Abstract

Flow in a rectangular enclosure with a square horizontal cross-section, whose lower horizontal surface is heated and whose upper horizontal surface is cooled and whose vertical side-walls are adiabatic, has been numerically studied. It has been assumed that the flow is laminar and that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces. The unsteady form of the governing equations, written in terms of the vector potential and vorticity vector functions and expressed in dimensionless form, have been solved using a finite-difference procedure based on the equations. The solution was started with no flow in the enclosure. The solution, in general, has the following parameters: The Rayleigh number Ra, the Prandtl number and the size A of the square cross-sectional shape compared to the height of the enclosure. Results have only been obtained for a Prandtl number of 0.7. Results for values of A between 1 and 4 for various relatively low values of Rayleigh number (up to 15000) have been obtained. The results have been used to determine the effect of A on the value of Ra below which there is no fluid motion in the enclosure and to examine the various flow patterns that arise as the value of Ra is increased. The effect of A on the variation of the mean Nusselt number with Ra has also been examined.

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