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

A dimensionless parameter ΠQ 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, Pr, and the modified Rayleigh number, Ra∗, as ΠQ∼Ra∗/(1+Pr−1). The development of ΠQ 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∼ΠQ1/5 and Nu∼ΠQ1/4 dependence for the laminar and turbulent heat transfer, respectively. Comparison of these correlations with existing published data shows a good agreement.