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A note on the stability of convection in a vertical slot

Published online by Cambridge University Press:  29 March 2006

A. E. Gill  and
C. C. Kirkham
A. E. Gill
Affiliation:
D.A.M.T.P., University of Cambridge
C. C. Kirkham
Affiliation:
Mathematical Laboratory, University of Cambridge
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Abstract

The study of natural convection in a rectangular cavity whose side walls are maintained at different fixed temperatures can be regarded as one of the classical problems of thermal convection (see Batchelor 1954; Elder 1965 and Gill 1966). One aspect of this problem is the question of stability of the laminar flow solution for given values of the three governing parameters, the Rayleigh number A = γgΔTL3/κν, the aspect ratio h = H/L and the Prandtl number σ = ν/κ. Here H is the height and L the width of the cavity, T is the temperature difference between the two walls and g the acceleration due to gravity. The fluid filling the container has coefficient of expansion γ, thermal diffusivity κ and kinematic viscosity ν. Instead of studying the stability of the exact laminar flow solution, which is not a parallel flow, the stability of the following solution of the governing eauations is examined instead:

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 42 , Issue 1 , 4 June 1970 , pp. 125 - 127
Copyright
© 1970 Cambridge University Press

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References

Batchelor, G. K. 1954 Quart. Appl. Math. 12, 20.
Elder, J. W. 1965 J. Fluid Mech. 23, 7.
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Gill, A. E. 1966 J. Fluid Mech. 26, 51.
Gill, A. E. & Davey, A. 1969 J. Fluid Mech. 35, 77.
Kirkham, C. C. 1969 Dissertation for the Diploma in Computer Science, University of Cambridge.
Rudakov, R. N. 1967 PMM 31, 36.
Vest, C. M. & Arpaci, V. S. 1969 J. Fluid Mech. 36, 1