Bifurcation to unsteady natural convection in square enclosure with a circular cylinder at Rayleigh number of 107

This study numerically investigates the effect of the location of an inner heated cylinder along a horizontal or diagonal line in a cooled enclosure on the fluid flow and heat transfer in the enclosure for a Rayleigh number Ra = 107. The flow and thermal fields bifurcate from the steady or unsteady to the unsteady or steady states at critical positions. This phenomenon occurs at both the horizontal and the diagonal lines. The major origin of the unsteady state depends on the position of the cylinder. Thus, the unsteadiness near the upper corners, the center of the enclosure, and the lower corners is governed by a series of cells known as Benard cells, the strong sway of the rising upwelling plume from the inner cylinder, and the inner vortices periodically merging and separating within the enlarged lower primary eddy, respectively. The variation in the local Nusselt number of the cylinder and enclosure is dominated by the gaps between the inner heated cylinder and the cooled enclosure, the upwelling and downwelling thermal plumes, and the upward returning flow.