Abstract
The flow near the end of a shallow laterally heated cavity enters a nonlinear convective regime when the Rayleigh number R, based on cavity height, is of the same order of magnitude as the aspect ratio L (length/height). In the case of thermally insulated horizontal boundaries the end-region solution determines a correction to the flow and temperature fields throughout the cavity. Numerical solution are obtained for the end-region flow for several different Prandtl numbers and for a range of values of the scaled Rayleigh number R/L using a Dufort-Frankel multigrid method. The results are compared with asymptotic predictions of the motion in the conductive limit R/L → 0 and the boundary-layer limit R/L → ∞.
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Wang, P., Daniels, P.G. Numerical solutions for the flow near the end of a shallow laterally heated cavity. J Eng Math 28, 211–226 (1994). https://doi.org/10.1007/BF00058437
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DOI: https://doi.org/10.1007/BF00058437