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Asymptotic solution for plume at very large and small Prandtl numbers

Published online by Cambridge University Press:  29 March 2006

H. K. Kuiken  and
Zeëv Rotem
H. K. Kuiken
Affiliation:
Department of Mechanical Engineering, University of British Columbia, Vancouver, Canada Present address: Philips Research Laboratories, N. V. Philips’ Gloeilampenfabrieker, Eindhoven, The Netherlands.
Zeëv Rotem
Affiliation:
Department of Mechanical Engineering, University of British Columbia, Vancouver, Canada
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Abstract

The investigation of laminar free convective plumes in an otherwise stationary environment has formed the basis of numerous investigations, initiated by Zeldovich (1937). For the non-rotating environment alone the authors have been able to locate twenty-nine papers: many of these repeat work previously undertaken. There are, however, two cases of some technological significance which have so far not been considered: (i) the plume in an otherwise quiescent environment for a fluid of very large Prandtl number, of importance in the heating of reservoirs of viscous fluid such as fuel oil; and (ii) the case of vanishingly small Prandtl number, of application to liquid metal-cooled nuclear reactors. Both of these cases have some theoretical interest, as will be shown. Their analysis leads to singular asymptotic perturbations and hence to matched-expansions techniques.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 45 , Issue 3 , 15 February 1971 , pp. 585 - 600
Copyright
© 1971 Cambridge University Press

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