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Laminar gravitational convection of heat in dead-end channels

Published online by Cambridge University Press:  20 April 2006

Terry W. Sturm
Affiliation:
School of Civil Engineering, Georgia Institute of Technology, Atlanta, Georgia

Abstract

A closed-form solution of the coupled momentum and thermal energy equations is obtained for laminar gravitational circulation of water resulting from a longitudinal temperature gradient in a dead-end channel. The temperature gradient is determined by the rate of heat loss from the water surface. The solution is shown to be dependent on a modified Rayleigh number which involves the local surface heat-transfer coefficient. An experimental study was conducted, and the results are compared with the closed-form solution.

Type
Research Article
Copyright
© 1981 Cambridge University Press

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References

Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209248.Google Scholar
Brocard, D. N., Jirka, G. H. & Harleman, D. R. F. 1975 Buoyancy driven circulations in side-arms of cooling lakes. Proc. A.S.C.E. National Convention, Denver, Colorado.
Brocard, D. N., Jirka, G. H. & Harleman, D. R. F. 1977 A model for the convective circulation in side-arms of cooling lakes. Ralph M. Parsons Lab. for Water Resources and Hydrodynamics Rep. no. 223. Massachusetts Institute of Technology.Google Scholar
Cormack, D. E., Leal, L. G. & Imberger, J. 1974 Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory. J. Fluid Mech. 65, 209229.Google Scholar
Imberger, J. 1974 Natural convection in shallow cavity with differentially heated end walls. Part 3. Experimental results. J. Fluid Mech. 65, 247260.Google Scholar
Keulegan, G. H. 1957 An experimental study of the motion of saline water from locks into fresh water channels. Nat. Bur. Stand. Rep. 5168.Google Scholar
Koh, R. C. Y. 1966 Viscous stratified flow towards a sink. J. Fluid Mech. 24, 555575.Google Scholar
Kreith, F. 1973 Principles of Heat Transfer, p. 392. Intext Press.
Phillips, O. M. 1966 On turbulent convection currents and the circulation of the Red Sea. Deep Sea Res. 13, 11491160.Google Scholar
Ryan, P. J., Harleman, D. R. F. & Stolzenbach, K. D. 1974 Surface heat loss from cooling ponds. Water Resources Res. 10, 930938.Google Scholar
Sturm, T. W. 1976 An analytical and experimental investigation of density currents in sidearms of cooling ponds. Ph.D. thesis, University of Iowa.
Turner, J. S. 1973 Buoyancy Effects in Fluids, p. 87. Cambridge University Press.