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Title of Journal: Heat Mass Transfer

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Abbravation: Heat and Mass Transfer

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Springer-Verlag

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DOI

10.1016/0005-2736(88)90134-4

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1432-1181

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Numerical study of transient laminar natural conve

Authors: Kanichi Saito Vasudevan Raghavan George Gogos
Publish Date: 2006/08/23
Volume: 43, Issue: 9, Pages: 923-
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Abstract

Transient laminar natural convection over a sphere which is subjected to a constant heat flux has been studied numerically for high Grashof numbers 105 ≤ Gr ≤ 109 and a wide range of Prandtl numbers Pr = 002 07 7 and 100 A plume with a mushroomshaped cap forms above the sphere and drifts upward continuously with time The size and the level of temperature of the transient cap and plume stem decrease with increasing Gr and Pr Flow separation and an associated vortex may appear in the wake of the sphere depending on the magnitude of Gr and Pr A recirculation vortex which appears and grows until “steady state” is attained was found only for the very high Grashof numbers 105 ≤ Gr ≤ 109 and the lowest Prandtl number considered Pr = 002 The appearance and subsequent disappearance of a vortex was observed for Gr  =  109 and Pr = 07 Over the lower hemisphere the thickness of both the hydrodynamic δH and the thermal δT boundary layers remain nearly constant and the sphere surface is nearly isothermal The surface temperature presents a local maximum in the wake of the sphere whenever a vortex is established in the wake of the sphere The surface pressure recovery in the wake of the sphere increases with decreasing Pr and with increasing Gr For very small Pr unlike forced convection the ratio δT/δH remains close to unity The results are in good agreement with experimental data and in excellent agreement with numerical results available in the literature A correlation has also been presented for the overall Nusselt number as a function of Gr and Pr

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