The Effect of Wall Conduction on the Stability of a Fluid in a Right Circular Cylinder Heated From Below

[+] Author and Article Information
J. C. Buell, I. Catton

Nuclear Energy Laboratory, School of Engineering and Applied Sciences, University of California, Los Angeles, Calif. 90024

J. Heat Transfer 105(2), 255-260 (May 01, 1983) (6 pages) doi:10.1115/1.3245571 History: Received December 01, 1980; Online October 20, 2009


The onset of natural convection in a cylindrical volume of fluid bounded above and below by rigid, perfectly conducting surfaces and laterally by a wall of arbitrary thermal conductivity is examined. The critical Rayleigh number (dimensionless temperature difference) is determined as a function of aspect (radius to height) ratio and wall conductivity. The first three asymmetric modes as well as the axisymmetric mode are considered. Two sets of stream functions are employed to represent a velocity field that satisfies the no-slip boundary condition on all surfaces and conservation of mass everywhere. The Galerkin method is then used to reduce the linearized perturbation equations to an eigenvalue problem. The results for perfectly insulating and conducting walls are compared with the work of Charlson and Sani[9].

Copyright © 1983 by ASME
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