Comparison of Natural Convection around a Circular Cylinder with a Square Cylinder Inside a Square Enclosure

Numerical calculations are carried out for natural convection induced by a temperature difference between a cold outer square enclosure and a hot inner cylinder with two different geometries (i.e. circular and square). A two-dimensional solution for natural convection is obtained, using the finite volume method for different Rayleigh numbers varying over the range of (103–105). The study goes further to investigate the effect of vertical position of the inner cylinder on the heat transfer and flow field. The location of the inner cylinder is vertically changed along the center-line of the square enclosure. The number, size and form of the vortices strongly depend on the Rayleigh number and the position of the inner cylinder. The results show that for both cylinders, at low Rayleigh numbers of 103 and104, the bifurcation from the bicellular vortices to an uni-cellular vortex occurs when an inner cylinder is placed at a certain distance from the center of the enclosure. When Ra =105, only a uni-cellular vortex is formed in the enclosure irrespective of the position of the inner cylinder. Also as the obtained total surfaces-averaged Nusselt numbers of the enclosure show, in all cases, at the same Rayleigh number, the rate of heat transfer from the enclosure which the circular cylinder is located inside is better.