Page 156 - Introduction to Transfer Phenomena in PEM Fuel Cells

Heat Transfer Phenomena 145
4.5.4. Water evaporation and condensation
When the water is in liquid form in part of the GDL and in the vapor
form in the other, at the interface between these two zones, the water
changes state and there will be production (or absorption) of the heat
[ROS 99]. The amount of heat required for vaporization or that released by
the condensation of a stream of water is estimated from the latent heat of
vaporization such as:

Q cond = L vap .N vap→ liq [4.40]
HO
2
and for the vaporization:


Q vapo =− L vap .N liq→ vap [4.41]
HO
2
where:

–2 –1
– N vap→ liq is the molar flow density of condensing steam, in [mol.m .s ];
HO
2
– N liq→ vap is the molar flow density of vaporizing liquid water, in
HO
2
–2
–1
[mol.m .s ].
These water flow densities are estimated from the water model found in
the literature. In addition, the passage of charged particles in a medium
causes, as already mentioned, the release of heat due to the Joule effect.
GDL and electrodes are made of carbon materials and they are good
electronic conductors; their electrical resistance is low and we neglect the
heat generated by the Joule effect due to the passage of electrons in the
electrodes, the GDL and also in the bipolar plates.

The electrical contact of the different layers is assumed to be perfect. In
summary, three heat sources (or sinks) coexist within the stack. The first is
localized at the electrodes and corresponds to the heats of reaction,
overvoltages and adsorption/desorption. The second is point sources of heat
in GDLs when there is a phase change of water. Finally, the third is a
“volume” heat source located in the membrane.