Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-13T01:33:47.914Z Has data issue: false hasContentIssue false
  • English
  • Français

Buoyancy-induced flows in water under conditions in which density extrema may arise

Published online by Cambridge University Press:  19 April 2006

Benjamin Gebhart  and
Joseph C. Mollendorf
Benjamin Gebhart
Affiliation:
Department of Mechanical Engineering, State University of New York, Buffalo
Joseph C. Mollendorf
Affiliation:
Department of Mechanical Engineering, State University of New York, Buffalo
Get access Rights & Permissions [Opens in a new window]

Abstract

The temperature dependence of the density of both pure and saline water, even to very high salinity and pressure levels, decreases at decreasing temperature toward an extremum. The nature of this variation precludes approximating the buoyancy-force density difference linearly with a temperature difference. This peculiar density variation of water has very significant effects, even at environmental temperature levels. A new equation has appeared which relates density to temperature, salinity and pressure with very high accuracy. Its form is especially suited to the analysis of convective motions. We consider here vertical boundary-layer flows. Analysis of flows arising from thermal buoyancy and from combined buoyancy effects shows the simplicity of the formulation. Relatively few new parameters arise. Extensive calculations for thermally buoyant flows show the large magnitude of the effects of the complicated density variation on transport. Buoyancy-force reversals and convective inversions are predicted. The latter are in close agreement with past experiments. A new Grashof number arises which is an accurate indication of the actual local flow vigour. The effects of specific temperature conditions are given in detail. The appreciable effect of the Prandtl number is calculated. Transport parameters are given for salinities and pressures up to 40 p.p.t. and 1000 bars, respectively.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 89 , Issue 4 , 27 December 1978 , pp. 673 - 707
Copyright
© 1978 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. 1977 The maximum-density points of saline water. Submitted to Deep-Sea Res.
Chen, C. T. & Millero, F. J. 1976 The specific volume of sea water at high pressures. Deep-Sea Res. 23, 595–612.Google Scholar
Codegone, C. 1939 Su un punto d'inversione dei moti convettivi. Acad. Sci. Torino 75, 167.Google Scholar
Doherty, B. T. & Kester, D. R. 1974 Freezing point of seawater. J. Mar. Res. 32, 285–300.Google Scholar
Dumoré, J. M., Merk, H. J. & Prins, J. A. 1953 Heat transfer from water to ice by thermal convection. Nature 172, 460–461.Google Scholar
Ede, A. J. 1951 Heat transfer by natural convection in refrigerated liquid. Proc. 8th Int. Cong. Refrigeration, London, p. 260. (See also The influence of anomalous expansion on natural convection in water. Appl. Sci. Res. 5 (1955), 458–460.)
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
Fujino, K., Lewis, E. L. & Perkinn, R. G. 1974 The freezing point of sea water at pressures up to 100 bars. J. Geophys. Res. 79, 1792–1797.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. & 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
Goren, S. L. 1966 On free convection in water at 4 C. Chem. Engng Sci. 21, 515–518.Google Scholar
Govindarajulu, T. 1970 Free convection flow of water at 4 C on vertical and horizontal plates. Chem. Engng Sci. 25, 1827–1828.Google Scholar
Joseph, D. D. 1971 Stability of convection in containers of arbitrary shape. J. Fluid Mech. 47, 257–282.Google Scholar
Lorenz, L. 1881 Über das Leitungsvermögen der Metalle für Wärme und Electricität. Ann. Phys. Chem. 13, 582–606.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
Oborin, L. A. 1967 Special features of free convection in water at temperatures below 277 K. J. Engng Phys. 13, 429–442.Google Scholar
Oberbeck, A. 1879 Uber die Wärmeleitung der Flussigkeiten bei der Berüchsichtigung der Strömungen infolge von Temperaturdifferenzen. Ann. Phys. Chem. 7, 271–292.Google Scholar
Perry, J. H. 1963 Chemical Engineers’ Handbook, 4th edn, 3, p. 70. McGraw-Hill.
Roy, S. 1972 Free convection in liquids under maximum density conditions. Indian J. Phys. 46, 245–249.Google Scholar
Schechter, R. S. & Isbin, H. S. 1958 Natural convection heat transfer in regions of maximum fluid density. A.I.Ch.E. J. 4, 81–89.Google Scholar
Schenk, J. & Schenkels, F. A. M. 1968 Thermal free convection from an ice sphere in water. Appl. Sci. Res. 19, 465–476.Google Scholar
Soundalgekar, V. M. 1973 Laminar free convection flow of water at 4 C from a vertical plate with variable wall temperature. Chem. Engng Sci. 28, 307–309.Google Scholar
Vanier, C. R. & Tien, C. 1967 Further work on free convection in water at 4 C. Chem. Engng Sci. 22, 1747–1751.Google Scholar
Vanier, C. R. & Tien, C. 1968 Effect of maximum density and melting on natural convection heat transfer from a vertical plate. Chem. Engng Prog. Symp. Ser. 64, 240–254.Google Scholar