Computational thermal conductivity in porous materials using homogenization techniques: Numerical and statistical approaches

Abstract

In this paper, the numerical homogenization technique and morphological analysis are used in order to compute the thermal conductivity in microscale of porous materials. The computational thermal homogenization is based on a 3D random material with spherical and ellipsoidal pores. Two types of microstructures are considered: microstructure 1 with random distribution of identical non overlapping pores and microstructure 2 with overlapping pores, based on the boolean model. The objective is to quantify the difference between these morphologies, in order to find some relationships between their morphological parameters and their macroscopic effective thermal conductivities. Periodic boundary conditions are applied on the representative volume element, RVE, of microstructures, for thermal modeling by finite element method. The covariance notion and integral range are introduced for morphological characterization. The deterministic RVE size is related with all microstructure parameters. The equivalent morphology concept for thermal conductivity is introduced after development of some relationships between morphological parameters.