Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T12:20:16.786Z Has data issue: false hasContentIssue false
  • English
  • Français

Convective stability of a variable-viscosity fluid in a vertical slot

Published online by Cambridge University Press:  21 April 2006

C. F. Chen  and
S. Thangam
C. F. Chen
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721
S. Thangam
Affiliation:
Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030
Get access Rights & Permissions [Opens in a new window]

Abstract

Stability of convective motion generated by a lateral temperature difference in a variable-viscosity fluid contained in a vertical slot was studied experimentally. The experiments were carried out in a narrow tank 30 cm high × 11.5 cm deep × 2 cm wide with glycerin–water solutions of 70, 80 and 90% glycerine. The onset of instabilities was detected by means of shadowgraphs. As the critical temperature difference was exceeded, a regular array of convection cells appeared. The critical Rayleigh number showed a slight decreasing trend as the Prandtl number of the fluid was increased, with a concomitant increase in the viscosity variation. The critical wavenumber remained practically constant for the three solutions used. At large Rayleigh numbers, approximately seven times the critical value, boundary layers along the walls became unstable and the cellular convection pattern became disrupted.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 161 , December 1985 , pp. 161 - 173
Copyright
© 1985 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 Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures. Q. Appl. Maths 12, 209–233.Google Scholar
Booker, J. R. 1976 Thermal convection with strongly temperature-dependent viscosity. J. Fluid Mech. 76, 741–754.Google Scholar
Busse, F. & Whitehead, J. A. 1971 Instabilities of convection rolls in a high Prandtl number fluid. J. Fluid Mech. 47, 305–320.Google Scholar
Eckert, E. R. G. & Carlson, W. O. 1961 Natural convection in an air layer enclosed between two vertical plates with different temperatures. Intl J. Heat Mass Transfer 2, 106–120.Google Scholar
Eckert, E. R. G. & Soehnghen, E. 1951 General discussion on heat transfer. In Proc. Meet. London, IME & ASME. p. 321.
Elder, J. W. 1965a Laminar free convection in a vertical slot. J. Fluid Mech. 23, 77–98.Google Scholar
Elder, J. W. 1965b Turbulent free convection in a vertical slot. J. Fluid Mech. 23, 99–111.Google Scholar
Hart, J. E. 1971 Stability of the flow in a differentially heated inclined box. J. Fluid Mech. 47, 547–576.Google Scholar
Lee, Y. & Kohpela, S. A. 1983 Multicellular natural convection in a vertical slot. J. Fluid Mech. 126, 91–121.Google Scholar
Richter, F. M. 1978 Experiments on the stability of convection rolls in fluids whose viscosity depends on temperature. J. Fluid Mech. 89, 553–560.Google Scholar
Richter, F. M., Nataf, H. C. & Daly, S. F. 1983 Heat transfer and horizontally averaged temperature of convection with large viscosity variations. J. Fluid Mech. 129, 173–192.Google Scholar
Segur, J. B. 1953 Physical properties of glycerol and its solutions. In Glycerol (ed. C. S. Miner & N. N. Dalton), pp. 238–334. Reinhold.
Seki, N., Fukusako, S. & Inaba, H. 1978 Visual observation of natural convective flow in a narrow vertical cavity. J. Fluid Mech. 84, 695–704.Google Scholar
Stengel, K. C., Oliver, D. S. & Booker, J. R. 1982 Onset of convection in a variable-viscosity Fluid. J. Fluid Mech. 120, 411–431.Google Scholar
Thangam, S. & Chen, C. F. 1984 Stability analysis on the convection of a variable viscosity fluid in an infinite vertical slot. Stevens Institute of Technology Tech. Rep. ME-RT-84015.
Torrance, K. E. & Turcotte, D. L. 1971 Thermal convection with large viscosity variations. J. Fluid Mech. 47, 113–125.Google Scholar
Vest, C. M. & Arpaci, V. S. 1969 Stability of natural convection in a vertical slot. J. Fluid Mech. 36, 1–15.Google Scholar