A constructal approach applied to the cooling of semi-elliptical blocks assembled into a rectangular channel under forced convection

This study investigates numerically the design of heated semi-elliptical blocks assembled inside of forced convective channel flows. The Constructal Design method, associated with the exhaustive search, was used to determine the restrictions, the degrees of freedom, the performance indicators, and the modality to sweep the search space of solutions. The degrees of freedom were defined as the ratios between the vertical and horizontal lengths of the semi-elliptical blocks, while the blocks and channel reference areas represented the constraints. The air flow (Pr = 0.72) is assumed as two-dimensional, incompressible, laminar, and steady-state. The fluid dynamic and thermal performances are evaluated for different Reynolds numbers (ReH =10, 50, and 100). The multi-objective assessment of the problem was carried out using the Technique for Order Preference by Similarity to Ideal Solution method. Conservation equations of mass, momentum, and energy are solved numerically using the Finite Volume Method. The results indicated important gains on the thermal and fluid dynamic performances of nearly 76% and 1275%, respectively when the best and worst shapes were compared in the first optimization level. It is worth mentioning that, in the multi-objective viewpoint, the employed method above-cited correctly indicated the best configurations and the gain of performance in comparison with the pressure drop minimization and the heat transfer rate maximization.