Generalized model of Kapitza conductance across rough interfaces

Abstract

This paper is devoted to the theoretical prediction of the interfacial heat transfer in nanostructured materials. The main task of this work is the analysis of interaction of elastic waves with the rough interface between two different solids. The presence of toughness leads to a significant increase in the resistance to heat transfer in nanostructures. This fundamental problem is discussed in relation to the commonly used method of wave scattering at rough surface: the Kirchhoff tangent plane method. The method assumes that at the point of the rough surface profile, the surface is regarded as locally smooth, and the reflection and transmission of the incident wave can be described by the scattering at the tangent plane of this point. Based on the elastic wave theory, we use the frequency-dependent continuity conditions to calculate the energy transmission coefficient at the interface. And then its effective value at the rough interface is estimated by using the Kirchhoff method. By substituting this effective value into the formula of Kapitza conductance, we can calculate the Kapitza conductance at the rough interface and analyze the effect of roughness on the interfacial heat transfer.