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Stability of the developing laminar flow in a parallel-plate channel

Published online by Cambridge University Press:  28 March 2006

T. S. Chen  and
E. M. Sparrow
T. S. Chen
Affiliation:
University of Minnesota, Minneapolis, Minnesota Present address: Department of Mechanical Engineering, University of Missouri at Rolla, Rolla, Missouri.
E. M. Sparrow
Affiliation:
University of Minnesota, Minneapolis, Minnesota
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Abstract

The hydrodynamic stability of the developing laminar flow in the entrance region of a parallel-plate channel is investigated using the theory of small disturbances. The stability of the fully developed flow is also re-examined. A wide range of analytical (i.e. asymptotic) and numerical methods are employed in the stability investigation. Among the asymptotic methods, each of three viscous solutions (singular, regular and composite) is used along with the inviscid solution to provide critical Reynolds numbers and complete neutral stability curves. Two numerical methods, finite differences and stepwise integration, are applied to calculate critical Reynolds numbers. The basic flow in the development region is treated from two stand-points: as a channel velocity profile and as a boundary-layer velocity profile. Extensive comparisons among the various methods and flow models disclose their various strengths and ranges of applicability. As a general result, it is found that the critical Reynolds number decreases monotonically with increasing distance from the channel entrance, approaching the fully developed value as a limit.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 30 , Issue 2 , 9 November 1967 , pp. 209 - 224
Copyright
© 1967 Cambridge University Press

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References

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