Natural convection in a circular enclosure with an internal cylinder of regular polygon geometry

This work presents a numerical investigation on the natural convection heat transfer in a circular enclosure with an internal cylinder at Ra=103-106 in both conduction and convection dominant regimes. The cross-section of the cylinder is of regular polygon geometry with various numbers of edges, including circle, triangle, square, pentagon and hexagon. The polygon cylinders are positioned at two orientations, i.e., the corner-upward and edge-upward orientations where one of the sharp corners or flat edges faces upward. The simulations are performed using our in-house fourth-order finite difference code which is well validated. Our objective is to explore the effects of cylinder geometry and orientation on the thermal and flow characteristics. The results are presented and analysed by the total equivalent conductivity coefficient for the quantitative assessment of the contribution of fluid circulation, the streamlines and thermal fields for the flow pattern and qualitative evaluation of heat transfer performance, and the distributions of local heat transfer rate on the surfaces of cylinder and enclosure. We also perform the first synergy principle analysis on this physical model to identify how the fluid circulation contributes to the heat transfer and its spatial behaviours. Numerical results reveal that the corner-upward orientation generally exhibits better heat transfer performance by permitting the well development of flow above the cylinder and in the top region of the enclosure.