Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-20T21:29:49.487Z Has data issue: false hasContentIssue false
  • English
  • Français

Experiments on the onset of thermal convection in horizontal layers of gases

Published online by Cambridge University Press:  28 March 2006

H. A. Thompson  and
H. H. Sogin
H. A. Thompson
Affiliation:
Department of Mechanical Engineering, Tulane University, New Orleans, Louisiana 70118
H. H. Sogin
Affiliation:
Department of Mechanical Engineering, Tulane University, New Orleans, Louisiana 70118
Get access Rights & Permissions [Opens in a new window]

Abstract

Precise data are presented on the Rayleigh-Jeffreys instability in air, argon and carbon dioxide at pressures between 0·6 and 6·0 atm in layers of depths 1/8, 1/4, and 3/4in. A new method yields better resolution and repeatability than the methods employed in the past. Here the gas layer is brought through the state of marginal stability by increasing the pressure while both the temperature and the temperature difference are held constant. The onset of convection is detected by means of a type of heat flow meter ascribed to Prof. L. M. K. Boelter. The equipment and procedure are described and analysed in detail.

The experimentally-determined value of the critical Rayleigh number is 1793, repeatable within a probable deviation of 1% due to random errors. Considering in addition the systematic errors of the instrumentation but not the uncertainties of property values, we place the absolute value within 1793 ± 80. The corresponding theoretical value is 1708.

Finite rates of pressure rise inhibit the development of convection. The results achieved at the least rates of pressure rise are in agreement with steady-state determinations.

The approach employed in this investigation shows great promise as a method for measuring the transport properties of gaseous mixtures or of gases at combined high temperature and high pressure.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 24 , Issue 3 , March 1966 , pp. 451 - 479
Copyright
© 1966 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

Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 1960 Transport Phenomena 10.4. New York: John Wiley.
Chandra, K. 1938 Instability of fluids heated from below. Proc. Roy. Soc., A 164, 231.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Instability, Chapters I and II. Oxford University Press.
De Graaf, J. G. A. & Van der Held, E. F. M. 1953 The relation between the heat transfer and the convection phenomena in enclosed plane air layers. Appl. Sci. Res., A 3, 393–409.Google Scholar
Hilsenrath, J., Beckett, C., Benedict, W. S., Fano, L., Hoge, H. J., Masi, J. F., Nutall, R. L., Touloukian, Y. S. & Woolley, H. W. 1955 Tables of Thermal Properties of Gases. N.B.S. Circular 564.
Jakob, M. 1957 Heat Transfer, volume II, pp. 13–33. New York: John Wiley.
Jeffreys, H. 1930 The instability of a compressible fluid heated below. Proc. Camb. Phil. Soc. 26, 170.Google Scholar
Ostrach, S. 1957 Convection phenomena in fluids heated from below. Trans. A.S.M.E. 79, 299.Google Scholar
Pellew, A. & Southwell, R. 1940 Proc. Roy. Soc., A 176, 312.
Rayleigh, Lord 1916 On convection currents in a horizontal layer of fluid when the higher temperature is on the under side. Phil. Mag. 32, 529Google Scholar
Schmidt, E. & Silverston, P. L. 1959 Natural convection in horizontal liquid layers. Chem. Engr. Progr. Symposium Series 29, 55, 163.Google Scholar
Schmidt, R. J. & Milverton, S. W. 1935 On the instability of a fluid when heated from below. Proc. Roy. Soc., A 152, 586.Google Scholar
Schmidt, R. J. & Saunders, O. A. 1938 On the motion of a fluid heated from below. Proc. Roy. Soc., A 165, 216.Google Scholar
Sparrow, E. M., Goldstein, R. J. & Jonsson, V. K. 1964 Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profile. J. Fluid. Mech. 18, 513.Google Scholar
Sutton, O. G. 1950 On the stability of a fluid heated from below. Proc. Roy. Soc., A 204, 297.Google Scholar
Thompson, H. A. 1964 A new and improved method for the determination of the critical Rayleigh number in gases. Ph.D. Thesis in Mechanical Engineering, Tulane University.