Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-19T03:14:49.640Z Has data issue: false hasContentIssue false
  • English
  • Français

Several plume flows in pure and saline water at its density extremum

Published online by Cambridge University Press:  20 April 2006

J. C. Mollendorf ,
R. S. Johnson  and
B. Gebhart
J. C. Mollendorf
Affiliation:
Department of Mechanical Engineering, State University of New York at Buffalo, Amherst, New York 14260
R. S. Johnson
Affiliation:
Department of Mechanical Engineering, State University of New York at Buffalo, Amherst, New York 14260 Present address: Harrison Radiator Division, General Motors Corporation, Lockport, NY 14094.
B. Gebhart
Affiliation:
Department of Mechanical Engineering, State University of New York at Buffalo, Amherst, New York 14260 Present address: Department of Mechanical Engineering & Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104.
Get access Rights & Permissions [Opens in a new window]

Abstract

An accurate representation of the motion-causing buoyancy force, in the vicinity of the maximum-density condition in water at low temperatures, is determined by using a very accurate and quite simple equation of state for both pure and saline water. The resulting general laminar boundary-layer flow equations admit similarity solutions and, in the absence of salinity diffusion, require only one additional new dimensionless variable, called R. For flows of constant heat content in an unstratified ambient fluid, similarity is found only when the far-field temperature is at the temperature of maximum density. The three flow situations considered here are two above a horizontal line heat source and one above a point heat source. The first flow is a freely rising plane plume and the second is a wall plume (flow over a vertical, adiabatic surface with a horizontal line source imbedded in it). The third flow is the freely rising axisymmetric plume. These are the models in laminar theory of many processes which arise in cold water. A primary objective here is to calculate the effect of using a nonlinear density relation for water, which is much more accurate at low temperatures than the conventional linear one used in ‘classical’ analyses. The downstream variations of the temperature and velocity fields are found to be very different from those for flows where the effect of a density extremum is not included.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 113 , December 1981 , pp. 269 - 282
Copyright
© 1981 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bendell, M. S. & Gebhart, B. 1976 Heat transfer and ice-melting in ambient water near its density extremum. Int. J. Heat Mass Transfer 19, 1081–1087.Google Scholar
Caldwell, D. R. 1974 Experimental studies on the onset of thermohaline convection. J. Fluid Mech. 64, 347–367.Google Scholar
Chen, C. T. & Millero, F. J. 1976 The specific volume of sea water at high pressures. Deep-Sea Res. 23, 595–612.Google Scholar
Fine, R. A. & Millero, F. J. 1973 Compressibility of water as a function of temperature and pressure. J. Chem. Phys. 59, 5529–5536.Google Scholar
Gebhart, B. 1971 Heat Transfer, 2nd edn. McGraw-Hill.
Gebhart, B. 1973 Boundary layer flows and instability in natural convection. Adv. Heat Transfer 9, 273–348.Google Scholar
Gebhart, B. & Mollendorf, J. C. 1977 A new density relation for pure and saline water. Deep-Sea Res. 24, 831–848.Google Scholar
Gebhart, B. & Mollendorf, J. C. 1978 Buoyancy-induced flows in water under conditions in which density extrema may arise. J. Fluid Mech. 89, 673–707.Google Scholar
Gebhart, B. & Pera, L. 1971 The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion. Int. J. Heat Mass Transfer 14, 2025–2050.Google Scholar
Gebhart, B., Pera, L. & Schorr, A. W. 1970 Steady laminar natural convection plumes above a horizontal line heat source. Int. J. Heat Mass Transfer 13, 161–171.Google Scholar
Merk, H. J. 1953 The influence of melting and anomalous expansion on the thermal convection in laminar boundary layers. Appl. Sci. Res. 4, 435–452.Google Scholar
Mollendorf, J. C. & Gebhart, B. 1973 Thermal buoyancy in round laminar vertical jets. Int. J. Heat Mass Transfer 16, 735–745.Google Scholar
Mollendorf, J. C. & Gebhart, B. 1974 Axisymmetric natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion. Proc. 5th Int. Heat Transfer Conf., Tokyo.
Pera, L. & Gebhart, B. 1972 Natural convection flows adjacent to horizontal surfaces resulting from the combined effects of thermal and mass diffusion. Int. J. Heat Mass Transfer 15, 269–278.Google Scholar