Laminar Natural Convection in a Square Cavity with a Horizontal Fin on the Heated Wall: A Numerical Study of Fin Position and Thermal Conductivity Effects

This study numerically examines laminar natural convection within a square cavity that has a horizontally attached adiabatic fin on its heated vertical wall. The analysis employed the finite element method to investigate how fin position, length, thickness, and thermal conductivity affect heat transfer behavior over a broad spectrum of Rayleigh numbers ( Ra = 10 to 10 6 ) and Prandtl numbers ( Pr = 0.1 to 10). The findings indicate that the geometric configuration and the properties of the fluid largely influence the thermal disturbances caused by the fin. At lower Ra values, conduction is the primary mechanism, resulting in minimal impact from the fin. However, as Ra rises, convection becomes increasingly significant, with the fin positioned at mid-height ( Y fin = 0.5), significantly improving thermal mixing and flow symmetry, especially for high- Pr fluids. Extending the fin complicates vortex dynamics, whereas thickening the fin improves conductive heat transfer, thereby enhancing convection to the fluid. A new fluid-focused metric, the normalized Nusselt ratio (NNR), is introduced to evaluate the true thermal contribution of fin geometry beyond area-based scaling. It exhibits a non-monotonic response to geometric changes, with peak enhancement observed at high Ra and Pr . The findings provide practical guidance for designing passive thermal management systems in sealed enclosures, such as electronics housings, battery modules, and solar thermal collectors, where active cooling is infeasible. This study offers a scalable reference for optimizing natural convection performance in laminar regimes by characterizing the interplay between buoyancy, fluid properties, and fin geometry.