Monte Carlo simulation of the effective thermal conductivity in two-phase material

A long-standing thermal transport problem is the analytical determination of the effective thermal conductivity in two-phase material where the values of the conductivities in the two phases differ. In this paper, we calculate the effective thermal conductivity using a Monte Carlo method that was based on methods developed for the corresponding problem in atomic transport. Results are presented for the effective thermal conductivities in several model two-phase systems consisting of dispersed cubes or spheres of up to two orders of magnitude higher or lower thermal conductivities than the matrix phase. When results are compared with analytical treatments, it is clear that overall Maxwell’s pioneering expression does the best.