Page 144 - Introduction to Transfer Phenomena in PEM Fuel Cells

Heat Transfer Phenomena 133
Δ
– T is the temperature difference between the solid structure and the
fluid.
The heat generated inside the stack can be described by Poisson’s
equation [INC 96]:
2
dT + q int = 0 [4.20]
dx 2 k
where q is the amount of heat generated per unit of volume; it is

int
considered as heat of electrical and ionic resistance and is written as:
2
q int = j ⋅ρ s [4.21]

In a porous medium, an effective thermal conductivity that takes into
account the porosity of the medium (ε) is used:

 ε 1− ε  − 1
k eff =− 2k +  +  [4.22]
s
 2k + k 3k s 
s

4.3.2. Heat dissipation by natural convection and radiation

The heat flow lost by the stack by natural convection and radiation into
the surrounding environment is written as [BAR 05]:

T − T
Q = s 0 [4.23]
dis
R th

where:
– T, T are the temperature of the stack and the environment,
s
0
respectively;
–1
– R is the thermal resistance [m.K.W ], which is given by:
th
1
R th = 1 1 [4.24]
R c + R R