An Improved Approach to Conductive Boundary Conditions for the Rayleigh-Bénard Instability

[+] Author and Article Information
J. H. Lienhard

Department of Applied Mechanics and Engineering Sciences and Project in Nonlinear Science, University of California at San Diego, La Jolla, CA 92093

J. Heat Transfer 109(2), 378-387 (May 01, 1987) (10 pages) doi:10.1115/1.3248091 History: Received November 05, 1985; Online October 20, 2009


A technique is developed for predicting the stability limit of conductively coupled horizontal fluid layers heated from below and cooled above. The approach presented gives exact solutions of the stability problem and is numerically much simpler than previous multilayer solutions. Critical Rayleigh numbers are obtained for the case of three and four fluid layers separated by equally spaced identical midlayers of various thicknesses and conductivities with isothermal outer walls and for the symmetric two-layer problem with outer walls of finite thermal conductivity. Other configurations are considered briefly.

Copyright © 1987 by ASME
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