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Title: Boundary-layer analysis of the thermal bar
Authors: Kay, Anthony
Kuiken, H.K.
Merkin, J.H.
Issue Date: 1995
Publisher: © Cambridge University Press
Citation: KAY, A., KUIKEN, H.K. and MERKIN, J.H., 1995. Boundary-layer analysis of the thermal bar. Journal of Fluid Mechanics Digital Archive, 303, pp. 253-278
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.
Description: This article was published in the Journal of Fluid Mechanics [© Cambridge University Press] and is also available at: http://journals.cambridge.org/action/displayAbstract?aid=340146
Version: Published
DOI: 10.1017/S0022112095004265
URI: https://dspace.lboro.ac.uk/2134/4236
ISSN: 0022-1120
Appears in Collections:Published Articles (Maths)

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