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Boundary-layer analysis of the thermal bar

Published online by Cambridge University Press:  26 April 2006

Anthony Kay ,
H. K. Kuiken  and
J. H. Merkin
Anthony Kay
Affiliation:
Loughborough University of Technology, Loughborough, Leicestershire, LE11 3TU, UK
H. K. Kuiken
Affiliation:
University of Leeds, Leeds, LS2 9JT, UK
J. H. Merkin
Affiliation:
University of Leeds, Leeds, LS2 9JT, UK
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Abstract

The thermal bar, a descending plane plume of fluid at the temperature of maximum density (3.98° C in water), is analysed as a laminar free-convection boundary layer, following the example of Kuiken & Rotem (1971) for the plume above a line source of heat. Numerical integration of the similarity form of the boundary-layer equations yields values of the vertical velocity and temperature gradient on the centre line and the horizontal velocity induced outside the thermal bar as functions of Prandtl number σ. The asymptotic behaviour of these parameters for both large and small σ is also obtained; in these cases, the thermal bar has a two-layer structure, and the method of matched asymptotic expansions is used. For the intermediate case σ= 1, an analytical calculation using approximate velocity and temperature profiles in the integrated boundary-layer equations yields good agreement with the numerical results. The applicability of the results to naturally occurring thermal bars (e. g. in lakes) is limited, but the laminar-flow analysis is likely to relate more closely to the phenomenon on a laboratory scale.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 303 , 25 November 1995 , pp. 253 - 278
Copyright
© 1995 Cambridge University Press

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