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The stability of natural convection in a vertical fluid layer

Published online by Cambridge University Press:  29 March 2006

Jiro Mizushima  and
Kanefusa Gotoh
Jiro Mizushima
Affiliation:
Department of Physics, Faculty of Science, University of Kyoto, Japan
Kanefusa Gotoh
Affiliation:
Research Institute for Mathematical Sciences, University of Kyoto, Japan
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Abstract

The stability of natural convection in fluid between two parallel vertical plates is investigated theoretically. The two plates are maintained at different temperatures and a uniform stable temperature gradient β is present in the vertical direction. The Prandtl number of the fluid is fixed at 7.5. An orthonormalization method is used in numerical integrations of the disturbance equations. It is shown how the critical Grashof number varies with β for both stationary and travelling disturbances. It is found that for β ≤ 7.1 × 10−3 the convection is unstable to stationary disturbances and for β ≥ 7.1 × 10−3 it is unstable to travelling disturbances. The critical Grashof number is given by \[ G_c = \left\{\begin{array}{@{}l@{\quad}c@{\quad}l@{}} 500 & {\rm for} & \beta < 1.0\times 10^{-3},\\ 1.3\times 10^6\beta^3 & {\rm for} &\beta > 4.1\times 10^{-2}, \end{array}\right. \] and even for intermediate values of β the variation of Gc is rather simple but not monotonic.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 73 , Issue 1 , 13 January 1976 , pp. 65 - 75
Copyright
© 1976 Cambridge University Press

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