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.

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“…Therefore, at the end of the gas generator's propellant burn (at about 22 s after inflation), the constants were forced in an exponentially decaying fashion to the more nominal values of 0.228 and 0.226, for C and m, respectively. These values are for gases or liquids within a spherical annulus and were reported by Weber et al [5].…”

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“…Correlations of the experimental and numerical data presented in the literature by Bishop et al 2 , Scanlan et al 4 , Weber et al 5 , Astill et al 6 and Wright and Douglass 10 are valid over a limited range of Rayleigh number, typically corresponding to boundary layer convection. The only model in the literature for the concentric spheres that is valid for the full range of Rayleigh numbers is presented by Raithby and Hollands 16 in terms of the dimensionless effective conductivity:…”

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