Transport properties of touching cylinder pairs and of the square array of touching cylinders

Abstract

We consider the solution of the scalar transport problem for a pair of touching cylinders of high conductivity. We obtain a closed-form expression for the set of multipole coefficients characterizing the potential function in this problem. We show that this expression permits the estimation of truncation errors occurring in the matrix solution of the transport problem for the square array of touching cylinders. Consequently, we are able to study the array conductivity for arbitrarily high cylinder conductivities, and confirm an asymptotic expression due to O’Brien. We derive a perturbation formula giving the effect of small cylinder separations on array conductivity.