Lower Bounds to the Critical Rayleigh Number in Completely Confined Regions

Published in: Journal of Applied Mechanics, v. 34, no. 2, June 1967, p. 308-312

Posted on RAND.org on December 31, 1966

by Michael Sherman, Simon Ostrach

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A method is presented for estimating lower bounds to the minimum Rayleigh number that will induce a state of convective motion in a quasi-incompressible (Boussinesq) fluid where the temperature gradient is in the direction of the body force. The fluid is completely confined by fixed-temperature, rigid bounding walls. For any arbitrary region, the critical Rayleigh number is greater than 1558(h/D)4 where h is the maximum dimension of the given region in the direction of the body force and D is the diameter of an equal volume sphere. In certain simple geometrical configurations, improved lower-bound estimates are calculated.

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