A dimensionless parameter Pi (Q) is introduced for the correlation of the heat transfer in natural convection induced by a constant wall heat flux. This dimensionless parameter depends on the Prandtl number, Fr, and the modified Rayleigh number, Ra*, as Pi (Q) similar to Ra* /(1 + Pr-1). The development of Pi (Q) is based on physical arguments and allows the use of a single heat transfer correlation over the entire Prandtl number range. Dimensional arguments in terms of the laminar boundary layer and turbulent microscale concepts lead to a Nu similar to Pi (1/5)(Q) and Nu similar to Pi (1/4)(Q) dependence for the laminar and turbulent heat transfer, respectively. Comparison of these correlations with existing published data shows a good agreement. (C) 2001 Elsevier Science Ltd. All rights reserved.