Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-18T20:43:39.708Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite amplitude axisymmetric thermoconvective flows in a bounded cylindrical layer of fluid

Published online by Cambridge University Press:  29 March 2006

G. S. Charlson  and
R. L. Sani
G. S. Charlson
Affiliation:
Department of Chemical Engineering, University of Illinois, Urbana
R. L. Sani
Affiliation:
Department of Chemical Engineering, University of Illinois, Urbana
Get access Rights & Permissions [Opens in a new window]

Abstract

Finite amplitude axisymmetric thermoconvective flows in a bounded cylindrical layer of fluid heated from beneath were calculated using Galerkin's method. Both systems with insulated and with conducting lateral boundaries were investigated for radius-to-depth ratios of 1, 2·25, 2·55 and 2·66. Flows bounded by a conducting lateral boundary were found to be unstable for Rayleigh numbers greater than 1·1 times the critical value. The cell size was found to be an increasing function of the Rayleigh number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 71 , Issue 2 , 23 September 1975 , pp. 209 - 229
Copyright
© 1975 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

Broyden, C. G. 1965 Math. Comp. 19, 577.
Busse, F. H. 1972 J. Fluid Mech. 52, 97.
Charlson, G. S. & Sani, R. L. 1970 Int. J. Heat Mass Transfer, 13, 1479.
Charlson, G. S. & Sani, R. L. 1971 Int. J. Heat Mass Transfer, 14, 2157.
Davis, S. H. 1968 J. Fluid Mech. 32, 619.
Finlayson, B. A. 1972 The Method of Weighted Residuals and Variational Principles. Academic.
Gershuni, G. Z., Zhukovitskii, E. M. & Tarunin, E. L. 1966 Mekh. Zh. i Gaza, 1, 93.
Goldstein, R. J. 1964 Chem. Engng Sci. 19, 997.
Hoard, C. Q., Robertson, C. R. & Acrivos, A. 1970 Int. J. Heat Mass Transfer, 13, 849.
Joseph, D. D. 1971 J. Fluid Mech. 47, 257.
Joseph, D. D. & Shir, C. C. 1966 J. Fluid Mech. 26, 755.
Koschmieder, E. L. 1966 Beitr. Phys. Atmos. 39, 1.
Koschmieder, E. L. 1967 Beitr. Phys. Atmos. 40, 216.
Koschmieder, E. L. 1969 J. Fluid Mech. 35, 527.
Koschmieder, E. L. 1974 Adv. in Chem. Phys. 26, 177.
Krishnamurti, R. 1970 J. Fluid Mech. 42, 295.
Liang, S. F., Vidal, A. & Acrivos, A. 1969 J. Fluid Mech. 36, 239.
Mitchell, W. T. & Quinn, J. A. 1966 A.I.Ch.E. J. 12, 1116.
Rossby, H. T. 1969 J. Fluid Mech. 36, 309.
Sani, R. L. 1964 J. Fluid Mech. 20, 315.
Sani, R. L. 1967 Mathematica Japonicae, 12, 81.
Schlüter, A., Lortz, D. & Busse, F. 1965 J. Fluid Mech. 23, 129.
Silveston, P. K. 1963 Phys. Fluids, 6, 313.
Somerscales, E. F. C. & Dougherty, T. S. 1970 J. Fluid Mech. 42, 755.
Stakgold, I. 1971 SIAM Rev. 13, 289.
Tarunin, E. L. 1967 Mekh. Zh. i Gaza, 2, 72.
Verhoeven, J. D. 1969 Phys. Fluids, 12, 1733.
Willis, G. E., Deardorff, J. W. & Somerville, R. C. J. 1972 J. Fluid Mech. 54, 351.