Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-18T22:47:30.061Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermal convection in a vertical circular cylinder

Published online by Cambridge University Press:  20 April 2006

S. Rosenblat
S. Rosenblat
Affiliation:
Department of Mathematics, Illinois Institute of Technology, Chicago, Il. 60616
Get access Rights & Permissions [Opens in a new window]

Abstract

A theoretical investigation is made of the onset of buoyancy-driven convection in a circular cylinder. Amplitude equations are derived for the weakly nonlinear evolution of critical disturbances at moderate values of the radius-to-height ratio. It is shown that the initial form of the convective motion a t Rayleigh numbers slightly above critical is not axisymmetric. Particular attention is paid to the neighbourhoods of points where two disturbances are simultaneously critical according to linear theory; the nonlinear evolution in such neighbourhoods is studied in detail.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 122 , September 1982 , pp. 395 - 410
Copyright
© 1982 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

Charlson, G. S. & Sani, R. L. 1971 Int. J. Heat Mass Transfer 14, 2157.
Charlson, G. S. & Sani, R. L. 1975 J. Fluid Mech. 71, 209.
Eckhaus, W. 1965 Studies in Non-Linear Stability Theory. Springer.
Koschmieder, E. L. 1974 Adv. Chem. Phys. 26, 177.
Liang, S. F., Vidal, A. & Acrivos, A. 1969 J. Fluid Mech. 36, 239.
Mitchell, W. T. & Quinn, J. A. 1965 Thermal correction in a completely confined fluid layer. Preprint no. 11B, Symp. on Selected Papers, Part II, 58th Annual Meeting A.I.Ch.E., Philadelphia.
Palm, E. 1975 A. Rev. Fluid Mech. 7, 39.
Rosenblat, S. 1979 Stud. Appl. Math. 60, 241.
Rosenblat, S., Davis, S. H. & Homsy, G. M. 1982 J. Fluid Mech. 120, 91.