Quasifractional approximants for effective conductivity of regular arrays of spheres

Abstract

We study the effective heat conductivity of regular arrays of perfectly conducting spheres embedded in a matrix with the unit conductivity. Quasifractional approximants allow us to derive an approximate analytical solution, valid for all values of the spheres volume fraction φ∈[0; φ_max] (φ_max is the maximum limiting volume of a sphere). As the bases we use a perturbation approach for φ→0 and an asymptotic solution for φ→φ_max. Three different types of the spheres space arrangement (simple, body and face-centred cubic arrays) are considered. The obtained results give a good agreement with numerical data.