Numerical Study of Natural Convection in a Square Enclosure with an Inner Circular Cylinder for Rayleigh Number of 10(7)

Numerical calculations are carried out for evaluating the natural convection induced by the temperature difference between a hot inner circular cylinder and a cold outer square enclosure. A two-dimensional solution for unsteady natural convection is obtained by using the finite volume method to model an inner circular cylinder that was designed by using the immersed boundary method (IBM) for a Rayleigh number of 10(7). In this study, we investigate the effect of the location (delta) of the inner cylinder, which is located along the vertical central axis of the outer enclosure, on the heat transfer and fluid flow. The natural convection changes from unsteady to steady state depending on the delta. The two critical lower bound and upper bound positions are delta(C,L) = 0.05 and delta(C,U) = 0.18, respectively. Within these defined bounds, the thermal and flow fields are in steady state.