Effective conductivity for densely packed highly conducting cylinders

We study the effective heat conductivity λ₃ of a periodic square array of nearly touching cylinders of conductivity h, embedded in a matrix material of conductivity 1. We construct a sequence of two-point Padé approximants for the effective conductivity. As the basis for the construction we use the coefficients of the expansions of λ_e at h=1 and h=∞. The two-point Padé approximants form a sequence of rapidly converging upper and lower bounds on the effective conductivity.