Natural convection in a differentially heated corner region
This is a fundamental study of the phenomenon of natural convection in the region formed by a vertical warm wall rising above a cold horizontal wall, or in the region between a cold vertical wall extending downward from a warm horizontal surface. The study consists of scale analysis, numerical simulations, and an asymptotic solution of the low Rayleigh number limit. The scale analysis predicts the persistence of a single cell in the corner region, regardless of Rayleigh number. The cell migrates toward the corner as the Rayleigh number Ra H increases: the flow rate and the net heat transfer rate vary as Ra H1/7. The scale analysis is verified qualitatively and quantitatively by means of numerical experiments in the range Ra H = 10 3-10 7, Pr = 0.7-7, H/L = 1-4, where Pr is the Prandtl number and H/L is the height/length ratio of the corner region. Additional numerical simulations are presented for cases where one or both walls have uniform heat flux; in these cases, the heat transfer rate shows nearly the same behavior as when the corner walls are both isothermal. The asymptotic solution for the Ra H→0 limit shows that the flow field is relatively insensitive to whether the wall temperature varies continuously or discontinuously through the corner point. © 1985 American Institute of Physics.
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