## 4 Model Validation  
The electrochemical modeling of fuel cells is numerically solved, and the results are compared with experimental data from [PERSON] [36]. In his study, an electrolyte-supported PCFC (Pt\(|\)SrCe\({}_{0.95}\)Yb\({}_{0.05}\)O\({}_{3\sim\alpha}\)\(|\)Pt) at normal atmospheric pressure fed with H\({}_{2}\) and air was used to investigate the cell performance at different temperatures. The PCFC performance is predicted using an electrochemical model, in which the electrolyte proton conductivity  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Components** & **Energy Analysis** & **Exergy Analysis** \\ \hline PCFC & \(\dot{\rm H}_{\rm out}+\dot{\rm W}_{\rm PCFC}=\dot{\rm H}_{\rm in,\rm a}+\dot{ \rm H}_{\rm in,\rm c}\) & \(\dot{\rm E}_{\rm out}+\dot{\rm W}_{\rm PCFC}=\dot{\rm E}_{\rm in,\rm a}+\dot{ \rm E}_{\rm in,\rm c}\) \\ Combustion chamber & \(\dot{\rm H}_{\rm out}=\dot{\rm H}_{\rm in}\) & \(\dot{\rm E}_{\rm out}=\dot{\rm E}_{\rm in}\) \\ Turbine & \(\dot{\rm H}_{\rm out}+\dot{\rm W}_{\rm T}=\dot{\rm H}_{\rm in}\) & \(\dot{\rm E}_{\rm out}+\dot{\rm W}_{\rm T}=\dot{\rm E}_{\rm in}\) \\ Air compressor & \(\dot{\rm H}_{\rm out}=\dot{\rm H}_{\rm in}+\dot{\rm W}_{\rm AC}\) & \(\dot{\rm E}_{\rm out}=\dot{\rm E}_{\rm in}+\dot{\rm W}_{\rm AC}\) \\ Pump & \(\dot{\rm H}_{\rm out}=\dot{\rm H}_{\rm in}+\dot{\rm W}_{\rm P}\) & \(\dot{\rm E}_{\rm out}=\dot{\rm E}_{\rm in}+\dot{\rm W}_{\rm P}\) \\ Heat exchanger & \(\dot{\rm H}_{\rm out,1}+\dot{\rm H}_{\rm out,2}=\dot{\rm H}_{\rm in,1}+\dot{ \rm H}_{\rm in,2}\) & \(\dot{\rm E}_{\rm out,1}+\dot{\rm E}_{\rm out,2}=\dot{\rm E}_{\rm in,1}+\dot{ \rm E}_{\rm in,2}\) \\ Mixer & \(\dot{\rm H}_{\rm out}=\dot{\rm H}_{\rm in,1}+\dot{\rm H}_{\rm in,2}\) & \(\dot{\rm E}_{\rm out}=\dot{\rm E}_{\rm in,1}+\dot{\rm E}_{\rm in,2}\) \\ Splitter & \(\dot{\rm H}_{\rm out,1}+\dot{\rm H}_{\rm out,2}=\dot{\rm H}_{\rm in}\) & \(\dot{\rm E}_{\rm out,1}+\dot{\rm E}_{\rm out,2}=\dot{\rm E}_{\rm in}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Energy and exergy analysis of the components used in PCFC/GT hybrid systems.  
is 225.92 exp (\(-\)6.3 \(\times\) 103/T) in S\(\cdot\)m\({}^{-1}\)[35; 40]. Pt porosity, tortuosity, and pore radius are 0.4, 5, and 0.5 [49; 50]. Our PCFC electrochemical model results show a good agreement with the experimental data as seen in Figure 4. The model established in this study is therefore reasonable and acceptable.  
Figure 4 also shows that the calculated data are approximately linear as the polarization in an electrolyte-supported cell is dominated by ohmic polarization, which has a more pronounced effect in the experiment data.  
Currently, most fuel cells are anode-supported for better performance. Therefore, in the following study, anode-supported cells are used with anode thickness of 220 \(\upmu\)m [39], cathode thickness of 50 \(\upmu\)m [8; 32; 40], and electrolyte thickness of 50 \(\upmu\)m [32; 40] to tackle the high fuel cell polarization of electrolyte-supported cells and to lower the ohmic polarization as the major loss can enhance the power of the cell. Also, this current study replaces the traditional Pt electrode material with Ni-SrCe\({}_{0.9}\)Y\({}_{0.1}\)O\({}_{3-\alpha}\) (anode) and La\({}_{0.6}\)Sr\({}_{0.4}\)Ce\({}_{0.2}\)Fe\({}_{0.8}\)O\({}_{3-\alpha}\) (cathode).  
The input properties of other components used, such as the isentropic efficiency of the turbine and compressor, are obtained from published data [27].