## 4 Results and Discussion  
### Model Validation  
Figure 5a,b present the validation results of the dynamic mechanistic model developed in the previous section by comparing the simulation results with the experimental data. The thermal effects on the stack performance are also analyzed using the simulation results. The hydrogen/air stoichiometric ratio is set to 1.3/2, and the operating temperature is 65 \({}^{\circ}\)C. As elaborated in the modeling section, the system voltage decay is mainly caused by the Nernst voltage and three voltage losses (activation, ohmic, concentration). The stack performance experiment verifies the trends of their fluctuations with the current density. The average error between simulation and experiment is 0.79%, and the maximum  
Figure 4: (a) Coolant inlet/outlet temperature difference mapping relative to flow rate and current; (b) particle swarm optimization algorithm; (c) artificial neural network structural diagram. error is 1.65%. The polarization curves of the simulation coincide with the experiment in Figure 5a. It can be concluded that the stack's performance is in good agreement with the experimental results. Figure 5c shows the thermographic images acquired during the temperature characterization experiment. In Figure 5(c1), in the startup stage, the temperature distribution inside the stack shows an increasing trend along the lateral direction while slightly decreasing on the rightmost side, and the higher temperature segments in the stack are concentrated in the middle, away from the coolant inlet. A possible reason for this phenomenon is that the segments near the coolant outlet have more heat exchange with the environment [13]. In addition, the electrochemical reaction generates a large amount of heat, which causes the coolant temperature to rise continuously after entering the stack, resulting in the stack temperature near the coolant outlet being significantly higher than that near the inlet. The maximum temperature difference reaches 9 \({}^{\circ}\)C. In Figure 5(c2,c3), when the current rises to 467 A and 507 A, the temperature increases with the rise in the current, and the temperature distribution characteristics are similar to those of the temperature distribution during the startup stage. The simulation results of the heat transfer model are plotted in Figure 5b. At the beginning of the simulation, the coolant inlet temperature is set to 45 \({}^{\circ}\)C, and the target temperature is 65 \({}^{\circ}\)C, the same as the experiment. For the simulation with Simulink, shown in (b3), the experimentally obtained cooling fan operating data are used as the control condition for the radiator. In (b1), starting from the 750 th second, the radiator controls the temperature near 65 \({}^{\circ}\)C through frequent start and stop. The temperature (\(\sim\)65 \({}^{\circ}\)C) is controlled, referring to the coolant temperature but with a deviation of about 1.5-2 \({}^{\circ}\)C caused by the heat dissipation. Since the temperature distribution on the stack surface usually varies, referring to the temperature distribution results from the experiments, a two-dimensional heat dissipation distribution of the 25 segments (except the surfaces of the end plates) is established in the model, denoted as  
\[Q_{atm}=\sum_{i=1}^{5}\sum_{j=1}^{5}h\cdot S_{ij}(T_{ij,st}-T_{atm}) \tag{35}\]  
Figure 5: (**a**) Polarization curves of simulation and experiment; (**b1**) coolant inlet temperature versus time without considering ambient heat dissipation; (**b2**) coolant inlet temperature versus time considering ambient heat dissipation; (**b3**) load current and fan speed versus time; (**c1**) thermographic image of the stack at startup; (**c2**) thermographic image of the stack operating at 467 A; (**c3**) thermographic image of the stack operating at 507 A.  
where \(h\) is the environmental heat dissipation coefficient and \(S_{ij}\) and \(T_{ij,st}\) are the area (m\({}^{2}\)) and average temperature (K) of the segment in row \(i\), column \(j\).