Constructal design of a semi-elliptical fin inserted in a lid-driven square cavity with mixed convection

The present study is focused on the geometric optimization, according to Constructal Design, of a semi-elliptical morphing fin, i.e. a fin that can vary its dimensions, inserted into a lid-driven square cavity under mixed convection. The fluid flow is considered incompressible, two-dimensional, laminar and at the steady state. Conservation equations of mass, momentum and energy are solved numerically by means of the Finite Volume Method. Moreover, buoyancy forces are modeled with Boussinesq approximation. The main purpose here is to maximize the dimensionless heat transfer rate between the heated fin and the surrounding flow for different Reynolds (ReH = 10, 102 and 103) and Rayleigh (RaH = 103, 104, 105 and 106) numbers keeping constant the Prandtl number (Pr = 0.71). The studied domain has two constraints (areas of fin and cavity) and one degree of freedom given by the aspect ratio between the height and length of the fin (H1/L1), which is evaluated in three different surfaces of the cavity and four different area fractions of the fin. Results showed that the optimal configurations presented a gain in the thermal performance on the order of 40% in relation to other geometries. Finally, it is worth to mention that the optimal shapes here discovered are highly influenced by Reynolds and Rayleigh numbers.