Optimizing Passive Thermal Enhancement via Embedded Fins: A Multi-Parametric Study of Natural Convection in Square Cavities

Internal fins are commonly utilized as a passive technique to enhance natural convection, but their efficiency depends on complex interplay between fin design, material properties, and convective strength. This study presents an extensive numerical analysis of buoyancy-driven flow in square cavities containing a single horizontal fin on the hot wall. Over 9000 simulations were conducted, methodically varying the Rayleigh number (Ra = 10 to 10⁵), Prandtl number (Pr = 0.1 to 10), and fin characteristics, such as length, vertical position, thickness, and the thermal conductivity ratio (up to 1000), to assess their overall impact on thermal efficiency. Thermal enhancements compared to scenarios without fins are quantified using local and average Nusselt numbers, as well as a Nusselt number ratio (NNR). The results reveal that, contrary to conventional beliefs, long fins positioned centrally can actually decrease heat transfer by up to 11.8% at high Ra and Pr due to the disruption of thermal plumes and diminished circulation. Conversely, shorter fins located near the cavity’s top and bottom wall edges can enhance the Nusselt numbers for the hot wall by up to 8.4%, thereby positively affecting the development of thermal boundary layers. A U-shaped Nusselt number distribution related to fin placement appears at Ra ≥ 10³, where edge-aligned fins consistently outperform those positioned mid-height. The benefits of high-conductivity fins become increasingly nonlinear at larger Ra, with advantages limited to designs that minimally disrupt core convective patterns. These findings challenge established notions regarding passive thermal enhancement and provide a predictive thermogeometric framework for designing enclosures. The results can be directly applied to passive cooling systems in electronics, battery packs, solar thermal collectors, and energy-efficient buildings, where optimizing heat transfer is vital without employing active control methods.