Effective Thermal Conductivity for Functionally Graded Materials

Abstract

In this paper, an analytical approach is presented to derive the effective thermal conductivity of a composite reinforced by FGM (Functionally Graded Materials) inclusions of spherical shape. The composite consists of spherical inclusions made of FGM embedded in an infinitely-extended matrix phase subject to uniform heat flux at infinity. The thermal conductivity of the FGM inclusion is assumed to vary linearly inside the FGM. The varying thermal conductivity inside the FGM inclusions results in a temperature distribution in the composite. The effective thermal conductivity is derived based on the exact temperature solution for a single FGM inclusion and by employing the self-consistent approximation. The derived values are found to be within the upper and lower bounds of the rule-ofmixtures.