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On the occurrence of cellular motion in Bénard convection

Published online by Cambridge University Press:  28 March 2006

E. Palm ,
T. Ellingsen  and
B. Gjevik
E. Palm
Affiliation:
Department of Mechanics, University of Oslo
T. Ellingsen
Affiliation:
Department of Mechanics, University of Oslo
B. Gjevik
Affiliation:
Department of Mechanics, University of Oslo
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Abstract

The interval of Rayleigh numbers in Bénard convection corresponding to cellular motion is determined in the case of free-free boundaries, rigid-free boundaries and rigid-rigid boundaries, taking into account the variation of the kinematic viscosity with temperature. Neglecting the effect of surface tension, it is shown that this interval is largest for the rigid-rigid case. The most important feature from the obtained formula (6.1) is, however, that the interval is extremely dependent on the depth of the fluid layer. To obtain a cellular pattern it is therefore necessary to have very small fluid depths. For example, with Silicone oil and a fluid depth of 7 mm, cellular motion will, according to the theory, be observed for Rayleigh numbers larger than the critical value and less than 1·07 times the critical value. For a fluid depth of 5 mm, however, the formula (6.1) gives that cellular motion will be observed for Rayleigh numbers up to 1·54 times the critical value.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 30 , Issue 4 , 22 December 1967 , pp. 651 - 661
Copyright
© 1967 Cambridge University Press

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References

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