Constructal tree-shaped fins

A tree-like fin is investigated and optimized by the constructal optimization method. The tree shape is not mimicked. Rather, the T-shaped fin-which was optimized in a previous paper-is enhanced geometrically. This fin is allowed to grow new branches to allow more of the fin-material to get to the surface area and transfer heat directly to the reservoir. For that, the new fin is adding more branches in each major step of the optimization process until an optimum shape-that delivers the maximum base heat-is found. Fin material (volume fraction) and fin allocated volume (frontal area) are constrained. In this paper the tree-shaped fin is kept uniform as in uniform thicknesses of the stem and the branches, and an equal length and equal thicknesses of all branches. The thermal performance of the optimized tree-shaped fin is found to be much better than the performance of the longitudinal fin and the optimized T-shaped fins, and it has a compact size.