Geometric optimization of T-shaped constructs coupled with a heat generating basement: A numerical approach motivated by Bejan’s constructal theory

Abstract

This work relies on constructal design to perform the geometric optimization of morphing T-shaped fins that remove a constant heat generation rate from a rectangular basement. The fins are bathed by a steady stream with constant ambient temperature and convective heat transfer. The body that serves as a basement for the T-shaped construct generates heat uniformly and it is perfectly insulated on the outer perimeter. It is shown numerically that the global dimensionless thermal resistance of the T-shaped construct can be minimized by geometric optimization subjected to constraints, namely, the basement area constraint, the T-shaped fins area fraction constraint and the auxiliary area fraction constraint, i.e., the ratio between the area that circumscribes the T-shaped fin and the basement area. The optimal design proved to be dependent on the degrees of freedom (L₁/L₀, t₁/t₀, H/L): first achieved results indicate that when the geometry is free to morph then the thermal performance is improved according to the constructal principle named by Bejan “optimal distribution of imperfections.”