A model for the effective thermal conductivity of metal-nonmetal particulate composites

Abstract

The effective thermal conductivity of particulate composites with oriented spheroidal metallic particles embedded in a dielectric matrix is analyzed under the framework of the two-temperature model of heat conduction. The obtained analytical results show that the effective thermal conductivity depends strongly on (1) the relative size of the particle inclusions with respect to the electron-phonon coupling length and (2) the ratio between the electron and phonon thermal conductivities. The effect of the electron-phonon coupling inside metallic particles is expressed by the reduction of the composite thermal conductivity with respect to its corresponding values obtained for an infinite electron-phonon coupling factor, where the analysis could be established based on the Fourier law of heat conduction. It is shown that the composite thermal conductivity has upper and lower bounds, which are determined by the particle size in comparison with the electron-phonon coupling length. The generalized model for spheroidal particles is then used to analyze the thermal conductivity for limiting cases on the particle shape including spheres, cylinders, and flat plates. For perfect electron-phonon coupling, the proposed model reduces to various previously-reported results. This study shows that the particle size dependence of the thermal conductivity of metal-nonmetal composites appears not only through the interfacial thermal resistance but also by means of the electron-phonon coupling. The results of this work could be useful for guiding the design of particulate composites with spheroidal metallic inclusions from macro/micro- to nanoscales.