Effect of Wall Conduction on the Stability of a Fluid in a Rectangular Region Heated from Below

[+] Author and Article Information
Ivan Catton

School of Engineering and Applied Science, University of California, Los Angeles, Calif.

J. Heat Transfer 94(4), 446-452 (Nov 01, 1972) (7 pages) doi:10.1115/1.3449966 History: Received February 10, 1971; Revised September 29, 1971; Online August 11, 2010


The initiation of natural convection in a fluid confined above and below by rigid, perfectly conducting surfaces and laterally by vertical walls of arbitrary thermal conductivity which form a rectangle is examined. The linearized perturbation equations are obtained in the usual manner and reduced to an eigenvalue problem. The Rayleigh number is the eigenvalue and is a function of the lateral-wall conductance and horizontal plan form (aspect ratios). The problem associated with satisfying the no-slip boundary conditions on all surfaces is surmounted by using the Galerkin method. Results are compared with experiments and shown to be in good agreement.

Copyright © 1972 by ASME
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