Lower Bounds to the Critical Rayleigh Number in Completely Confined Regions

[+] Author and Article Information
M. Sherman

Aero-Astronautics Department, The RAND Corporation, Santa Monica, Calif.

S. Ostrach

Case Institute of Technology, Cleveland, Ohio

J. Appl. Mech 34(2), 308-312 (Jun 01, 1967) (5 pages) doi:10.1115/1.3607683 History: Received May 24, 1966; Revised December 12, 1966; Online September 14, 2011


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.

Copyright © 1967 by ASME
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