On the effect of inclusion shape on effective thermal conductivity of heterogeneous materials

Abstract

In this paper, a numerical homogenization technique is used to estimate the effective thermal conductivity of random two-dimensional two-phase heterogeneous materials. The thermal computational leads essentially bring out the effect of the voids/inclusions morphology on the effective physical properties. This is achieved using two different heterogeneous materials: microstructure 1 with non-overlapping spherical pores and microstructure 2 with non overlapping spherical rigid inclusions taking into account five different volume fractions from each case. The notion of the representative volume element is introduced for numerical simulations using periodic boundary conditions and uniform gradient of temperature conditions. The obtained effective material properties on the representative microstructures are compared with different analytical models as: series model, parallel model, effective medium theory and Maxwell models, for different morphologies of rigid inclusions and voids. This paper compares the performance of several classical effective medium approximations. Finally, an analytical expression developing the Maxwell model is proposed to estimate the effective thermal conductivity of heterogeneous materials taking into account the inclusion morphology.