Vol 52, No 2 (2000)

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Quasifractional approximants for effective conductivity of regular arrays of spheres

I. Andrianov, V. Danishevs'kyy, S. Tokarzewski

Arch. Mech. 52 (2), 319-327, 2000

Keywords:


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; φmax] (φmax 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→φmax. 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.

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