Abstract

The problem of natural convection from a uniformly heated vertical plate has long been investigated due to its relevance to many industrial applications. Attempts have been made over the years to develop generalized heat transfer correlations that would cover a large range of Prandtl numbers. Here we introduce, on fundamental grounds, a new dimensionless parameter for the correlation of natural convection induced by a vertical plate subject to a constant wall heat flux. This dimensionless parameter, which depends on the Prandtl number, Pr, and the modified Rayleigh number, Ra*, is used to correlate the heat transfer over the entire Prandtl number domain. The development is based on physical and dimensional arguments and leads to correlations relating the laminar Nusselt number to the new parameter. Comparison with published empirical, numerical, and theoretical results leads to excellent agreement over the Prandtl number domain studied, which spans the range between 0.001 and 1000.

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