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Title

Stability of mixed-convection flow in a tall vertical channel under non-Boussinesq conditions

Author(s)

Suslov, Sergey A.;  Paolucci, Samuel

Abstract

We have examined the linear stability of the fully developed mixed-convection flow in a differentially heated tall vertical channel under non-Boussinesq conditions. The three-dimensional analysis of the stability problem was reduced to an equivalent two-dimensional one by the use of Squire's transformation. The resulting eigenvalue problem was solved using an integral Chebyshev pseudo-spectral method. Although Squire's theorem cannot be proved analytically, two-dimensional disturbances are found to be the most unstable in all cases. The influence of the non-Boussinesq effects on the stability was studied. We have investigated the dependence of the critical Grashof and Reynolds numbers on the temperature difference. The results show that four different modes of instability are possible, two of which are new and due entirely to non-Boussinesq effects.

Publication type

Journal article

Source

Journal of Fluid Mechanics, Vol. 302 (Nov 1995), pp. 91-115

Publication year

1995

FOR Code(s)

0203 Classical Physics

Keyword(s)

Channel flow;  Chebyshev approximation;  Convection;  Eigenfunctions;  Eigenvalues;  Flow stability;  Heat convection;  Integral Chebyshev pseudo spectral method;  Integral equations;  Mathematical transformations;  Mixed-convection flow;  Modes of instability;  Non-Boussinesq conditions;  Numerical analysis;  Reynolds number;  Squire transformation;  Stability;  Temperature;  Three dimensional;  Two dimensional

Publisher

Cambridge University Press

ISSN

0022-1120

Publisher URL

http://dx.doi.org/10.1017/S0022112095004022

Copyright

Copyright © 1995 Cambridge University Press. Published version of the paper reproduced here with the kind permission of the publisher.

Full text

Peer reviewed