Influences of Prandtl Number on Transition of Steady Natural Convection Flows in a Square Enclosure with a Circular Cylinder

Numerical investigations are carried out for steady natural convection within domains with curved geometry by using an immersed-boundary method. The method is first validated with flows induced by natural convection in the annulus between concentric circular cylinder and square enclosure as Rayleigh number equals to 106, and the grid-function convergence tests are also examined. The Prandtl number effect is further investigated within the range of 7.0 − 0.2 and the transient development of the flow is considered as well. Local and average heat transfer characteristics are fully studied around the surfaces of both inner cylinder and outer enclosure. The results show that the flow exists a transition as Prandtl number decreases to a critical value and the transition improve the internal energy transport in the present study.