This research aims to comprehensively analyze the convective heat transfer in various polygonal-shaped geometries, ranging from 4-sided to 7-sided, employing common fluids such as air/water or CuO-water nanofluid. Understanding the thermal performance in different geometric configurations is crucial for optimizing thermal systems across diverse applications. Numerical simulations with appropriate validations are conducted in this study. Dimensionless parameters such as the Hartmann number (Ha), Rayleigh number (Ra), and Prandtl number (Pr) play a crucial role in assessing thermal performance, particularly with regard to the Nusselt number (Nu). Notably, the working fluid volume, heating, and cooling surfaces remain consistent across all the polygonal-shaped systems. The results demonstrate that under sidewall differential heating–cooling arrangement, the heat transfer generally enhances with the augmentation of polygon sides. The enhancement in heat transfer goes up to 11.16% (with air), 11.02% (with water), and 6.60% (with nanofluid). The findings arising from this investigation hold practical significance when it comes to enhancing and crafting the design of thermal systems with polygonal geometries, spanning diverse applications.