Understanding fluid dynamics and heat transfer is crucial for designing and improving various engineering systems. This study examines the heat transfer characteristics of a buoyancy-driven natural convection flow that is laminar and incompressible. The investigation also considers entropy generation (E_gen) within an octagonal cavity subject to a cold cylinder inside the cavity. The dimensionless version of the governing equations and their corresponding boundary conditions have been solved numerically using the finite element method, employing triangular mesh elements for discretization. The findings indicated that incorporating a cold cylinder inside the octagonal cavity resulted in a higher heat transfer (HT) rate than in the absence of a cold cylinder. Furthermore, using the heat flux condition led to a higher average Nusselt number (Nu_avg) and a lower Bejan number (Be) than the isothermal boundary condition. The results also showed that HT and E_gen were more significant in the Al₂O₃-H₂O nanofluid than the basic fluids such as air and water, and HT increased as χ increased. The current research demonstrates that employing the heat flux condition and incorporating nanoparticles can enhance the rate of HT and Egen. Furthermore, the thermo-fluid system should be operated at low $Ra$ to achieve greater HT effectiveness for nanofluid concerns.

In cold climates or winter countries, maintaining optimal room temperatures is essential for comfort and energy efficiency. Conventional square or rectangle‐shaped rooms often face challenges in achieving efficient heat transfer (HT) and uniform temperature distribution. To address these limitations, this study has been explored using curved corner cavities, varying their aspect ratio (AR = 1.0 and 0.5), and incorporating a circular shape cooler to enhance HT within the room. The curved corners promote better airflow circulation, creating a more efficient HT environment. The dimensionless governing equations and corresponding boundary conditions are solved numerically using the finite element method. This research aims to assess the optimized HT and entropy production within a curved corner cavity, varying their AR and enclosing a circular shape cooler to determine the most effective configuration for maximizing HT and energy efficiency in winter conditions. This study reveals that in the case without a cooler (WOC), the average Nusselt number () is higher in the curved rectangle cavity compared with the curved square cavity for all values. Using the curved square (AR = 1.0), increases by 191.86%, while with the curved rectangle (AR = 0.5), increases by 302.63% at . Additionally, in the case with a cooler (WC), is higher than the case WOC and , and an average total entropy increases for both the WOC and WC cases for all values. Transitioning from a square to a curved rectangle (AR = 0.5) WC, increases by 329.34% at . Furthermore, in the WOC case, the curved square cavity and, in the WC case, the curved rectangle show better energy efficiency and reduce environmental impact.