A micromechanics-based analytical solution for the effective thermal conductivity of composites with orthotropic matrices and interfacial thermal resistance

TL;DR

This paper presents a micromechanics-based analytical solution for predicting the effective thermal conductivity of composites with orthotropic matrices and spherical inclusions, incorporating interfacial thermal resistance, validated against finite element simulations.

Contribution

It introduces a modified Eshelby tensor accounting for interfacial resistance and derives an analytical expression for effective thermal conductivity using the Mori-Tanaka method.

Findings

Analytical predictions agree within 10% of finite element results for up to 10% inhomogeneity volume fraction.

Derived a closed-form modified Eshelby tensor considering interfacial thermal resistance.

Validated the analytical model with numerical simulations, demonstrating accuracy.

Abstract

We obtained an analytical solution for the effective thermal conductivity of composites composed of orthotropic matrices and spherical inhomogeneities with interfacial thermal resistance using a micromechanics-based homogenization. We derived the closed form of a modified Eshelby tensor as a function of the interfacial thermal resistance. We then predicted the heat flux of a single inhomogeneity in the infinite media based on the modified Eshelby tensor, which was validated against the numerical results obtained from the finite element analysis. Based on the modified Eshelby tensor and the localization tensor accounting for the interfacial resistance, we derived an analytical expression for the effective thermal conductivity tensor for the composites by a mean-field approach called the Mori-Tanaka method. Our analytical prediction matched very well with the effective thermal conductivity obtained from finite element analysis with up to 10% inhomogeneity volume fraction.