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The long-wave instability in heated or cooled inclined liquid layers

Published online by Cambridge University Press:  26 April 2006

Marc K. Smith
Marc K. Smith
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
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Abstract

A thin liquid layer flowing down an inclined plane exhibits a long-wave interfacial instability at a critical value of the Reynolds number. Past work on this problem has shown that heating or cooling the layer does not significantly change the characteristics of this instability. We show that this is not correct when the Prandtl number of the liquid is large and that both heating and cooling from below can destabilize the layer depending on the interfacial heat-transfer conditions. The mechanism for this unstable behaviour involves the direct expansion of the liquid as it experiences a temperature perturbation produced by the deformation of the interface. When the layer is heated from below, this additional effect changes the critical angle at which longitudinal, buoyancy-driven rolls are preferred relative to the long-wave interfacial instability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 219 , October 1990 , pp. 337 - 360
Copyright
© 1990 Cambridge University Press

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References

Bankoff, S. G.: 1971 Intl J. Heat Mass Transfer 14, 377.
Benguria, R. D. & Depassier, M. C., 1987 Phys. Fluids 30, 1678.
Benjamin, T. B.: 1957 J. Fluid Mech. 2, 554.
Chandrasekhar, S.: 1961 Hydrodynamic and Hydromagnetic Stability. Dover.
Debruin, G. J.: 1974 J. Engng Maths 8, 259.
Floryan, J. M., Davis, S. H. & Kelly, R. E., 1987 Phys. Fluids 30, 983.
Goussis, D. & Kelly, R. E., 1985 Phys, Fluids 28, 3207.
Kelly, R. E. & Goussis, D., 1982 Heat Transfer 1982 – Proc. 7th Intl Heat Transfer Conf., vol. 5, p. 319. Hemisphere.
Kelly, R. E., Goussis, D. A., Lin, S. P. & Hsu, F. K., 1989 Phys. Fluids A 1, 819.
Kirchgáussner, K.: 1962 Ing. Arch. 31, 115.
Lin, S. P.: 1975 Lett. Heat Mass Transfer 2, 361.
Marschall, E. & Lee, C. Y., 1973 Intl J. Heat Mass Transfer 16, 41.
Renardy, Y.: 1986 Phys. Fluids 29, 356.
Roca, R.: 1966 J. Méc. 5, 117.
Scott, M. R. & Watts, H. A., 1975 Rep. SAND75-0198, Sandia Labs, Albuquerque, NM.
Scott, M. R. & Watts, H. A., 1977 SIAM J. Numer. Anal. 14, 40.
Smith, M. K.: 1989 Phys. Fluids A 1, 494.
Smith, M. K.: 1990 The mechanism for the long-wave instability in thin liquid films. J. Fluid Mech. (in press).Google Scholar
Sreenivasan, S. & Lin, S. P., 1978 Intl J. Heat Mass Transfer 21, 1517.
ünsal, M. & Thomas, W. C. 1978 Trans. ASME C: J. Heat Transfer 100, 629.
Yih, C.-S.: 1963 Phys. Fluids 6, 321.
Yih, C.-S.: 1986 Phys. Fluids 29, 1769.