Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T01:23:44.886Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of departures from the Oberbeck-Boussinesq approximation on the heat transport of horizontal convecting fluid layers

Published online by Cambridge University Press:  19 April 2006

Guenter Ahlers
Guenter Ahlers
Affiliation:
Bell Laboratories, Murray Hill, New Jersey 07974
Get access Rights & Permissions [Opens in a new window]

Abstract

Measurements are presented of the Nusselt numbers N and Rayleigh numbers R for shallow layers of 4He gas heated from below. By choosing different temperatures between 2·3 K and 5·1 K and different pressures between 0·07 bar and 1 bar, the extent Q of departures from the Oberbeck-Boussinesq approximation was varied. When R was evaluated at the static temperature at the midplane of the cell, both the critical Rayleigh number Rc and the initial slope N1 of the Nusselt number were found to be independent of Q within experimental scatter. This result agrees with the prediction of Busse (1967). When R was evaluated at the cold end temperature of the cell, both Rc and N1 depended strongly upon Q.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 98 , Issue 1 , 15 May 1980 , pp. 137 - 148
Copyright
© 1980 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

Ahlers, G. 1971 Heat capacity near the superfluid transition in 4He at saturated vapor pressure. Phys. Rev. A 3, 696–716.Google Scholar
Ahlers, G. 1974 Low temperature studies of the Rayleigh-Bénard instability. Phys. Rev. Lett. 33, 1185–1188.Google Scholar
Ahlers, G. 1975 The Rayleigh-Bénard instability at helium temperatures. In Fluctuations. Instabilities, and Phase Transitions (ed. T. Riste), pp. 171–193. Plenum.
Ahlers, G. 1978 Thermal conductivity of 4He vapor as a function of density. J. Low Temp. Phys. 31, 429–439.Google Scholar
Becker, E. W., Misenta, R. & Schmeissner, F. 1954a Viscosity of gaseous He3 and He4 between 1·3 °K and 4·2 °K. Phys. Rev. 93, 244.Google Scholar
Becker, E. W., Misenta, R. & Schmeissner, F. 1954b Die Zähigkeit von gasförmigem He3 und He4 zwischen 1·3 °K und 4·2 °K. Z. Phys. 137, 126–136.Google Scholar
Behringer, R. P. & Ahlers, G. 1977 Heat transport and critical slowing down near the Rayleigh-Bénard instability in cylindrical containers. Phys. Lett. A 62, 329–331.Google Scholar
Boussinesq, J. 1903 Théorie Analytique de la Chaleur, vol. 2. Paris: Gauthier-Villars.
Busse, F. H. 1962 Dissertation, University of Munich. [English translation by S. H. Davis, Rand Rep. LT-66-19, Rand Corp., Santa Monica, California.
Busse, F. H. 1967 The stability of finite amplitude cellular convection and its relation to an extremum principle. J. Fluid Mech. 30, 625–649.Google Scholar
Charlson, G. S. & Sani, R. L. 1970 Thermoconvective instability in a bounded cylindrical fluid layer. Int. J. Heat Mass Transfer 13, 1479–1496.Google Scholar
Davis, S. H. & Segel, L. A. 1968 Effects of surface curvature and property variation on cellular convection. Phys. Fluids 11, 470–476.Google Scholar
Dubois, M., Berge, P. & Wesfried, J. 1978 Non-Boussinesq convective structures in water near 4 °C. J. Phys. 39, 1253–1257.Google Scholar
Hirschfelder, J. O., Curtiss, C. F. & Bird, R. B. 1954 Molecular Theory of Gases and Liquids. Wiley.
Hoard, C. Q., Robertson, C. R. & Acrivos, A. 1970 Experiments on cellular structure in Bénard convection. Int. J. Heat Mass Transfer 13, 849–855.Google Scholar
Joseph, D. D. 1971 Stability of convection in containers of arbitrary shape. J. Fluid Mech. 47, 257–282.Google Scholar
Keller, W. E. 1969 Helium-3 and Helium-4. Plenum.
Kerrisk, J. F. & Keller, W. E. 1969 Thermal conductivity of fluid He3 and He4 at temperatures between 1·5 and 4·0 K and for pressures up to 34 atm. Phys. Rev. 177, 341–351.Google Scholar
Koschmieder, E. L. & Pallas, S. G. 1974 Heat transfer through a shallow, horizontal convecting fluid layer. Int. J. Heat Mass Transfer 17, 991–1002.Google Scholar
Oberbeck, A. 1879 Über die Wärmeleitung der Flüssigkeiten bei der Berücksichtigung der Strömungen infolge von Temperaturdifferenzen. Ann. Phys. Chem. 7, 271–292.Google Scholar
Palm, E., Ellingsen, T. & Gjevik, B. 1967 On the occurrence of cellular motion in Bénard convection. J. Fluid Mech. 30, 651–661.Google Scholar
Rossby, H. T. 1969 A study of Bénard convection with and without rotation. J. Fluid Mech. 36, 309–335.Google Scholar
Schlüter, A., Lortz, D. & Busse, F. 1965 On the stability of steady finite amplitude convection. J. Fluid Mech. 23, 129–144.Google Scholar
Somerscales, E. F. C. & Dougherty, T. S. 1970 Observed flow patterns at the initiation of convection in a horizontal liquid layer heated from below. J. Fluid Mech. 42, 755–768.Google Scholar