Fundamental correlations for laminar and turbulent free convection from a uniformly heated vertical plate

A dimensionless parameter Pi (Q) is introduced for the correlation of the h eat transfer in natural convection induced by a constant wall heat flux. Th is dimensionless parameter depends on the Prandtl number, Fr, and the modif ied Rayleigh number, Ra*, as Pi (Q) similar to Ra* /(1 + Pr-1). The develop ment of Pi (Q) is based on physical arguments and allows the use of a singl e heat transfer correlation over the entire Prandtl number range. Dimension al arguments in terms of the laminar boundary layer and turbulent microscal e 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. Com parison of these correlations with existing published data shows a good agr eement. (C) 2001 Elsevier Science Ltd. All rights reserved.