Convective Instabilities in Fully Developed Flows

[+] Author and Article Information
M. Sherman

Department of Geophysics and Astronomy, The RAND Corp., Santa Monica, Calif.

J. Heat Transfer 90(1), 84-86 (Feb 01, 1968) (3 pages) doi:10.1115/1.3597465 History: Received March 23, 1967; Online August 25, 2011


This paper considers the possibility of inducing a convective secondary flow in the fully developed channel flow of a quasi-incompressible (Boussinesq) fluid. Instabilities of this type can only occur when the temperature gradient in the direction of the body force exceeds a certain critical value. This temperature gradient is proportional to the Rayleigh number of the fluid. We find that for channels of arbitrary cross section, the critical Rayleigh number is Rc ≥ 1360 (h/d)4 where h is the arbitrary channel’s maximum dimension in the body force direction and d is the diameter of an equal area circular channel. For two special geometries it is possible to improve the foregoing lower bound estimate to the critical Rayleigh number. In a circular channel Rc ≥ 3450 and in a square channel Rc ≥ 2480.

Copyright © 1968 by ASME
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