Effective thermal conductivity of composite ellipsoid assemblages with weakly conducting interfaces

Abstract

In this work, a coated ellipsoid assemblage model for the prediction of the effective thermal conductivity of composites with imperfect interfaces is developed. Based on the Green’s function technique, the study proposes a new formulation of the composite ellipsoid assemblage model with an imperfect interface between the inclusion and the surrounding matrix. The solution of the integral equation is obtained thanks to the concept of interior- and exterior-point Eshelby’s conduction tensors. Thereafter, the analytical expressions of the heat intensity and the effective thermal conductivity are proposed for ellipsoidal inclusion and anisotropic thermal conductivity per local phase. In order to test the relevance of the model, its predictions have been compared with the exact solutions of spherical and cylindrical inclusion. Moreover, the capability of the model to well describe the thermal behaviour of composites with high volume fractions of inclusions has been tested through some comparisons with numerical results proposed in the literature. A parametric study is then conducted to analyse the effects of the morphology and the volume fraction of the inclusion, the interface thermal resistance and contrast of thermal conductivity of local phases, on the predictions of the developed model.