Page 105 - Introduction to Transfer Phenomena in PEM Fuel Cells

94 Introduction to Transfer Phenomena in PEM Fuel Cells


(
eff
⋅∇
– ∇ρ⋅
D
w is the Fick’s term for the diffusion of species in a
) i
i
porous medium.
The source term (S s,i) is cancelled out everywhere in the cell with the
exception of the catalytic layer where the species are consumed or generated
during the electrochemical reaction. In this case, the source term is given by
the following equations [BAR 05]:
– for H 2:
M H
S s,H 2 = − i ⋅ 2F 2 [3.19]
a
– for O 2:
M O
S s,O 2 =− i ⋅ 4F 2 [3.20]
c
– for H 2O (vapor):
S s,HO(g) =δ .A ⋅ ( w sat − w HO(g) ) [3.21]
fg
2
2
– for H 2O (liquid):

M
HO
S s,H O(l) =+ i ⋅ 2F 2 − δ .A ⋅ ( w sat − w H O(g) ) [3.22]
fg
c
2
2
where:
–2
–1
– δ is the evaporation coefficient, in [kg.m .s ];
–1
– A is the phase change area per volume unit, in [m ];
fg
– w sat is the maximum mass fraction of water vapor in the dry gas (at

saturation), in kg HO ⋅ kg gas   − 1   ;

2
– w HO(g) is the mass fraction of the water vapor in the dry gas, in
2
 kg ⋅ kg − 1  .
 HO gas   
2