Optimization of fin geometry in heat convection with entransy theory

The entransy theory developed in the recent years is used to optimize the aspect ratio of plate fin in heat convection. Based on a two-dimensional model, the theoretical analysis shows that the minimum thermal resistance defined with the concept of entransy dissipation corresponds to the maximum heat transfer rate when the temperature of the heating surface is fixed. On the other hand, when the heat flux of the heating surface is fixed, the minimum thermal resistance corresponds to the minimum average temperature of the heating surface. The entropy optimization is also given for the heat transfer processes. It is observed that none of the minimum entropy generation, the minimum entropy generation number, and the minimum revised entropy generation number always corresponds to the best heat transfer performance. In addition, the influence factors on the optimized aspect ratio of plate fin are also discussed. The optimized ratio decreases with the enhancement of heat convection, while it increases with fin thermal conductivity increasing.