A set of analytic formulae are presented for the effective thermal conductivity of either a square or a hexagonal array of parallel tubes which have distinct core, tube and fill conductivities. The formulae are based on a generalization of Rayleigh’s [Phil. Mag. 34(5), 481-502 (1892)] method to include hexagonal (as well as square) arrays, tubes (as well as solid rods), and higher-order terms in the analytic series. The accuracy of the analytic formulae is determined by comparison with essentially exact numerical calculations. The formulae are applied to the problem of an array of dry, spent, nuclear fuel rods.