Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-18T23:56:52.352Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent free convection in a vertical slot

Published online by Cambridge University Press:  28 March 2006

J. W. Elder
J. W. Elder
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Cambridge
Present address: Institute of Geophysics and Planetary Physics, University of California, La Jolla, California.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is a continuation of the experimental study (Elder 1965), of free convection in a vertical slot, to unsteady and turbulent motion. The flow is specified by three dimensionless parameters: σ, the Prandtl number; h = H|L, the aspect ratio and $A = \gamma g \Delta TL^3|kv$, the Rayleigh number. The present experiments are generally for σ = 7 (water), h = 10–30 and A > 106.

For A above about 8 × 108S|h3, travelling, wave-like motions grow up the hot wall of the slot and also down the cold wall. These waves grow most readily mid-way between the two ends. At higher values of the Rayleigh number when the wave amplitude is finite, the phase of successive wave fronts becomes increasingly random till near A = 1·0 × 1010|h3 an intense entrainment and mixing process commences between the wall region and the interior. The middle portion of the interior is then turbulent, the extent of the region growing further toward the ends as A increases.

Measurements of the mean temperature and the probability distribution of temperature fluctuations of the turbulent flow are reported. Except within the thin wall layers and distant form the ends, the interior has a mean temperature, uniform to within 0·1%, superimposed on which is a nearly Gaussian fluctuation-field of variance of order 0·01ΔT. A comparison is made with recent theories of turbulent convection; moderate agreement is found with the similarity ideas of Priestley (1959). The wall layer is seen as a marginally unstable sublayer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 23 , Issue 1 , September 1965 , pp. 99 - 111
Copyright
© 1965 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

Batchelor, G. K. 1954 Quart. Appl. Math. 12, 209.
Eckert, E. R. G. & Soehnghen, E. 1951 Proceedings of the General Discussion on Heat Transfer. London. Inst. Mech. Engrs, p. 321.
Eckert, E. R. G., Soehngen, E. & Schneider, P. J. 1955 50 Jahre Grenzschichtforschung, p. 407. Berlin: Vieweg & Sohn.
Elder, J. W. 1965 J. Fluid Mech. 23, 77.
Gershuni, G. Z. 1955 Zh. tekh. Fiz. 25, 351.
Jakob, M. 1949 Heat Transfer. New York: Wiley.
Kurtz, E. F. & Crandall, S. H. 1962 J. Math. Phys. 41, 264.
Malkus, W. V. R. 1963 Theory and Fundamental Research in Heat Transfer (ed. J. A. Clarke), p. 203. London: Macmillan.
Mordchelles-Regnier, G. & Kaplan, C. 1963 Proc. Int. Heat & Mass Transf. Conf. p. 94.
Priestley, C. H. B. 1959 Turbulent Transfer in the Lower Atmosphere. Chicago: University Press.
Szewczyk, A. A. 1962 Int. J. Heat & Mass Transf. 5, 903.
Townsend, A. A. 1959 J. Fluid Mech. 5, 209.
Tritton, D. J. 1963 J. Fluid Mech. 16, 269, 417.