Constructal T-shaped fins

Abstract

This paper reports the geometric (constructal) optimization of T-shaped fin assemblies, where the objective is to maximize the global thermal conductance of the assembly, subject to total volume and fin-material constraints. Assemblies of plate fins and cylindrical fins are considered. It is shown that every geometric feature of the assembly is delivered by the optimization principle and the constraints. These optimal features are reported in dimensionless terms for this entire class of fin assemblies. Corresponding results are developed for more evolved versions of the T-shaped assembly, namely, the tau-shaped assembly where the free ends of the thinner fins are bent, the tau-shaped assembly that is narrower than the space allocated to it, and the umbrella-shaped construct containing cylindrical fins. The results show that some of the optimized geometrical features are relatively robust, i.e., insensitive to changes in some of the design parameters.