Heat Transfer by Natural Convection between Vertically Eccentric Spheres

Abstract

Natural convection to a cooled sphere from an enclosed, vertically eccentric, heated sphere is described in this paper. Water and two silicone oils were utilized in conjunction with four different combinations of sphere sizes and six eccentricities for each of these combinations. Both heat-transfer rates and temperature profiles are presented. The effect of a negative eccentricity (inner sphere below center of outer sphere) on the temperature distribution was an enhancement of the convective motion, while a positive eccentricity tended to stabilize the flow field and promote conduction rather than convection. As for concentric spheres, a multicellular flow pattern was postulated to explain the thermal field observed for the largest inner sphere utilized. In all cases the heat-transfer rates were increased by moving the inner sphere to an eccentric position, and the utilization of a conformal-mapping technique to transform the eccentric spheres to concentric spheres enabled the application of existing empirical correlations for concentric spheres to the eccentric-sphere data. It is significant to note that this technique yields a single correlation equation, in terms of only keff/k and a modified Rayleigh number, which is valid for an extremely wide range of diameter ratios, eccentricities, Rayleigh numbers, and Prandtl numbers.