Page 93 - Introduction to Transfer Phenomena in PEM Fuel Cells

82 Introduction to Transfer Phenomena in PEM Fuel Cells
At the cathode:
 S = j c

s φ
 [2.84]
  S φ m =− j c
For the remaining areas of the fuel cell:
S = 0 [2.85]
φ

For charge transport in diffusion layers, it is governed by Ohm’s law:

 
j =−σ eff ⋅∇ϕ s [2.86]
s

The charge retention is described in the electrodes by the following
continuity relation:

 
∇= [2.87]
j0

For charge transport in the membrane, the charge balance in the
membrane is written as follows:
 
∇⋅ ( −σ ⋅∇ϕ m ) 0= [2.88]
m

2.10. Conclusion

In this chapter, we were able to highlight the different theoretical values
of the reversible voltage and the voltage losses. Electrode overpotentials
were also defined, estimated and then calculated from thermodynamic
considerations. As for the actual voltage, it varies according to the required
intensity, the type of fuel cell and the operating conditions (temperature,
pressure, etc.); it is approximately 0.5 to 1.0 V.