1999•Proceedings of the Royal Society A Mathematical Physical and Engineering SciencesRequires access
Free-surface flow in a shallow laterally heated cavity
R. R. Poles
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Abstract
The steady two-dimensional free–surface flow in a shallow laterally heated cavity with adiabatic horizontal boundaries is discussed in this paper. The regions close to the vertical walls where the flow is turned through 180° are of particular interest and allow a first–order correction to the parallel core flow in the main part of the cavity to be determined. The end–region solutions decay into the parallel flow in the core of the cavity. The effect of the Rayleigh and Prandtl numbers on the scale of this decay is investigated. An asymptotic expansion of the end–region solution is presented to give an analytic description of the flow in the whole cavity in the limit of small Rayleigh number and the results are compared with full numerical solutions.