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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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