Convection in rectangular cavities with differentially heated end walls

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Abstract
This paper describes an experimental study of free convection in an enclosed rectangular cavity, the end walls of which are maintained at uniform but different temperatures. The experiments are carried out for a variety of Rayleigh numbers, R = αgΔTh4/κνl, and aspect ratios, L = l/h, for fluids with Prandtl number σ ≥ 10. For R ∼ O(103) it is shown that the basic structure of the flow field is a single two-dimensional cell for 0·25 ≤ L ≤ 9. When R > O(104) the boundary layers on the vertical walls control the flow field, but the basic overall structure remains unicellular. At greater values of R secondary vortices appear for all L ≥ 0·5. As R increases the intensity and then the number of these vortices increases. Measurements of the end-wall boundary-layer profiles at different values of R and L confirm Gill's boundary-layer analysis. The effects of variations of viscosity with temperature are discussed in the context of the observed boundary-layer profiles.Core shear profiles and mass flux measurements are also reported. For L = 1 the observed shear profiles are in good agreement with numerical solutions of the Boussinesq equations. However, when L > 1 the observations suggest that the horizontal boundary layers have a significant effect on the core flow field. The stream function is demonstrated to be L-dependent in the boundary-layer regime, where variations due to R are second order. Similarities between the results of the present work and earlier observations by Elder and by Seki, Fukusaka & Inaba for tall slender cavities (L [Lt ] 1) are discussed.

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