Geometrical optimization of an isothermal double Y-shaped cavity employing differential evolution algorithm with a constructal approach

This numerical work deals with constructal design (CD) to investigate a complex isothermal double-Y-cavity geometry inserted for chilling a rectangular heat-generating solid body. The purpose is to minimize the dimensionless maximum temperature excess in the solid domain for the geometry with four constraints and seven degrees of freedom (DOF), giving more freedom compared with previous cavities. The optimization process is performed with exhaustive search (ES) and differential evolution (DE) from the fourth DOF onward to reproduce the effect of the analyzed DOFs on the performance indicator and design. For square solids, the optimal geometries were obtained when the branches of the investigated cavity were stretched, covering the solid body and distributing the hot regions more homogeneously, i.e., following the optimal distribution of imperfections principle. For square solids, the performance of the present cavity was 82%, 74%, 70%, 45%, 35%, and 25% superior to I-, T-, Y-, X-, double T-, and H-cavities, and 1.0% inferior to ψ configuration. For low and high height/length (H/L) ratios of the solid domain, the optimal configurations were obtained when the double Y-shaped cavity changed to double T and I configurations, respectively, showing the impact of the constraints on the design of the cavity.