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

Nu merical calcu lations are carried out for natural convection induced by a temperature difference between a cold outer square enclosure and a hot inner cy linder with two different geo metries (i.e. circular and square). A two-dimensional solution for natural convection is obtained, using the finite volu me method for different Rayleigh nu mbers varying over the range of (10 3 -10 5 ). 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 nu mber and the position of the inner cylinder. The results show that for both cylinders, at low Rayleigh numbers of 10 3 and 10 4 , the bifurcation fro m 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 = 10 5 , only a uni-cellu lar vortex is formed in the enclosure irrespective of the position of the inner cylinder. A lso 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 fro m the enclosure which the circular cylinder is located inside is better.