Page 153 - Introduction to Transfer Phenomena in PEM Fuel Cells

142 Introduction to Transfer Phenomena in PEM Fuel Cells
rev
Sørensen and Kjelstrup [SOR 02] indicated that ΔS = 163.12 [J.mol .K ],

reac
for T = 353 K. The corresponding heat flow Q
expressed in [kW.m ] is
written for a current density,i , and for water in the liquid form: –1 –2 –1
– for the heat flow at the anode, we write:

Q reac = j .Q reac [4.30]
a
a
2F
– for the cathode:

Q reac = j .Q reac [4.31]
c
c
2F
The two electrodes are therefore sources of heat. However, few relevant
values exist for the half-reaction occurring at the anode, the authors of
[KJE 03, WU 07] believed that the reaction is athermic, that is, the heat is
considered to be produced at the cathode. According to their results, we will
only have to consider the heat flow for the cathode:
Q act =− 48.7 j [4.32]
a
2F
4.5.2.2. Heat flow by electrochemical activation
The irreversibility of electrochemical reactions results in overvoltages at
the electrodes [ROS 03]. According to the theory of the activated complex,
these electrochemical reactions are responsible for the degradation of part of
the energy created by the reaction [RAM 09]. The writing of the Butler–
Volmer law, modeling the reaction activation phenomena or the modeling of
the coupled mass and charge transfers at the electrode, makes it possible to
estimate the corresponding heat sources. These quantities of heat are written
according to the variation in entropy, such that:

Q act =− T ⋅Δ S irr [4.33]
a
a
and:

Q act =− T ⋅Δ S irr [4.34]
c
c