Effectiveness of multi-fin array orientations on convective heat transfer in viscous fluid-filled square enclosures

Enhancing natural convection with finned surfaces is essential yet challenging for effective thermal management in electronic devices, industrial cooling units, and heat-dissipation systems. This study investigates the thermal performance of four heated fin configurations—Bottom-Multi-Fin, Top-Multi-Fin, Left-Multi-Fin, and Right-Multi-Fin—placed inside a square enclosure filled with an incompressible viscous fluid, a set of configurations not previously examined in a unified framework. The walls opposite the heated fins are maintained at a cold temperature, while the adjacent walls are insulated, representing practical passive cooling conditions. The non-dimensional governing equations are solved using the Galerkin finite element method to assess the influence of the Rayleigh number number ( 10 3 ≤ R a ≤ 6 × 10 5 ) on flow structure, temperature distribution, and both local and average Nusselt numbers. Results show that the Bottom-Multi-Fin and Top-Multi-Fin configurations are conduction dominated and provide minimal enhancement in natural convection, even at high Rayleigh numbers. In contrast, the Left-Multi-Fin and Right-Multi-Fin configurations generate stronger buoyancy-driven circulation and significantly improve heat transfer. The Right-Multi-Fin arrangement delivers the highest cooling performance at elevated Rayleigh numbers, making it the most efficient orientation for natural convection applications.