Effective thermal conductivity of functionally graded random micro-heterogeneous materials using representative volume element and BEM

This work introduces a numerical methodology for the computation of the effective thermal conductivity (ETC) of random micro-heterogeneous materials using representative volume elements and the Fast Multipole Boundary Element Method (FMBEM). The methodology is applied to solve two-dimensional foam-like materials consisting of random distributions of circular isolated holes. The computed ETC values are successfully used to predict the temperature fields of two materials with functionally graded ETCs. Numerical and analytical results are experimentally validated. The proposed methodology is flexible and versatile, as it is capable to account for both, the geometrical and topological details of the material microstructure.