NUMERICAL ANALYSIS OF FREE CONVECTION AROUND AN ISOTHERMAL SPHERE (EFFECTS OF SPACE AND PRANDTL NUMBER).

Numerical solutions of full Navier-Stokes and energy equations for two-dimensional laminar free convection between two concentric spheres are obtained for Pr equals 0. 7 approximately 120, Ra equals 1 approximately 10**3 and radius ratios of the outer to inner sphere r//2/r//1 equals 5 approximately 60. With decrease of r//2/r//1, the heat transfer coefficient for the inner sphere decreases first due to suppression of convective flow and then increases due to predominance of conduction heat transfer. The heat transfer coefficient at r//2/r//1 greater than equivalent to 60 can be regarded as that for a single sphere immersed in an infinite medium for Pr equals 0. 7 and Ra equals 1. The higher the Rayleigh number, the smaller is the radius ratio at which the Nusselt number can be regarded as that for a single sphere. An accurate correlation equation for the Nusselt number is proposed. A correlation equation for the relation among drag force induced by free convection flow, Rayleigh number and Prandtl number is also presented.