A numerical study of three-dimensional natural convection in a low aspect ration horizontal enclosure with a uniform heat flu x on the lower surface

摘要

Flow in a rectangular enclosure with a square horizontal cross-section and with a uniform heat flux applied across the lower horizontal surface and with the upper horizontal surface cooled to a uniform low temperature has been numerically studied. The vertical side-walls of the enclosure are adiabatic. 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 heat flux Rayleigh number Ra{sub}q, 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 0.5 and 3 for various relatively low and moderate values of Rayleigh number (up to 40000) have been obtained. The results have been used to determine the effect of A on the value of Ra{sub}q below which there is no fluid motion in the enclosure and to examine the various flow patterns that arise as the value of Ra{sub}q is increased with various values of A. The effect of A on the variation of the mean dimensionless lower surface temperature with Ra has also been examined.