## 5 Results and Discussion  
In this study, the proposed two-phase model is used to describe the different physical through-plane transport processes by eight coupled PDEs (electron transport, proton transport, heat conduction, dissolved water transport, water vapor diffusion, hydrogen diffusion, oxygen diffusion, and liquid water transport). Among them, water transport considerably affects the performance of the fuel cell. The coexistence of unsaturated vapor and liquid water is considered causing the complexity of calculation solutions. The generation of dissolved water is important in proton conductivity, and the liquid water may fill the pores of the ionomer, which becomes an obstacle in gas transport. This model is mainly developed at macroscopical aspects based on many professional and special experimental devices. The study referred to many previous studies from others' research because the involved parameters are difficult to obtain. The polarization curve as the main characteristic of fuel cell performance is shown in Figure 4 with experimental data. The power density information also shows in Figure 4. The simulation curve is almost identical to the experimental curve. Under different cell voltages, the Galvani potential difference between the electron and proton-conducting phases is presented in Figure 5a,b. Figure 5a shows the conduction of protons in ACL, PEM, and CCL, whereas Figure 5b represents the conduction process of the electron in AGDL, ACL, CCL, and CGDL. The corresponding fluxes are shown in Figure 5c,d. Over time, the anode side of the fuel cell continues to expel liquid water. Although multiple processes such as water generation, evaporation, and liquefaction are continuously occurring simultaneously in the anode of the fuel cell, the internal relative humidity of the anode of the fuel cell can be considered 100% after it enters the steady state. The relative humidity in the cathode cannot be directly determined by analysis because the axial flow fan blows directly on the cathode channel. Hence, the experimental data are obtained through the sensor measurement applied on the simulation shown in Figure 6.  
Figure 4: Polarization curve and power density of fuel cell. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Explanation** & **Value** \\ \hline \(RH_{C}\) & Relative humidity in cathode GC & 20\% \\ \(S_{C}\) & Liquid saturation at CGDL/GC interface & 0.12 \\ \(T_{A}\) & Temperature of anode plate and GC & 60 \({}^{\circ}\)C \\ \(T_{C}\) & Temperature of cathode plate and GC & 58 \({}^{\circ}\)C \\ \(\alpha_{H_{2}}\) & Hydrogen mole fraction in dry fuel gas & 1.00 \\ \(\alpha_{O_{2}}\) & Oxygen mole fraction in dry oxidant gas & 0.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Operation condition. The processes of evaporation and condensation involve thermal absorption/desorption. The non-isothermal phenomenon existing in MEA is indisputable. The temperature distribution is modeled by PDE, and the result is shown in Figure 7. The temperatures of the open-cathode PEM fuel cell at the anode and cathode sides are different because the cathode channel is coupled with the cooling channel. The axial fan cools the channel directly, causing the temperature of the cathode side to be 2 \({}^{\circ}\)C below than that of the  
Figure 5: At different cell voltages, calculation of the electrode-electrolyte potentials on through-plane. Subdomain boundaries are indicated by vertical lines. The anode is on the left, the cathode on the right-hand side. (**a**) The Galvani potential of proton-conducting phase; (**b**) the Galvani potential of electron-conducting phase; (**c**) the flux of proton-conducting phase; (**d**) the flux of electron-conducting phase. Figure 6: Measurement of relative humidity variation at the cathode: (**a**) power density varied condition; (**b**) relative humidity of cathode. anode side. The heat flux \(j_{T}\) determined by Fourier's low is described in all subdomains as shown in Figure 7b.