Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-18T14:41:37.728Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bénard, H. 1901 Ann. Chem. Phys. 23, 62.
Jenssen, O. 1963 Acta Polytechnica Scandinavica Ph. 24.
Koschmieder, E. L. 1966 Beitr. Phys. Atmos. 39, 1.
Malkus, W. V. R. & Veronis, G. 1958 J. Fluid Mech. 4, 225.
Palm, E. 1960 J. Fluid Mech. 8, 183.
Palm, E. & Oiann, H. 1964 J. Fluid Mech. 19, 353.
Pellew, A. & Southwell, R. V. 1940 Proc. Roy. Soc. A 176, 312.
Reid, W. H. & Harris, D. L. 1958 Phys. Fluids, 1, 102.
Schlüter, A., Lortz, D. & Busse, F. 1965 J. Fluid Mech. 23, 129.
Segel, L. A. 1965 J. Fluid Mech. 21, 359.
Segel, L. A. & Stuart, J. T. 1962 J. Fluid Mech. 13, 286.
Silveston, P. L. 1958 Forsch. Ing. 24, 29–32 and 59–69.