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Bifurcation in steady laminar mixed convection flow in horizontal ducts

Published online by Cambridge University Press:  20 April 2006

K. Nandakumar ,
Jacob H. Masliyah  and
Hin-Sum Law
K. Nandakumar
Affiliation:
Department of Chemical Engineering, University of Alberta, Edmonton. T6G 2G6, Canada
Jacob H. Masliyah
Affiliation:
Department of Chemical Engineering, University of Alberta, Edmonton. T6G 2G6, Canada
Hin-Sum Law
Affiliation:
Department of Chemical Engineering, University of Alberta, Edmonton. T6G 2G6, Canada
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Abstract

The fully developed laminar mixed-convection flow in horizontal ducts of rectangular, circular and semicircular cross-sections has been studied using a numerical model of the governing equations of motion, subject to the Boussinesq approximation and an axially uniform heat-flux condition. Dual solutions with a two- and a four-vortex flow pattern have been observed in all cases. The rectangular geometry, with its aspect ratio and Grashof number as parameters, is posed as a two-parameter problem. In this parameter-space, the critical points where the transition between the two- and the four-vortex pattern occur, follow a tilted cusp. This is akin to the phenomenon in the Taylor problem which has been thoroughly investigated by Benjamin and co-workers in a general study of bifurcation phenomena for viscous flow problems. The bifurcation phenomenon in circular ducts, which is essentially a one-parameter problem, has features similar to that observed for the Dean problem, by Nandakumar and Masliyah.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 152 , March 1985 , pp. 145 - 161
Copyright
© 1985 Cambridge University Press

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