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Numerically computed multiple steady states of vertical buoyancy-induced flows in cold pure water

Published online by Cambridge University Press:  20 April 2006

Ibrahim El-Henawy ,
Brian Hassard ,
Nicholas Kazarinoff ,
Benjamin Gebhart  and
Joseph Mollendorf
Ibrahim El-Henawy
Affiliation:
Department of Mathematics, SUNY/B, 106 Diefendorf Hall, Buffalo, NY 14214
Brian Hassard
Affiliation:
Department of Mathematics, SUNY/B, 106 Diefendorf Hall, Buffalo, NY 14214
Nicholas Kazarinoff
Affiliation:
Department of Mathematics, SUNY/B, 106 Diefendorf Hall, Buffalo, NY 14214
Benjamin Gebhart
Affiliation:
MEAM, Towne Building, University of Pennsylvania, Philadelphia, PA 19104
Joseph Mollendorf
Affiliation:
Department of Mechanical and Aerospace Engineering, 335 Engineering East (R3), SUNY/B, Amherst, NY 14260
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Abstract

The laminar, boundary-layer, natural convection flow adjacent to a vertical, heated or cooled, flat surface submerged in quiescent cold water was studied. The results demonstrate for the first time the existence of multiple steady-state solutions in a natural convection flow. The calculated velocity profiles, over a range of the parameters, are compared with recent corresponding velocity measurements of Wilson & Vyas (1979) and of Carey & Gebhart (1981). The newly found additional steady-state solutions are of considerable practical interest because the heat-transfer rates for a pair of solutions (with determining physical parameters and boundary conditions otherwise identical) are sometimes vastly different. An important consequence of this study is the possible relationship of multiple steady-state solutions to the recently observed unsteadiness in some such flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 122 , September 1982 , pp. 235 - 250
Copyright
© 1982 Cambridge University Press

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