Page 138 - Introduction to Transfer Phenomena in PEM Fuel Cells

Heat Transfer Phenomena 127
direction across the membrane. Wöhr et al. [WÖH 98] developed a thermal
model (1D) for heat and mass transfer across the plane direction of the
PEMFC stack. While taking into account the entropic heat and that due to
the irreversibility of the reaction, the authors of this work obtained the
temperature profiles through the membrane and predicted the maximum
temperature according to the number of cells contained in the stack. Rowe
and Li [ROW 01] also developed a model (1D) taking into account the
entropy, the heat released by the irreversibility of the reaction and the latent
heat of phase change. They also took into account the heat released by the
Joule effect in the membrane and at the electrodes. Since 2002, several
studies have already been conducted to model heat transfer in a PEMFC.

Other studies agree on the importance of dealing simultaneously with
heat transfers and material transfers in the stack. Thus, Djilali and Lu [DJI
02] presented the temperature profiles in the electrode membrane assembly
(EMA) obtained from a one-dimensional model in a steady state.

The convective transport of reactive gases and water is taken into
account, but the water remains in vapor form. Weber et al. [WEB 06] and
Wang [WAN 06] set up coupled models of water and two-dimensional heat
transfers taking into account changes in water conditions. The water flows in
the GDL are not calculated by diffusion, but they are estimated from the
streams of water vaporizing in the electrodes and condensing in the
channels. These one-dimensional approaches allow a good understanding of
the phenomena in the stack core, but the variations in concentration or
temperature in the channels, resulting in a non-uniform distribution of the
current densities in the cell, are not taken into account.

4.2. Energy balances for a PEMFC

4.2.1. Energy balance for a stack

The energy balance for a PEMFC stack is described as the sum of the
incoming energies, which is equal to the sum of the outgoing energies. It is
written as follows [BAR 05]:

in 
 Q − Q out = W + Q dis + Q c [4.1]
el