A numerical technique for computing effective thermal conductivity of fluid-particle mixtures

Periodic arrays of particles, foams, and other structures impregnated with a static fluid play an important role in heat transfer enhancement. In this article, we develop a numerical method for computing conduction heat transfer in periodic beds by exploiting the periodicity of heat flux and the resulting linear variation of mean temperature. The numerical technique is developed within the framework of an unstructured finite-volume scheme in order to enable the computation of effective thermal conductivity for complex fluid-particle arrangements. The method is applied to the computation of effective thermal conductivity of ordered as well as random beds of spheres and rods. The effects of varying surface area, aspect ratio, volume fraction, orientation, and distribution are studied for various solid-to-fluid conductivity ratios. Unlike classical theories which predict only a dependence on volume fraction, these direct simulations show that aspect ratio, distribution, and alignment of particles have an important influence on the effective thermal conductivity of the bed.