Natural convection in a rectangular cavity heated from below and cooled from top as well as the sides

A three-dimensional, numerical simulation of Rayleigh–Benard convection in a cavity, having aspect ratios $A_x\text{=4}$ and $A_y\text{=4}$ has been performed using multigrid method, for $\mathrm{Ra}{\text{⩽1×10}}^4.$ The effect of the thermal boundary conditions of the vertical side walls on the flow bifurcations has been investigated by considering isothermal and conducting side wall cases. It has been found that the steady state flow patterns and the critical Rayleigh numbers for transition from one pattern to the other are completely different for each of the above mentioned boundary conditions. The local heat transfer distributions at the bottom and top plates are obtained and variations of the average Nusselt number for the isothermal and conducting side wall boundary conditions are compared for the range of Rayleigh numbers investigated.