## 5 Conclusions  
In order to obtain the best performance of the plate-fin heat exchanger, in this paper, the heat transfer quantity, oil pressure drop and oil outlet temperature of a plate-fin heat exchanger used in the extended-range hybrid vehicle engine were taken as the optimization objectives, and the three parameters of fin angle, oil flow rate, and water flow rate were optimized. A heat exchanger fluid-solid coupling model was established based on porous media, and the correctness of the model was verified by the \(\eta\)-NTU method. Based on 45 cases of simulation results, a regression model of the optimization objective was established with SVR, and then the NSGA-II algorithm was applied to obtain a Pareto solution set containing 2000 optimal solutions. Finally, the optimal solution was evaluated comprehensively by using TOPSIS. The main conclusions are summarized as follows:  
1. There is a contradiction between heat transfer quantity and pressure drop of heat exchanger, and there is no inevitable relationship between oil outlet temperature and heat transfer quantity.
2. The heat transfer quantity of the heat exchanger is mainly influenced by the fin angle, oil flow rate, and water flow rate. The heat transfer quantity decreases as the decrease of the fin angle. When the oil flow rate is less than or equal to 10 L/min, the change of heat transfer quantity mainly depends on the oil flow rate. When the oil flow rate is greater than 10 L/min, the change of heat transfer quantity mainly depends on the water flow rate.
3. The pressure drop in the heat exchanger is mainly influenced by the fin angle and the flow rate. As the fin angle decreases from 90\({}^{\circ}\) to about 60\({}^{\circ}\), the pressure drop also decreases. However, as the fin angle continues to decrease, the pressure drop increases. The oil flow rate or the water flow rate does not affect the pressure drop variation on the other side.
4. When the fin angle is 63.01\({}^{\circ}\), the oil flow rate is 9.7 L/min and the water flow rate is 6.45 L/min, the heat exchanger achieves the best performance. Under this condition, the heat transfer quantity of the heat exchanger is 9.76 kW, the oil pressure drop is 14 kPa, and the oil outlet temperature is 65 \({}^{\circ}\)C.  
Conceptualization, S.L. and D.L.; methodology, S.L. and D.L.; software, S.L.; resources S.L; investigation, S.L. and Z.D.; data curation J.L. and Z.D.; writing-original draft preparation, S.L.; writing-review and editing, D.L.; visualization, S.L. and J.L.; funding acquisition, D.L. The manuscript was reviewed by all authors. All authors have read and agreed to the published version of the manuscript.  
University-Enterprise technical cooperation project (ZQS-JS-2020004).  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Optimization Parameters**} & \multicolumn{3}{c}{**Optimization Objectives**} \\ \hline  & \begin{tabular}{c} **Fin Angle** \\ **(Degree)** \\ \end{tabular} & \begin{tabular}{c} **Oil Flow** \\ **Rate (L/min)** \\ \end{tabular} & \begin{tabular}{c} **Water Flow** \\ **Rate (L/min)** \\ \end{tabular} & \begin{tabular}{c} **Heat Transfer** \\ **Quantity (kW)** \\ \end{tabular} & \
\begin{tabular}{c} **Oil Pressure** \\ **Drop (kPa)** \\ \end{tabular} &
\begin{tabular}{c} **Oil Outlet** \\ **Temperature (\({}^{\circ}\)C)** \\ \end{tabular} \\ \hline Optimization & 63.01 & 9.7 & 6.45 & 9.76 & 14 & 65 \\ Simulation results & 63.01 & 9.7 & 6.45 & 9.79 & 13.63 & 65.11 \\ Error (\%) & & & & 0.31 & 2.64 & 0.17 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of optimization results and simulation results under optimal parameters.