
492 Fuel Cells
For j = 0.5 A/cm
2
,
H
2
O
and L
e
= 0.01 cm, Equation
E11.3-3 reduces to
44. β
o2
4
6
exp 5.978 10
0.5 0.01
3.86 10
14+×
×
×
=
−
−
C ..095
4.4β
o
+ 2.169 C
2
= 14.095 (E11.3-4)
Solving Equations E11.3-2 and E11.3-4, we get
β
o
= −1.3965 and C
2
= 9.3314.
Variation of water content in the membrane is given by Equation
E11.3-1 as
λ
m
= −6.1446 + 9.3314 exp(154.8705jz). (E11.3-5)
For j = 0.5 A/cm
2
, the equation reduces to
λ
m
= −6.1446 + 9.3314 exp(77.435z). (E11.3-6)
Substituting, the average water content in the membrane is given as
m
e
m
d
e
=
∫
1
0
L
x
L
λ
m
e
77.435
d
e
=− +
∫
1
6 1446 9 3314
0
L
z
z
L
..e
λ
m
e
=−
6 1446
722 577
1
77 435
.
.
.
e
.