"Bounds on Laminar Natural Convection from Isothermal Disks and Finite Plates of Arbitrary Shape for all Orientations and Prandtl Numbers"

Abstract: Upper and lower bounds on Nusselt-Rayleigh, Nu - Ra, correlation equations are developed for natural convection heat (mass) transfer from isothermal (isopotential) square plates or circular disks which have one-to-two sides active, facing upward, downward and vertical, with and without adiabatic extensions of negligible or very large extent. The upper bound corresponds to a horizontal plate or disk with one side active facing upward located in a quiescent medium of infinite extent; and the lower bound correponds to a horizontal plate or disk with one side active located in an infinite adiabatic plane in contact with a quiescent medium of semi-infinite extent. The Nu - Ra results for vertical or inclined plates or disks with both sides active lie between the proposed bounds. The bounds, developed for Pr = Sc = 0.71, are extended to include all values of Prandtl or Schmidt numbers. The proposed upper and lower bounds Nu - Ra correlation equations are shown to be in complete agreement with all previously published correlation equations, and the proposed bounds remove the apparent discrepancies between them.

ASME Winter Annual Meeting, New Orleans, Louisiana, Nov.28 - Dec.3, HTD-Vol.264, p93

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