# A Multiscale Approach to the Numerical Simulation of the Solid Oxide Fuel Cell
## 5 Results of the Numerical Computations and Discussion
### Power Generation within the Cell  
For the discussion of the current generation, the cell which works under voltage \(0.8\,\mathrm{V}\) or load \(0.36\,\mathrm{A}\,\mathrm{cm}^{-2}\) was chosen. The wall and inlet temperatures were \(750\,\mathrm{\SIUnitSymbolCelsius}\), the fuel composition was \(\chi_{\mathrm{H_{2}}}=0.6\) and \(\chi_{\mathrm{N_{2}}}=0.4\). The total pressure in both channels equals \(101.325\,\mathrm{Pa}\). The flow rates were \(0.28\,\mathrm{L}\,\mathrm{min}^{-1}\) at the anode channel inlet and \(3.2\,\mathrm{L}\,\mathrm{min}^{-1}\) at the cathode channel inlet.  
Figure 12 shows the distribution of the averaged potential along the cell depth (the \(y\)-direction), as well as the distribution of the averaged volumic current density. The potential of the electron conducting phase is almost constant along the electrode depth, whereas the ionic potential gradually falls from the value similar to the OCV to the value a little bit higher than the operating voltage. As can be noticed, the averaged volumic current density at the TPB and DPB, and the ionic potentials, expect a large change near the interface between the electrodes and electrolyte. Most of the current is produced in this region. This is caused by the fact that the majority of the electrochemical reactions take place near the electrolyte because the mobility of oxygen ions inside the anode and cathode is low.  
Figure 13a-c show the distribution of the \(\mathrm{H_{2}}\), \(\mathrm{H_{2}O}\) and \(\mathrm{O_{2}}\) partial pressures, respectively. As can be observed, at the anode side, a large change occurs near the inlet. However, the fall in hydrogen partial pressure and the water production can be also seen in the electrolyte vicinity in almost all the length of the cell, which is caused by the electrochemical consumption of \(\mathrm{H_{2}}\) and the production of  
Figure 11: Comparison of the experimental and numerical data for the different inlet fuel compositions (\(T_{\mathrm{fur}}=750\,\mathrm{\SIUnitSymbolCelsius}\)).  
Figure 10: Comparison of the experimental and numerical data for the different furnace temperatures (\(\chi_{\mathrm{H_{2}}}=0.6\), \(\chi_{\mathrm{N_{2}}}=0.4\)).  
H\({}_{2}\)O. The smooth change in the oxygen partial pressure is observed in Figure 13c--the oxygen partial pressure changes almost only in the horizontal direction.  
Figure 12: Distribution of the averaged electronic and ionic potentials, and the average volumic current density in cell depth direction.  
Figure 13: Partial pressure distribution inside the system (not in the scale).  
Figure 14 presents the temperature distribution inside the single planar SOFC. The gases are heated near the electrodes, where the source heats are present. However, the overall temperature rise is not significant, about 1 K and the temperature field is very smooth. This effect may be caused by the thin channels filled with porous material (which enhance the heat transfer) and large inlet temperature (the same as the furnace temperature). In this configuration (the fuel cell enclosed in the constant temperate furnace, which is represented by the Dirichlet boundary conditions on the top and bottom of the system), the cell behaves as an isothermal system. However, this phenomena is desirable, since it prevents against large thermal stresses along the cell.