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Heat transfer at high Péclet number from a small sphere freely rotating in a simple shear field

Published online by Cambridge University Press:  29 March 2006

Andreas Acrivos
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University
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Abstract

The problem of heat transfer at high Péclet number Pe from a sphere freely rotating in a simple shear field is considered theoretically for the case of small shear Reynolds numbers. It is shown that the present problem is in many respects similar to that of heat transfer past a freely rotating cylinder which was recently solved by Frankel & Acrivos (1968). By taking advantage of the close analogy between these two problems, an approximate method of solution is developed according to which the asymptotic Nusselt number for Pe → ∞ is 9, i.e. 4½ times its value for pure conduction. As in the corresponding case of the cylinder, the fact that the asymptotic Nusselt number is independent of Pe results from the presence of a region of closed streamlines which completely surrounds the rotating sphere.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 46 , Issue 2 , 29 March 1971 , pp. 233 - 240
Copyright
© 1971 Cambridge University Press

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References

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