Page 160 - Introduction to Transfer Phenomena in PEM Fuel Cells

cathode is uniform and constant (Dirichlet condition); the thermal balance of
the region (1) is written as:
T − T Heat Transfer Phenomena 149
Q = e e C e BP,A e = h air × ( BP,A − T air ) [4.44]
T
1
λ m + λ A + λ GDL + λ BP
BP
m
A
GDL
where:
– T i is the temperature at the interface (i), in [K];
– e i is the width of interface (i), in [m];
–2
–1
– h is the thermal convection coefficient, in [W.m .K ];
–1
–1
– λ is the thermal conductivity, in [W.m .K ].
Similarly for region (2):

T − T
Q = e C BP,C = h air × ( BP,C − T air ) [4.45]
T
2
e
λ GDL + λ BP
GDL
BP
The temperature distribution is obtained from Fourier’s law:
∂ T ∂  ∂ T  ∂  T  ∂ ∂  ∂ T 
ρc =  λ +   λ  +  λ  + S [4.46]
t ∂ x ∂  x ∂  y ∂  y ∂ z ∂   z ∂ 

For one-dimensional heat transfer in a steady state and without a source
term, we have:

∂ 2 T = 0 [4.47]
x ∂ 2

The solution of this equation is in the form:
⋅
+
=
T(x) c x c 2 [4.48]
1