Eur. Phys. J. Plus (2022) 137: 275
https://doi.org/10.1140/epjp/s13360-022-02451-x

Regular Article

Constructal entropy generation rate minimization of heat conduction for leaf-shaped quadrilateral heat generation body

¹ Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, 430205, Wuhan, People’s Republic of China
² Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, 430205, Wuhan, People’s Republic of China
³ School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, 430205, Wuhan, People’s Republic of China

^b lingenchen@hotmail.com, 2506715339@qq.com

Received: 11 January 2022
Accepted: 7 February 2022
Published online: 25 February 2022

Abstract

Combining the constructal theory with the entropy generation minimization theory, the heat conduction constructal optimization of the leaf-shaped quadrilateral heat generation body (HGB) established in the existing literature is obtained. The constructal optimization of the leaf-shaped quadrilateral HGB with the entropy generation rate (EGR) as optimization objective is studied. The influence of the number ($n$) of branches of the central high thermal conductivity channel (HTCC) and the angle ($\theta$) between the branch HTCCs and the central HTCC on the optimal construct of the leaf-shaped quadrilateral HGB is studied. The difference between the optimal constructs of the leaf-shaped quadrilateral HGB with the EGR and the maximum temperature difference (MTD) as the optimization objectives are compared. The results show that the optimal aspect ratio and EGR of the leaf-shaped quadrilateral HGB decrease slightly with the increase in the number ($n$) of branches of the central HTCC ($n\ge 20$). Therefore, increasing the complexity of the HTCCs in the HGB can reduce the EGR of the HGB. When the porosity of HTCCs of leaf-shaped quadrilateral HGB is equal to 0.15 and the number ($n$) of branches of the central HTCC is 30, the dimensionless minimum EGR with minimum EGR is 5.204, while the dimensionless minimum EGR with minimum MTD is 5.521, and the optimal aspect ratio with minimum EGR is 1.172, while the optimal aspect ratio with minimum MTD is 0.828, and their optimal constructs are both branch HTCCs perpendicular to the central HTCC.