This is the concluding portion of a four-part numerical investigation. The first was limited to the prediction of the velocity field, a prerequisite for the prediction of convection. The second concerned the prediction of the Nusselt number for uniform heating on the inner wall only, and the third the prediction of the Nusselt numbers for most of the other thermal boundary conditions that occur in practice. Herein, generalized predictive equations are presented for all of these conditions. The number of such equations and coefficients is minimized by the use of superposition and generalized expressions for the dependence on Re and Pr, and to some extent on the aspect ratio. (c) 2005 Elsevier Ltd. All rights reserved.