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Three-dimensional natural convection in a box: a numerical study

Published online by Cambridge University Press:  12 April 2006

G. D. Mallinson  and
G. De Vahl Davis
G. D. Mallinson
Affiliation:
Department of Defence, Aeronautical Research Laboratories, Melbourne, Australia
G. De Vahl Davis
Affiliation:
Department of Defence, Aeronautical Research Laboratories, Melbourne, Australia
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Abstract

The solution of the steady-state Navier–Stokes equations in three dimensions has been obtained by a numerical method for the problem of natural convection in a rectangular cavity as a result of differential side heating. In the past, this problem has generally been treated as though it were two-dimensional. The solutions explore the three-dimensional motion generated by the presence of no-slip adiabatic end walls. For Ra = 104, the three-dimensional motion is shown to be the result of the inertial interaction of the rotating flow with the stationary walls together with a contribution arising from buoyancy forces generated by longitudinal temperature gradients. The inertial effect is inversely dependent on the Prandtl number, whereas the thermal effect is nearly constant. For higher values of Ra, multiple longitudinal flows develop which are a delicate function of Ra, Pr and the cavity aspect ratios.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 1 , 1 November 1977 , pp. 1 - 31
Copyright
© 1977 Cambridge University Press

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