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Rayleigh instability of a thermal boundary layer in flow through a porous medium

Published online by Cambridge University Press:  28 March 2006

R. A. Wooding
R. A. Wooding
Affiliation:
Emmanuel College, Cambridge
Present address: D.S.I.R., Box 8018, Wellington, N.Z.
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Abstract

It is supposed that a heated liquid is rising very slowly through a semi-infinite porous medium towards the permeable horizontal surface, where it mixes with a layer of cool overlying fluid. In the steady state a thermal boundary layer of exponential form exists in the medium. It is shown that the layer is stable provided that the Rayleigh number for the system does not exceed a critical positive value, and that the wave-number of the critical neutral disturbance is finite. The stability properties of the layer are explained qualitatively from physical considerations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 9 , Issue 2 , October 1960 , pp. 183 - 192
Copyright
© 1960 Cambridge University Press

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References

Chandrasekhar, S. 1954 Mathematika, 1, 5.
Lapwood, E. R. 1948 Proc. Camb. Phil. Soc. 44, 508.
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. New York: McGraw-Hill.
Nicholson, J. W. 1917 Proc. Roy. Soc. A, 93, 506.
Pellew, A. & Southwell, R. V. 1940 Proc. Roy. Soc. A, 176, 312.
Saffman, P. G. & Taylor, Sir Geoffrey 1958 Proc. Roy. Soc. A, 245, 312.
Wooding, R. A. 1959 Proc. Roy. Soc. A, 252, 120.