highly conductive inclusions

Thermal conductivity is one of the key material properties to understand the effective thermo-mechanical behavior of advanced composites. Experimental studies show that when highly conductive inclusions are embedded in a less thermally conductive matrix, the effective thermal conductivity of the composite changes drastically with the increase of volume fraction (V_f) of the inclusions. This study presents a theoretical model to predict the effective thermal conductivity of two-phase particulate composites containing highly conductive inclusions in a polymeric matrix. The probabilistic approach presented by Tsao (1961) has been modified and extended for predicting the effective thermal conductivity of two-phase composites. The expression for the effective thermal conductivity of a unit cube of two-phase composite is derived implicitly in terms of distribution function, V_f and thermal conductivity of the constituents. Different distribution functions of the inclusions are proposed and the optimum function is obtained to describe the effective thermal conductivity of highly conductive particulate composites. Results of the effective thermal conductivity of a cubic unit cell obtained from different distributions of inclusions are compared with published experimental data, and other analytical and numerical models for particulate composites available in the literature. The results show a linear distribution of inclusions gives reasonable estimates of the effective thermal conductivity of the particulate composites. It is anticipated that the proposed approach can be used to develop models for the effective thermal conductivity of advanced composites containing highly conductive inclusions.