Conductivity of N-dimensional composites containing hyperspherical inclusion

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11 Scopus citations


A problem of determining the macroscopic or effective thermal conductivity of an N-dimensional composite medium containing N-dimensional nonoverlapping hyperspherical inclusions is considered. Since the macroscopic conductivity is expected to become less sensitive to the detailed spatial distribution of the inclusions for N ≥4, only the special case of periodic arrangement of the inclusions is considered. An expression for the macroscopic conductivity correct to O(χ3N+8), χ being the ratio of 'diameter' of the inclusions to the spacing between them, is derived and the numerical results for the conductivity are presented as a function of χ and N for the two special cases of perfectly conducting and insulating inclusions. The effective conductivity of the composite is found to approach that of the continuous matrix in higher dimensions.

Original languageEnglish (US)
Pages (from-to)64-73
Number of pages10
JournalSIAM Journal on Applied Mathematics
Issue number1
StatePublished - 1990
Externally publishedYes

ASJC Scopus subject areas

  • Applied Mathematics


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