Asymptotic studies of closely spaced, highly conducting cylinders

Abstract

We consider the solution of the scalar transport problem for a pair of nearly touching cylinders of high conductivity. We obtain an expression for the set of multipole moments of the potential distribution for this problem in terms of the hypergeometric function. We apply this expression in the estimation of truncation errors occurring in the matrix solution of the corresponding transport problem for the square array of cylinders. Consequently, we are able to calculate the array transport coefficient for arbitrarily high cylinder conductivities, and arbitrarily small cylinder separations. We derive and verify an expression for this coefficient which is uniformly valid throughout the whole asymptotic region when highly conducting cylinders approach touching.