Constructal optimization for leaf-like body based on maximization of heat transfer rate

A model of a first order leaf-like body (FOLLB), which is assembled by many elemental leaf-like bodies (ELLBs), is established in this paper by using Constructal theory. The maximum dimensionless heat transfer rate (DHTR) and the optimal structure of the FOLLB are obtained. It shows that there exist an optimal dimensionless cross-sectional area of the elemental vein, an optimal dimensionless thickness of the FOLLB, as well as an optimal number of ELLBs in the FOLLB which lead to the triple maximum DHTR of the FOLLB. The heat transfer performance (HTP) of the FOLLB becomes better with the increases in Biot number and the thermal conductivity ratio. When the optimal construct of the FOLLB was compared with that of the ELLB, it was found that the maximum DHTR of the FOLLB is increased by 69.83% for the same body volume, and the HTP of the body can be greatly improved.