
477Simulation Model for Analysis and Design of Fuel Cells
where
C
j
F
M
D
n
1
1
=
m
dryHOm
drag
sat
()
. (11.54c)
Integrating,
λ
m,h
= C
2
exp(C
1
z), (11.55)
where C
2
is the constant of integration.
The particular solution is given as
λ
β
m,p
o
drag
sat
=
11
n
.
(11.56)
Combining a homogeneous and particular solution, the solution of water
distribution in the polymer membrane is given as
λ
ρ
β
m2
m
dryHO
drag
sat
o
dra
exp
211
11
2
=
+C
j
F
M
D
n
z
n
gg
sat
.
(11.57)
Equation 11.57 represents the variation of water distribution in the Naon
membrane involving two unknowns β
o
and C
2
, which are determined using
boundary conditions given by Equation 11.53.
Example 11.2
Determine water content ...