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Buoyancy-driven circulation in free-surface channels

Published online by Cambridge University Press:  20 April 2006

Subhash C. Jain
Subhash C. Jain
Affiliation:
Iowa Institute of Hydraulic Research, The University of Iowa, Iowa City, Iowa 52242
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Abstract

The convective circulation driven by a surface buoyancy flux in a dead-end open channel is analysed. On the assumption of similarity profiles for velocity and temperature, the governing partlial differential are reduced to two nonlinear ordinary differential equations by integrating over the flow depth. A closed-form solution of the differential equations is presented. The solution is a function of the Grashof number G and the modified Prandtl–Grashof number PmG½ defined ih (21). The velocity and temperature along the channel vary linearly as the distance and as the square of the distance respectively. Analytical expressions for the rate of total heat loss from the channel and the rateof flow in the channel are derived. The analytical results compare well with the available experimental data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 122 , September 1982 , pp. 1 - 12
Copyright
© 1982 Cambridge University Press

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References

Ames, W. F. 1968 Nonlinear Ordinary Differential Equations in Transport Processes. Academic.
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, Mit, Rep. no. 223.Google Scholar
Brocard, D. N. & Harleman, D. R. F. 1980 Two-layer model for shallow horizontal convective circulation. J. Fluid Mech. 100, 129–146.Google Scholar
Edinger, J. R. & Geyer, J. C. 1965 Cooling water studies for Edison Electric Institute. The Johns Hopkins University, Project RP-49: Heat Exchange in the Environment.
Jain, S. C. 1980 Density currents in sidearms of cooling ponds. Proc. A.S.C.E., Energy Div. 106 (EY1), 9–21.Google Scholar
Phillips, O. M. 1966 On turbulent convection currents and the circulation of the sea. Deep-Sea Res. 13, 1149–1160.Google Scholar
Ryan, P. J., Harleman, D. R. F. & Stolzenbach, K. D. 1974 Surface heat loss from cooling ponds. Water Resources Res. 10, 930–938.Google Scholar
Sturm, T. W. 1976 An analytical and experimental investigation of density currents in sidearms of cooling ponds. Ph.D. thesis, Department of Mechanics and Hydraulics, University of Iowa.
Sturm, T. W. & Kennedy, J. F. 1980 Heat loss from sidearms of cooling lakes. Proc. A.S.C.E. Hydraul. Div. 106 (HY5), 783–804.Google Scholar