Natural Convection in a Quadrantal Cavity Heated and Cooled on Adjacent Walls

In this study, experimental and numerical analyses of natural convection in a quadrantal cavity heated and cooled on adjacent walls have been made to examine heat and fluid flow. Experimental studies involve the use of the particle tracing method that enables us to visualize the flow pattern in the enclosure. Numerical solutions are obtained using a commercial computational fluid dynamics package, FLUENT, using the finite volume method. Water is used as the working fluid. Effects of the Rayleigh number, Ra, on the Nusselt number, Nu, as well as velocity and temperature fields are investigated for the range of Ra from $103$ to $107$⁠. A new approach is suggested to overcome the singularity at the corner joining the differentially heated isothermal walls when determining Nu. This novel approach is justified through the purely analytical conduction solution. The experimental and numerical results are shown to agree fairly well. Finally, a correlation for Nu is developed.