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Buoyancy-driven convection in cylindrical geometries

Published online by Cambridge University Press:  29 March 2006

S. F. Liang ,
A. Vidal  and
Andreas Acrivos
S. F. Liang
Affiliation:
Department of Chemical Engineering, Stanford University, California Present address: Chicago Bridge and Iron, Plainfield, Illinois.
A. Vidal
Affiliation:
Department of Chemical Engineering, Stanford University, California
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University, California
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Abstract

Numerical solutions to the Boussinesq equations containing a temperature-dependent viscosity are presented for the case of axisymmetric buoyancy-driven convective flow in a cylindrical cell. Two solutions, one with upflow and the other with downflow at the centre of the cell, were found for each set of boundary conditions that were considered. The existence of these two steady-state régimes was verified experimentally for the case of a cylindrical cell having rigid insulating lateral boundaries and isothermal top and bottom planes.

Using a perturbation expansion it is also shown that only one of these solutions remains stable in the subcritical régime. This, however, seems to be confined to a very narrow range of Rayleigh numbers, beyond which, according to all the evidence presently at hand, both solutions are equally stable for those values of the Rayleigh and Prandtl numbers for which axisymmetric motions occur.

Finally, certain fundamental differences between the problem considered here and that of thermal convection in a layer of infinite horizontal extent are briefly discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 36 , Issue 2 , 14 April 1969 , pp. 239 - 258
Copyright
© 1969 Cambridge University Press

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