Onset of convection in top-cooled enclosures with discrete heat sources

The onset of natural convection in an liquid filled enclosure with five discrete heated sections on one vertical wall and cooled from the top is predicted numerically. Finite element simulations were conducted for six height-to-width ratios ranging from 3.67 to 12.22, and for a modified Rayleigh number, Ra*_H (based on the length scale of enclosure height H), range of 1 to 2.5 x 10⁸. The fluid medium in the enclosure is ethylene glycol which has a Prandtl number of 130 - 140. The effect of aspect ratio on velocity and temperature field in conduction and convection flow regimes are investigated. Multicellular flow is observed in the conduction regime for enclosures with aspect ratio value larger than 5. The isotherms indicated a typical conduction heat transfer mode in the conduction flow regime even though fluid motion is observed. A single flow cell is observed in the center of the enclosure for aspect ratio smaller than 5, and the flow cell moves upward as the modified Rayleigh number increases. The analysis of the results indicated that the modified Rayleigh number Ra*_W,T (based on the heat flux at the top surface q_T, and the length scale W) is the parameter of fluid thermal behavior. The onset of convection for aspect ratio in the range of 3.67 to 12.22 is predicted to occur at Ra*_W,T = 600 ± 50, corresponding to a conduction Nusselt number of Nu_H,Y = 2.75 ± 5%, A comparison between predictions of the current study and the experimental data of Carmona and Keyhani is carried out, and agreement in the high Rayleigh number convection flow regime is obtained.