Computing the thermal transport properties of three-dimensional discontinuous systems with interfacial thermal resistance

Abstract

This study proposes a practical method based on the step-balanced random walk for evaluating thermal transport properties in complex three-dimensional discontinuous systems incorporating interfacial thermal resistance (ITR). The random walk preserves detailed balance by using the ratio of thermal effusivities—representing the material’s ability to exchange energy—across interfaces as the penetration probability. ITR is introduced by assigning each interface a thermal effusivity bI smaller than that (b) of the constituent phases. Applications to two representative models—a two-phase slab structure and a spherical filler dispersion—demonstrate that the proposed approach predicts physically consistent dependencies of thermal conductivity on interfacial density and filler size. Furthermore, the ITR per unit area, RI, can be expressed through a simple relation involving b, bI, and the base step length Δr0: RI = const. × Δr0 (b − bI)/bI.