Asymptotic analysis of interactions between highly conducting cylinders

We consider the conduction of heat or electricity between a pair of equal, touching cylinders embedded in a matrix. We solve exactly a problem in which each cylinder contains a heat source, and analyse the solution asymptotically for the case in which the conductivity of the fibres is much greater than that of the matrix. Using this analysis, we assess the accuracy of approximate schemes for calculating the interactions between the fibres of a composite material. We conclude that the approximate solutions are better at predicting global quantities, such as total flux, than they are at predicting pointwise quantities such as the temperature field.