A Numerical Analysis of Free Convection around an Isothermal Sphere : Effects of Space and Prandtl Number

Abstract

Numerical solutions of full Navier-Stokes and energy equations for two dimensional laminar free convection between two concentric spheres are obtained for Pr=0.7∼120, Ra=1∼10³ and radius ratios of outer to inner spheres r₂/r₁=560. With decrease of r₂/r₁, the heat transfer coefficient for the inner sp. here decreases first due to suppression of convective flow and then increases as the conduction heat transfer becomes predominant. For Pr=0.7 and Ra=1, the heat transfer coefficient at r₂/r₁≥60 can be regarded as that for a single sphere immersed in an infinite medium. The higher the Rayleigh number, the smaller the radius ratio at which the Nusselt number can be regarded as that for a single sp. here. An accurate expression of the Nusselt number is proposed. An expression for the relation among drag force induced by free convection flow, Rayleigh number and Prandtl number is also presented.