Document Type

Article

Date

January 1990

Keywords

Laplace equation in N-dimensions, random walk, effective conductivity or diffusivity in inhomogeneous media

Disciplines

Chemical Engineering

Description/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.

Additional Information

Copyright 1990 SIAM Journal on Applied Mathematics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and SIAM Journal on Applied Mathematics. The article may be found at http://www.jstor.org/stable/2102100

 
 

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