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 to approximately 120, Ra equals 1 to approximately 10**3 and radius ratios of the outer to inner sphere r//2/r//1 equals 5 to 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 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 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 forces induced by free convection flow, Rayleigh number and Prandtl number is also presented.