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 ( \({\phi }_{T}=\) ${\varphi }_T=$ 0.1) and two scenarios were studied (ϕ₁ = 0.05, ϕ₂ = 0.04, ϕ₃ = 0.01 and ϕ₁ = 0.01, ϕ₂ = 0.04, ϕ₃ = 0.05). The best performance was achieved when the fin 3 had the largest area and the highest H₃/L₃ ratio. The results suggest that fin 3 dominance enhances thermal exchange, particularly for higher H₃/L₃ ratios, while fin 2 predominance is observed for lower H₃/L₃ ratios. The optimal geometry was identified as H₁/L₁ = 0.1, (H₂/L₂)_o = 0.5, and (H₃/L₃)_oo = 19.0, resulting in the highest heat transfer rate for the configuration ϕ₁ = 0.05, ϕ₂ = 0.04, and ϕ₃ = 0.01. The best-performing geometry investigated was H₁/L₁ = 0.1, (H₂/L₂)_o = 0.5, and (H₃/L₃)_oo = 19.0, \({\widetilde{q{\prime}}}_{mm}\) ${\widetilde{q\prime }}_{\mathit{mm}}$ = 22.8491, which is 63.9% better than the worst geometry (H₁/L₁ = 0.1, H₂/L₂ = 0.5, and H₃/L₃ = 5.0).