Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-19T06:07:04.127Z Has data issue: false hasContentIssue false
  • English
  • Français

Surface-tension-driven Bénard convection in small containers

Published online by Cambridge University Press:  26 April 2006

E. L. Koschmieder  and
S. A. Prahl
E. L. Koschmieder
Affiliation:
College of Engineering, The University of Texas at Austin, Austin, TX 78712, USA
S. A. Prahl
Affiliation:
College of Engineering, The University of Texas at Austin, Austin, TX 78712, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The onset and the form of surface-tension-driven convection in three different small circular and one small square container has been studied experimentally. In the smallest circular container, with increasing aspect ratio, the pattern consisted of first a circular roll and then segments of a circle outlined by different numbers of azimuthal nodal lines, with up to six segments. Simple solutions in the square container were the one-cellular pattern and a pattern consisting of four square cells. Unexpected solutions formed when the number of the cells in the square container was not a square number. When the aspect ratio permitted two cells, two triangular cells were observed. With space for three cells, one square cell and two wedge-shaped cells formed. The onset of convection in all fluid layers was characterized by a steep increase of the critical Marangoni number with decreasing aspect ratio.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 215 , June 1990 , pp. 571 - 583
Copyright
© 1990 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

Bénard, H. 1900 Rev. Gen. Sci. Pure Appl. 1, 1261–1271, 1309–1328.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Charlson, G. S. & Sani, R. L. 1970 Intl J. Heat Mass Transfer 13, 1479–1496.
Charlson, G. S. & Sani, R. L. 1971 Intl J. Heat Mass Transfer 14, 2157–2160.
Davis, S. H. 1967 J. Fluid Mech. 30, 465–478.
Dijkstra, H. A. & van de Vooren, A. I. 1989 Numer. Heat Transfer 16, 59–75.
Koschmieder, E. L. 1967 J. Fluid Mech. 30, 9–15.
Koschmieder, E. L. & Biggerstaff, M. I. 1986 J. Fluid Mech. 167, 49–64.
Koschmieder, E. L. & Pallas, S. G. 1974 Intl J. Heat Mass Transfer 22, 535–546.
Nield, D. A. 1964 J. Fluid Mech. 19, 341–352.
Pearson, J. K. A. 1958 J. Fluid Mech. 4, 489–500.
Rosenblat, S. 1982 J. Fluid Mech. 122, 395–410.
Rosenblat, S., Davis, S. H. & Homsy, G. M. 1982a J. Fluid Mech. 120, 91–122.
Rosenblat, S., Homsy, G. M. & Davis, S. H. 1982b J. Fluid Mech. 120, 123–138.
Winters, K. H., Plesser, Th. & Cliffe, K. A. 1988 Physica D 29, 387–401.