Quasifractional Approximants in the Theory of Composite Materials

We study the effective heat conductivity of regular arrays of perfectly conducting spheres embedded in a matrix with 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 volume fraction of a spheres). As a starting point we use a perturbation approach for ϕ → 0 and an asymptotic solution for ϕ → ϕmax. Three different spatial arrangements of the spheres, simple cubic, body centred and face centred cubic arrays, are considered. Results obtained give a good agreement with numerical data.

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