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 phi belongs to [0; phi[max]] (phi[max] is the maximum limiting volume of a sphere). As the bases we use a perturbation approach for phi --> 0 and an asymptotic solution for phi --> phi[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.
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