Solutions for the conductivity of multi-coated spheres and spherically symmetric inclusion problems

Variational results on the macroscopic conductivity (thermal, electrical, etc.) of the multi-coated sphere assemblage have been used to derive the explicit expression of the respective field (thermal, electrical, etc.) within the spheres in d dimensions ( d = 2 , 3 ). A differential substitution app...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2018-02, Vol.69 (1), p.1-14, Article 13
Main Author: Pham, Duc Chinh
Format: Article
Language:English
Subjects:
Dilution
Effective medium theory
Electrical resistivity
Engineering
Mathematical Methods in Physics
Mathematical problems
Spherical shells
Theoretical and Applied Mechanics
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Summary:Variational results on the macroscopic conductivity (thermal, electrical, etc.) of the multi-coated sphere assemblage have been used to derive the explicit expression of the respective field (thermal, electrical, etc.) within the spheres in d dimensions ( d = 2 , 3 ). A differential substitution approach has been developed to construct various explicit expressions or determining equations for the effective spherically symmetric inclusion problems, which include those with radially variable conductivity, different radially variable transverse and normal conductivities, and those involving imperfect interfaces, in d dimensions. When the volume proportion of the outermost spherical shell increases toward 1, one obtains the respective exact results for the most important specific cases: the dilute solutions for the compound inhomogeneities suspended in a major matrix phase. Those dilute solution results are also needed for other effective medium approximation schemes.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-017-0905-6