Constructal design of three fins inside a lid-driven cavity

This study investigates the heat transfer between three fins in the bottom of a lid-driven cavity and the flowing fluid to find the best designs to improve heat transfer and to understand the role of geometric parameters on the system's thermal performance. The constructal design method and the exhaustive search are employed to evaluate the system and to guide the maximization of the dimensionless heat transfer rate, based on a set of numerical results. The numerical model for the flow system assumes steady, incompressible, laminar, and two-dimensional flow with stable stratification conditions. Prandtl, Richardson, and Reynolds's numbers were equal to 6.0, 0.1, and 400, respectively. The conservation equations of mass, momentum, and energy were solved with the finite volume method (FVM). The fraction of area occupied by the three fins was kept constant (phi(T) = 0.1) and two scenarios were studied (phi(1 )= 0.05, phi(2) = 0.04, phi(3) = 0.01 and phi(1) = 0.01, phi(2) = 0.04, phi(3) = 0.05). The best performance was achieved when the fin 3 had the largest area and the highest H-3/L-3 ratio. The results suggest that fin 3 dominance enhances thermal exchange, particularly for higher H-3/L-3 ratios, while fin 2 predominance is observed for lower H-3/L-3 ratios. The optimal geometry was identified as H-1/L-1 = 0.1, (H-2/L-2)(o) = 0.5, and (H-3/L-3)(oo) = 19.0, resulting in the highest heat transfer rate for the configuration phi(1) = 0.05, phi(2) = 0.04, and phi(3) = 0.01. The best-performing geometry investigated was H-1/L-1 = 0.1, (H-2/L-2)(o) = 0.5, and (H-3/L-3)(oo) = 19.0, (q ') over tilde mm = 22.8491, which is 63.9% better than the worst geometry (H-1/L-1 = 0.1, H-2/L-2 = 0.5, and H-3/L-3 = 5.0).