ISSN:
1572-9036
Keywords:
effective properties
;
homogenization
;
composites
;
conductivities
;
bounds
;
Padé approximants
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1006455311626
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