Free Convection in a Square Cavity with a Partially Heated Wall and a Cooled Top

Free-convective flow in a rectangular cavity which has one "side" wall partially heated to a uniform temperature and the "top" wall cooled over its entire surface to a uniform lower temperature has been considered. All remaining well surfaces are adiabatic. The cavity is, in general, inclined at an angle to the vertical. The flow has been assumed to be laminar and two dimensional. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being treated by means of the Boussinesq approximation. The governing equations, expressed in terms of stream function and vorticity, have been written in dimensionless form. The resultant equations, subject to the assumed boundary conditions, have been solved using the finite-element method. Because of the possible applications that motivated the study, results have only been obtained for a Prandtl number of 0.7. Attention has been restricted to a cavity with an aspect ratio of 1, i.e., a square cavity. Results have then been obtained for Rayleigh numbers between 3,000 and 100,000 for a variety of heated wall-portion sizes and positions for angles of inclination between 0 deg and 180 deg. These results have been used to study the effects of the governing parameters on the mean heat transfer rate and these effects have been related to changes in the induced flow pattern within the cavity.