A transcendental approximation for natural convection at small prandtl numbers

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Abstract
An improved method of approximation for natural convection at small Prandtl numbers is described. It involves simple transcendental functions for profile representation. The method utilizes a physically significant model of the velocity distribution in which regions of the thermal boundary layer and viscous boundary layer are distinguished. The shape of the velocity profile is allowed to vary with Prandtl number. The method is checked against known exact results for natural convection on a vertical flat plate and is used to obtain results for a horizontal cylinder.