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Surface tension and buoyancy effects in cellular convection

Published online by Cambridge University Press:  28 March 2006

D. A. Nield
D. A. Nield
Affiliation:
Mathematics Department, University of Auckland, New Zealand
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Abstract

The cells observed by Bénard (1901) when a horizontal layer of fluid is heated from below were explained by Rayleigh (1916) in terms of buoyancy, and by Pearson (1958) in terms of surface tension. These rival theories are now combined. Linear perturbation techniques are used to derive a sixth-order differential equation subject to six boundary conditions. A Fourier series method has been used to obtain the eigenvalue equation for the case where the lower boundary surface is a rigid conductor and the upper free surface is subject to a general thermal condition. Numerical results are presented. It was found that the two agencies causing instability reinforce one another and are tightly coupled. Cells formed by surface tension are approximately the same size as those formed by buoyancy. Bénard's experiments are briefly discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 19 , Issue 3 , July 1964 , pp. 341 - 352
Copyright
© 1964 Cambridge University Press

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