Page 86 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Thermodynamics 63

It should be mentioned that any reactant must have the same thermodynamic
state in the case of the reversible cell. This is, for example, not the case if we use
air as the oxidant gas. We can calculate cases like this with Eq. (2 7) of the Nernst
voltage, but however we use the ideal process the total process is not reversible
any more. The oxidation of hydrogen (Eq. (7)) is a good example to illustrate this.
Using pi as the partial pressure of the component i we get

(34)
Pi = Yi . Pj
writing yi for the molar concentration of the component i and p for the total
pressure of the system. Using Eq. (1 1) we can write

if we consider the molar flow of the fuel F as the product of the molar
concentration y and the total molar flow at the inlet I and the outlet 0 of the
anode side An. U’will be used as a variable thus the outlet 0 can be interpreted as
a space variable along the axis of the parallel flowing fuel and air defined by a
certain Uj to be obtained. The local Nernst voltage V,(Uf) depends on the local
gas concentration. The molar flow on the anode side is constant in our example
of the hydrogen oxidation and we get

and Eq. (3 5) yields

u,2 = 1 --. YH2,O (3 7)
YH2.Z

The equation of the reaction (7) shows that the molar flow of the utilised fuel is
equal to the molar flow of the produced water at the outlet 0

nH2.U = nH20.0 (38)
if the used hydrogen is dry (gH2,1 = 1). This yields

nH&C
ufH2 =---- - nH20,O (39)
n* n* - YH20,O.
Following Eq. (7) we can write for the cathode side

Practical SOFC systems operate with air instead of oxygen and with an excess
air h > 1. The incoming air flow is defined by the inlet flow of the cathode