Geometric optimization of a lid-driven cavity with two rectangular intrusions under mixed convection heat transfer: A numerical investigation motivated by constructal design

The present work aims at the geometric optimization, by means of constructal design and exhaustive search, of two rectangular fins inserted in a lid-driven cavity subjected to unsteady, incompressible, laminar, two-dimensional mixed convective flow with stable stratification. The main purpose is to maximize the dimensionless heat transfer rate ( ) and time and spatial-averaged Nusselt number ( ). The domain presents three constraints: cross-sectional areas for each fin and total area of the cavity. Two degrees of freedom are investigated, height/length ratios of the left and right rectangular fin (H1/L1 and H2/L2), considering three different fraction areas for fins and two different Richardson numbers Ri = 0.1 and 1.0, representing two conditions for mixed convective flow. All cases have constant Reynolds and Prandtl numbers (ReH = 400 and Pr = 6.0). The conservation equations of mass, momentum, and energy are solved using the Finite Volume Method. Recommendations for fins shapes were strongly affected by the performance indicators chosen. Results also indicated that asymmetric configurations for the fins with different fraction areas for each fin led to the best thermal performance. Moreover, the optimal shapes and the effect of degrees of freedom over performance indicators were also affected by the Richardson numbers investigated.