Heat transfer assessment incorporated with entropy generation within a curved corner structure enclosing a cold domain

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 ($N{u}_{avg}$) is higher in the curved rectangle cavity compared with the curved square cavity for all $Ra$ values. Using the curved square (AR = 1.0), $N{u}_{avg}$ increases by 191.86%, while with the curved rectangle (AR = 0.5), $N{u}_{avg}$ increases by 302.63% at $Ra=10^6$. Additionally, in the case with a cooler (WC), $N{u}_{avg}$ is higher than the case WOC and $N{u}_{avg}$, and an average total entropy $\left(E{n}_{avg}\right)$ increases for both the WOC and WC cases for all $Ra$ values. Transitioning from a square to a curved rectangle (AR = 0.5) WC, $N{u}_{avg}$ increases by 329.34% at $Ra=10^6$. 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.