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Bifurcation phenomena and cellular-pattern evolution in mixed-convection heat transfer

Published online by Cambridge University Press:  21 April 2006

L. Fung ,
K. Nandakumar  and
J. H. Masliyah
L. Fung
Affiliation:
Department of Chemical Engineering, University of Alberta, Edmonton, Alberta, T6G 2G6, Canada
K. Nandakumar
Affiliation:
Department of Chemical Engineering, University of Alberta, Edmonton, Alberta, T6G 2G6, Canada
J. H. Masliyah
Affiliation:
Department of Chemical Engineering, University of Alberta, Edmonton, Alberta, T6G 2G6, Canada
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Abstract

This investigation is concerned with the numerical calculation of multiple solutions for a mixed-convection flow problem in horizontal rectangular ducts. The numerical results are interpreted in terms of recent observations by Benjamin (1978a) on the bifurcation phenomena for a bounded incompressible fluid. The observed mutations of cellular flows are discussed in terms of dynamic interchange processes. Each cellular flow may be represented by a solution surface in the parametric space of Grashof number Gr and aspect ratio γ, which is delimited by stability boundaries. Such a stability map has been generated for each type of cellular flow by a series of numerical experiments. Once these boundaries are crossed one cellular flow mutates into another via a certain dynamical process. Although the nature of the singular points on this map have not been determined precisely, a plausible general structure of the cellular-flow exchange process emerges from this map with several features in common with the Taylor-Couette flow. The primary modes appear to exchange roles via the formation of tilted cusp. Other salient features such as primary-mode hysteresis and quasi-critical range for cellular development appear to be present. However no anomolous modes have been observed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 177 , April 1987 , pp. 339 - 357
Copyright
© 1987 Cambridge University Press

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