Optimization of Heat Transfer in a Circular Cavity With and Without a Cold Cylindrical Insert

ABSTRACT This study presents a numerical investigation focused on optimizing natural convection heat transfer (HT) inside a circular cavity that features alternating heated, cooled, and insulated wall segments. The analysis addresses configurations both with and without a centrally inserted cold cylinder. The research involves two‐dimensional, steady, laminar flow of incompressible fluids, such as air (Pr = 0.71) and water (Pr = 7.1), and variation of Rayleigh numbers (Ra) ranging from 10³ to 10⁵ solved using the finite element method (FEM) in COMSOL Multiphysics. Key parameters such as the average Nusselt number (Nu avg ), entropy generation due to fluid friction ( E ff ), entropy generation due to heat transfer ( E HT ), total entropy generation ( E gen ), and Bejan number (Be) were computed to evaluate the thermal and thermodynamic performance of the system. The results indicate that Ra plays a significant role in governing convective strength and HT, while Pr has a relatively minor impact on flow structure. The introduction of a cold inner cylinder enhances fluid mixing and thermal circulation, leading to Nu avg increases of 23%, 25%, and 44% for Ra values of 10³, 10⁴, and 10⁵, respectively. While the total E gen increased by only 0.5% to 4% due to higher frictional irreversibility, the overall thermal performance showed significant improvement. Moreover, the increase in Nu avg using the internal cylinder can compensate for the adverse effect of the cylinder on the hydraulic performance. Response surface methodology (RSM) confirmed the strong correlation of Nu avg and E gen with Ra and the cylinder radius ( r ), demonstrating excellent model reliability with R ² > 0.99. The proposed configuration offers practical potential for thermal optimization in lab‐on‐chip devices, microreactors, and energy‐efficient thermal control applications.