## 4 Discussion and Conclusions  
### Discussion  
As mentioned in this work, by means of numerical simulations, five designs of bipolar plate geometries of fuel cells were made and compared to different air flow fields adjacent to a PEMFC oxygen cathode. Based on the obtained results, we can mention that in Designs 1 and 2 (Figure 2), the flow rate observed was very slow at the square corners when the flow changed direction abruptly (Figure 2A). In this sense, it is possible to suppose that the water of the system could accumulate in the mentioned corners, and consequently, an uneven distribution of gas and current can be observed. A region of very slow flow velocity was not observed when the direction of flow gradually changed (Figure 2B). Figure 2C,D presents the electric current distributions at a high potential of a high cathode (0.8 V). Figure 3 shows the variation of electric current in the axis, and the electric current gradually decreased along the axis and with the maximum value near the input. Several reports showed the comparisons of designs in terms of pressure drop with the increase in the Reynolds number (Equation (9)). According to [PERSON] [31] and [PERSON] [32], for the square serpentine geometries (Design 1) the pressure drops are higher compared to the designs with curves (Design 2). A large pressure drop leads to inefficient fuel cell performance. In addition, because the lack of fuel is more likely to occur in Design 1, Design 2 was selected as the standard to be modified to create Design 3; see Figure 1C. The mass fraction distributions were more uniform in Designs 4 and 5 than in Designs 1, 2, and 3. With a cathode overpotential of 0.66 V, the final mass fraction of oxygen in the gas diffusion layer was slightly below 0.123 in Design 3. In contrast, in Designs 4 and 5, the final oxygen mass fractions were slightly higher than 0.137. In Figure 6, the current density distributions for Designs 3-5 can be observed under a cell voltage of 0.52 V, and the highest current density was obtained at the input where the oxygen concentration was the highest. Figure 6 clearly shows that the electrical current density at the output was lower in Design 3, and consequently, less efficient cell performance was expected. Designs 4 and 5 produced more uniform distributions of electric current density over the porous cathode than Design 3. Therefore, Designs 4 and 5 can offer higher yields. At low electrical demands, the performance of all fuel cells was governed by the kinetics of the electrode (Equation (6)). In this case, the differences between the gas distribution designs were minimal. The performance of Design 3 became limited in mass transport. With higher electrical demands, the performance of Design 3 deteriorated further (Table 5). With an overpotential of 0.82 V, the total current (1811 mA) was significantly less than the total electric current for Design 5 (2127 mA). The distributions of the oxygen mass fraction for Designs 3-5 are shown in Figure 5. These appeared to be more uniform in Design 4 or 5 than in Designs 1, 2, and 3. [PERSON] [9] and [PERSON] [33] showed that the profiles of current density exhibited better distributions with the re-direct pattern design, to produce a more efficient fuel cell. Our results were in agreement with those presented by this author. On the other hand, [PERSON] [33] observed poor current distributions with parallel flow fields. Figure 6 shows the current density distributions for Designs 3-5, for which the cell voltage fell below 0.52 V (that is, 0.66 V of cathode over potential). The highest current density was obtained at the entrance where the oxygen concentration was the highest. Figure 6 clearly shows that the electrical current density at the output was lower in Design 3, and consequently, less efficient cell performance was expected. With an overpotential of 0.82 V, the total current was 1811 mA. It was significantly lower than the total electric current for Design 5 (2127 mA).