Numerically predicted values of the Nusselt number are presented for annuli with uniform heating, of the outer surface only, uniform equal heating of both surfaces, and uniform heating of one surface and equal cooling of the other. Results are also presented for a parallel-plate channel with isothermal heating of one wall and equal isothermal heating of both walls. The predictions are based on semi-theoretical expressions for the dimensionless turbulent shear stress but are insensitive to the limited empiricism within the model for convection. The predicted values of Nu are in good agreement with the somewhat limited experimental data for these less frequently encountered thermal boundary conditions. The results encompass all values of the Prandtl number and all values of the Reynolds number of practical concern. These values, together with those in a preceding paper for uniform heating of the inner wall only, and together with the generalizations described in a succeeding paper, permit the accurate prediction of the Nusselt number from theoretically based algebraic expressions for essentially all of the thermal conditions that result in fully developed convection. (C) 2004 Elsevier Ltd. All rights reserved.