Constructal Design of Rectangular Fin Intruded into Different Surfaces of Forced Convective Lid-Driven Cavity Flow

The present work shows a numerical study about laminar, steady and forced convective lid-driven square cavity flow with rectangular fin inserted on different cavity surfaces. The main purpose is to maximize the heat transfer between fin and cavity flow and evaluate geometry influence by means of Constructal Design. The problem is subject to two constraints: lid-driven cavity and intruded fin areas. The ratio between the fin and cavity areas is kept fixed (phi = 0.05). The investigated geometry has two degrees of freedom (DOFs), the aspect ratio of the cavity, which is H/L = 1, and the fin aspect ratio (H-1/L-1) which is swept in the range 0.1 <= H-1/L-1 <= 10. The effect of the fin geometry over the spatial-averaged Nusselt number (Nu(H)) over bar is investigated for several Reynolds numbers: Re-H = 10, 50, 100, 200, 500 and 1000. For all simulations the Prantdl number is fixed (Pr = 0.71). The fin is intruded in the middle point of three different surfaces of lid-driven cavity (upstream, downstream or lower). The conservation equations of mass, momentum and energy are numerically solved with the Finite Volume Method. As expected, fin geometry had strong influence over (Nu(H)) over bar for all evaluated Re-H. The highest (Nu(H)) over bar was obtained for fins intruded in the downstream surface for 50 <= Re-H <= 500, while for Re-H = 1000, the intrusion of the fin in the upstream surface led to the highest thermal performance, i.e., the best shape and placement of the fin depends on the magnitude of Re-H.