Unified treatment of natural convection in tall narrow and flat wide rectangular enclosures

Numerical simulation was used to investigate natural convection in rectangular enclosures ranging in aspect ratio from tall, narrow shapes to flat, wide shapes. For each of the selected aspect ratios, the Rayleigh number was varied over a range of approximately four decades. Two fundamental thermal boundary conditions were considered. One of these, commonly designed as heating from below, involved the imposition of a temperature at the lower bounding wall that is higher than that at the upper bounding wall. The side walls of the enclosure were maintained adiabatic for this case. The second employed boundary condition was side walls at different uniform temperatures and adiabatic upper and lower boundaries. For each aspect ratio and for both types of boundary conditions, the onset of natural convection from the regime of pure conduction occurred at a definitive value of the Rayleigh number, termed the critical Rayleigh number. Once that threshold value was exceeded, the Nusselt number increased markedly with increasing Rayleigh number, the sharpness of the increase being greater for the bottom-heated case. For that case and for aspect ratios (height/width) greater than one, the breakdown of a flow pattern characterized by a single recirculation zone caused a sudden halt to the increase of the Nusselt number. This breakdown was followed by a rapid reformation of the flow pattern into a pair of recirculation zones, one situated above the other. The critical Rayleigh number was insensitive to the aspect ratio for flat, wide enclosures but, on the contrary, the critical value increased markedly with increasing aspect ratio for tall, narrow enclosures. In general, a critical Rayleigh number for the bottom-heated case exceeded that for the side-heated case by a factor of 12.