Natural convection in an enclosure with distributed heat sources

Presented in this article is a computational analysis of the heat transfer due to an array of distributed heat sources on the bottom wall of a horizontal enclosure. The heat sources are modeled as flush-mounted sources with prescribed heat flux boundary conditions. Optimum heat transfer rates and the onset of thermal instability triggering various regimes are found to be governed by the length and spacing of the sources and the width-to-height aspect ratio of the enclosure. With respect to source spacing, we found that spacing equal to that of the source length provides effective convective heat transfer, and increasing the source spacing further does not result in significant improvements. The transition from a conduction-dominated regime to a convection-dominated regime is found to be characterized by a range of Rayleigh numbers, in contrast to the classical bottom wall heating problem. The range of Rayleigh numbers at which transition takes place decreases as the source length increases. At the transition region for very small source lengths, the Rayleigh-Benard cell structure grows significantly to form fewer and larger cells, which accounts for higher heat transfer rates compared to configurations with longer heat sources where the cell structure remains the same throughout transition. Following the transition to a convection-dominated regime, bifurcations in the Rayleigh-Benard cell structures as well as further regime changes are observed, reflecting the instabilities in the physical system.