## 2 Methods
### Data Acquisition
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Temperature, \(T_{0}\) & 353.15 K \\ Cathode inlet velocity, \(u_{\text{c}}\) & 10.0 m\(\cdot\)s\({}^{-1}\) \\ Cathode relative humidity, \(RH_{\text{c}}\) & 1.0 \\ Thickness of the GDL; MPL; CL; membrane, & 300.0 \(\upmu\)m; 40.0 \(\upmu\)m; \\ \(\delta_{\text{GDL}}\); \(\delta_{\text{MPL}}\); \(\delta_{\text{CL}}\); \(\delta_{\text{m}}\) & 10.0 \(\upmu\)m; 25.4 \(\upmu\)m \\ Length; Width; Depth of the channel, & 10 cm; 1 mm; 1 mm \\ \(L\); \(W\); \(d\) & 2.0 \(\times\) 10\({}^{-4}\) m\({}^{2}\) \\ Activation area, \(A_{\text{act}}\) & 1.0 \(\times\) 10\({}^{-4}\) m\({}^{2}\) \\ Contact area between the GDL and channel, \(A_{\text{CH}}\) & 1.0 \(\times\) 10\({}^{-4}\) m\({}^{2}\) \\ Inlet area, \(A_{\text{in}}\) & 1.0 \(\times\) 10\({}^{-6}\) m\({}^{2}\) \\ Porosity of the GDL; MPL; CL & 0.6; 0.4; 0.3 \\ \(\epsilon_{\text{GDL}}\); \(\epsilon_{\text{MPL}}\); CL & 110\({}^{\circ}\); 120\({}^{\circ}\); 95\({}^{\circ}\) \\ Contact angle of the GDL; MPL; CL, & 1.0 \(\times\) 10\({}^{-11}\) m\({}^{2}\); 1.0 \(\times\) 10\({}^{-12}\) m\({}^{2}\); \\ Permeability of the GDL; MPL; CL; membrane, & 1.0 \(\times\) 10\({}^{-11}\) m\({}^{2}\); 1.0 \(\times\) 10\({}^{-12}\) m\({}^{2}\); \\ \(K_{\text{GDL}}\); \(K_{\text{MPL}}\); \(K_{\text{CL}}\); \(K_{\text{m}}\) & 1.0 \(\times\) 10\({}^{-13}\) m\({}^{2}\); 2.0 \(\times\) 10\({}^{-20}\) m\({}^{2}\) \\ Ionomer fraction of the anode and cathode CL, \(\omega_{\text{a}}\); \(\omega_{\text{c}}\) & 0.25, 0.25 \\ Transfer coefficient, \(\alpha\); & 0.5 \\ Reference exchange current density of & 2.0 \(\times\) 10\({}^{3}\) A\(\cdot\)m\({}^{-2}\); 1.0 \(\times\) 10\({}^{-5}\) A\(\cdot\)m\({}^{-2}\) \\ anode and cathode \(t_{0,\text{a}}^{\text{ref.}}\); \(t_{0,\text{c}}^{\text{ref.}}\) & 2.0 \(\times\) 10\({}^{3}\) A\(\cdot\)m\({}^{-2}\); 1.0 \(\times\) 10\({}^{-5}\) A\(\cdot\)m\({}^{-2}\) \\ Reference reactant concentration of & & \\ anode and cathode, \(c_{\text{H}_{2}}^{\text{ref.}}\); \(c_{\text{O}_{2}}^{\text{ref.}}\) & 41 mol\(\cdot\)m\({}^{-3}\); 41 mol\(\cdot\)m\({}^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PEM fuel cell parameters. of control volumes along the channel; \(L\) (m) is the channel length; \(J\) (mol\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\)) is the convection flux along the channel; \(\rho\) (kg\(\cdot\)m\({}^{-3}\)) is the density; \(M\) (kg\(\cdot\)mol\({}^{-1}\)) is the molar weight; \(s\) is the liquid volume fraction; \(d\) (m) is the channel height. The superscripts and subscript: in and out represent the inlet and outlet of the control volume or channel, respectively; \(k-1\) and \(k\) represent the time step; \([n]\) represents the control volume along the channel; \(i\) represents gas species; CH represents the channel; CH-GDL represents the interface between the channel and gas diffusion layer (GDL); act represents the activation; lq represents liquid water; w represents water. For the anode recirculation mode, liquid water in the channel could be quickly blown away and removed by the liquid-vapor separator. We assume that the liquid fraction is fixed as zero in the anode channel, and Equation (3) can be ignored. Mass and heat transfer in the electrodes are diffusion-dominated along the through-plane direction.