Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-18T21:57:31.567Z Has data issue: false hasContentIssue false
  • English
  • Français

Laminar 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 is largely an experimental study of the interaction of buoyancy and shear forces in the free convective flow of a liquid in a rectangular cavity across which there is a uniform temperature difference, ΔT, produced by maintaining the two vertical walls at two different temperatures. The height of the cavity, H, is made larger than the width of the cavity, L, and the cavity is sufficiently long in the third dimension for the mean flow to be nearly everywhere two-dimensional. The flow is specified by three dimensionless parameters: σ, the Prandtl number; h = H|L, the aspect ratio; A = γgΔTL3|κν, the Rayleigh number. The experiments are generally restricted to h = 1–60, σ ÷ 103 and A < 108.

For A < 103 the temperature field closely satisfies Laplace's equation but a weak stable unicellular circulation is generated. The flow is vertical throughout the slot except for regions within a distance of order L from the ends.

For 103 < A < 105, large temperature gradients grow near the walls, and in an interior region a uniform vertical temperature gradient is established. The flow is similar to that near an isolated, heated, vertical plate except that the vertical growth of the wall layers is inhibited in the central part of the slot by the presence of the other layer which prevents entrainment of fluid.

Near A = 105 the interior region of the flow generates a steady secondary flow. A regular cellular pattern becomes superimposed on the basic flow to produce a ‘cats-eye’ pattern of streamlines. Near A = 106 when the secondary cell amplitude is large, a further steady cellular motion is generated in the weak shear regions between each cell.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 23 , Issue 1 , September 1965 , pp. 77 - 98
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. & Carlson, W. O. 1961 Int. J. Heat & Mass Transfer, 2, 106.
Goldstein, S. 1938 Ed. Modern Developments in Fluid Dynamics. Oxford University Press.
Martini, W. R. & Churchill, S. W. 1960 A.I.Ch.E.J. 6, 251.
Mordchelles-Regnier, G. & Kaplan, C. 1963 Proc. Int. Heat & Mass Transfer Conf. 94.
Pillow, A. F. 1952 Austr. Aero. Res. Rep. no. A 79.
Schlichting, H. 1960 Boundary Layer Theory. London: Pergamon Press.
Weinbaum, S. 1964 J. Fluid Mech. 18, 409.