Numerical study of heat transfer and flow of natural convection in an enclosure with a heat-generating conducting body

A numerical study has been conducted to investigate steady state heat transfer and flow characteristics of natural convection in a vertical square enclosure when a temperature difference exists across an enclosure and, at the same time, a conducting body generates heat within the enclosure. Dimensionless governing equations indicate that the heat transfer and flow characteristics of this system are governed by the Rayleigh and Prandtl numbers, the area ratio, the conductivity ratio, and the temperature-difference ratio. Here the temperature-difference ratio is defined as the ratio of a temperature difference across the enclosure to that caused by the heat source. In the present study, the Rayleigh number ranges from 10(3) to 10(4) and the temperature-difference ratio from 0 to 50 while the Prandtl number, the area ratio, and the conductivity ratio are kept constant at 0.71, 0.25, 1, respectively. The analysis is performed by observing variations of streamlines, isotherms, heatlines, and the average Nusselt numbers on the hot and cold walls with respect to temperature difference ratios for each Rayleigh number. The results show that, as the temperature difference ratio increases, the flow dominated by the temperature difference across the enclosure proceeds to that dominated by the temperature difference due to the heat source, i.e., the ratio of the average Nusselt number of the hot wall to that of the cold wall changes from 1 to -1. As the Rayleigh number becomes greater, the temperature difference ratio should be much greater to achieve the average Nusselt number ratio of -1 because of convection effects caused by the temperature difference across the enclosure.