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We obtained an analytical solution for the effective thermal conductivity ofcomposites composed of orthotropic matrices and spherical inhomogeneities withinterfacial thermal resistance using a micromechanics-based homogenization. Wederived the closed form of a modified Eshelby tensor as a function of theinterfacial thermal resistance. We then predicted the heat flux of a singleinhomogeneity in the infinite media based on the modified Eshelby tensor, whichwas validated against the numerical results obtained from the finite elementanalysis. Based on the modified Eshelby tensor and the localization tensoraccounting for the interfacial resistance, we derived an analytical expressionfor the effective thermal conductivity tensor for the composites by amean-field approach called the Mori-Tanaka method. Our analytical predictionmatched very well with the effective thermal conductivity obtained from finiteelement analysis with up to 10% inhomogeneity volume fraction.

scientific reports

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