A finite-element representation and the FIDAP(TM) code were used to solve the equations of conservation for mass, momentum and energy for fully developed angular flow and fully developed convection in the annulus between two concentric cylinders. Local Nusselt numbers were determined for a complete range of heat flux density ratios, both positive and negative, on the inner and; outer surfaces, for Dean numbers up to 21/2 times the critical value for the onset of vortical motion. The Nusselt numbers are found to depend strongly on the heat flux : density ratio as well as on the Dean number. The applicability of the results to double-spiral heat exchangers is discussed.