HEAT-SOURCE DRIVEN CONVECTION IN A CAVITY WITH VARIABLE FIXED/FREE UPPER SURFACE
This investigation describes two-dimensional free convection in a rectangular cavity driven by a constant rate of internal energy generation. The aspect ratio is fixed with depth/width = L/W = 0.5. The side and bottom walls are adiabatic, and the temperature of the upper boundary is constant. The bottom and side walls are rigid, no-slip surfaces. The upper surface is variably fixed at a ratio of X/W. Five cases are studied: 1.00 (fully closed cavity), 0.75, 0.50, 0.25, and 0.00 (fully open cavity or free surface). The normalized turbulent equations of conservation of mass, momentum, and energy are solved using under-relaxation, steady-state modeling techniques. Mesh convergence is confirmed. Rayleigh numbers range from 102 to 105 for the fixed Prandtl number of 6.5. Temperature, stream function, turbulent kinetic energy, and velocity vectors are calculated for each of these cases and selected results are presented. Conduction is noted for all ratios of X/W for the Rayleigh number of 102. Convection is noted for all ratios of X/W at the Rayleigh number of 105. A flow and heat transfer transition zone exists at the intermediate Rayleigh numbers. Decreasing the ratio of X/W markedly increases the turbulence in the flow field and the Nusselt number. It also decreases the transition Rayleigh number for conduction. Varying the ratio of X/W gives insight into the mechanism of increased heat transfer at the free surface.