  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.
