## 7 Conclusions  
In this study, the thermal hydraulic mathematical model of the air-to-air heat exchanger with cross-corrugated triangular ducts is developed and verified. The PSO is introduced for single and multi-objective optimization of the heat exchanger. The \(j\) factor and \(f\) factor, and the thermal-economics and irreversibility are two sets of mutually conflicting objectives optimized in this work. Based on this algorithm, the channel length of fresh air \(L\), exhaust air channel length \(L_{\text{e}}\), the apex angle \(\theta\) of the isosceles triangle channels, the channel height \(H\), the heat exchanger height \(L_{\text{h}}\), and the plate thickness \(\delta_{\text{plate}}\) are considered as optimization parameters. A sensitivity analysis is carried out for investigating the effect of the design parameters on the multi-objective optimizations. The main conclusions of this study are drawn as follows:  
1. The optimum comprehensive heat transfer enhancement performance is by selecting the best result from 50 operations, when the fresh air channel length \(L_{\text{f}}\) = 0.3673 m; the exhaust air channel length \(L_{\text{e}}\) = 0.3662 m; the apex angle \(\theta\) = 0.7553 rad; the channel height is 0.0032 m; the plate thickness \(\delta_{\text{plate}}\) = 0.0006 m, and the heat exchanger height \(L_{\text{h}}\) = 0.5299 m. In addition, five sets of the selected parameters to balance between \(j\) factor and \(f\) factor are achieved as selectable to design the heat exchanger with cross-corrugated triangular ducts since each of them is a trade-off on improves heat transfer and reduces friction. 2. Five sets of optimal design parameters are selected in the thermal-economic and irreversibility multi-objective optimization. A thinner plate thickness, larger channel length, and larger heat exchanger height are propitious to balance the entropy generation rate and total annual cost. These obtained Pareto-optimal points can be selected by the designer based on the project's constraints and the available investment. 3. In this design, the apex angle \(\theta\), the channel height \(H\), and the heat exchanger height \(L_{\text{h}}\) are the most influential parameters in the global sensitivity analysis for all of the optimization objectives. Figure 7: Variation of the entropy generation rate and total annual cost with three key variables: (**a**) channel height; (**b**) apex angle; and (**c**) heat exchanger height. **Acknowledgments:** This project was jointly supported by The National Natural Science Foundation of China, No. 51566002, Guangxi Colleges and The University Key Lab of Unmanned Aerial Vehicle (UAV), No. WRJ2015 KF04, and by the Innovation Project of Guet Graduate Education, Guilin, China, No. 2016 YJCX96. **Author Contributions:** The paper was a collaborative effort of all authors. [PERSON] proposed the design ideas, made very useful comments and suggestions, contributed to the English editing and revised the article; [PERSON] performed the simulation and wrote the paper; [PERSON] analyzed the data, [PERSON] and [PERSON] gave some academic advice. **Conflicts of Interest:** The authors declare no conflict of interest. **Nomenclature**