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Conductivity of N-Dimensional Composites Containing Hyperspherical Inclusion

A. S. Sangani
SIAM Journal on Applied Mathematics
Vol. 50, No. 1 (Feb., 1990), pp. 64-73
Stable URL: http://www.jstor.org/stable/2102100
Page Count: 10
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Conductivity of N-Dimensional Composites Containing Hyperspherical Inclusion
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Abstract

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.

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