Geometrical Assessment of Rectangular Fins at Different Surfaces and Positions on Nusselt Number of Lid-Driven Cavities under Laminar Forced Convection

This work focused on the geometric assessment by the lens of the Constructal Design of a rectangular fin placed at different surfaces and positions of lid-driven cavities under laminar forced convection. This study aims to maximize the Nusselt number (NuH) from the isothermal fin for Reynolds numbers (ReH) ranging from 10 to 1000 and a fixed Prandtl equal to 0.71. The fin was placed at the lower, upstream, and downstream cavity surfaces in five positions (S* = 0.1; 0.3; 0.5; 0.7; 0.9). The domain presents two constraints: the cavity area and the ratio fin area to cavity area kept constant for all cases (φ = 0.05). The degrees of freedom explored to maximize the Nusselt number were the ratio between the height and length of the fin (H1/L1) and the fin position along each cavity surface. The results indicated that the fin geometry and positions significantly affected the Nusselt number. The highest Nusselt number was achieved for the fin positioned on the downstream cavity surface with H1/L1 = 2.0 and S* = 0.9, improving the Nusselt number by 63.1% and 5.8% compared to the optimal shapes in the lower and upstream cavity surfaces.