TRANSIENT LAMINAR NATURAL CONVECTION HEAT TRANSFER FROM ISOTHERMAL SPHERES

Abstract

Transient natural convection over a sphere has been studied numerically for 10¹ < Gr < 10⁸ and Pr = 0,72. Shortly after the sphere temperature is raised, a vortex of small radial extent appears in the wake of the sphere for very high Gr, which grows radially until the plume formed on the top of the sphere is fully developed. The evolving plume has a mushroom-shaped cap for moderate and high Gr, and in agreement with experiment, presents a temperature peak on the cap's base, an off-axial peak in the middle of the cap, and an axial peak near the cap's leading edge. The mechanism driving the onset of significant convection has been clearly delineated, and the relevant critical Rayleigh numbers have been obtained. The temperature gradient at θ = 90^° seems to lead the onset of convection.

Notes

Address correspondence to Dr. G. Gogos, Department of Mechanical Engineering, University of Nebraska-Lincoln, 255 Walter Scott Engineering Center, P.O. Box 880656, Lincoln, NE 68588-0656, USA.