Page 335 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Cell. Stack and System Modelling 3 11

heat generation (always exothermic). Reversible heat generation is associated
with the change of entropy occurring as a result of the electrochemical reaction.
It is generated at the two electrodes in unequal amounts. In the case of hydrogen
oxidation, the reversible heat generation at the anode per unit of projected area
of the anode is

Here Si is the entropy of the species i; that is, SO2 is the entropy of 02, S& is
the transported entropy of the oxygen ion, and SEI is the transported entropy
of the electrons. The effect represented by Eq. (28a) is positive but relatively
small [33]. The reversible heat generated at the cathode per unit projected area

-
Qrev,c = T(S@ - $SO, 2gJi/2F (28b)
is much larger and negative. Because the sum of the effects is equal to

it follows that almost the entire entropic heat effect of the hydrogen oxidation
reaction is released at the cathode. In some designs (with relatively thick
electrolyte or thick anode) this may lead to significant temperature gradients,
especially because cathode polarisation is usually dominant over anode
polarisation, which further contributes to local heating at the cathode.
Conceptually, one can split the overall entropic effect, Eq. (28c), in two equal
but opposite heat effects occurring at the two electrode-electrolyte interfaces. For
example, the heat effect at the anode is
Qw.a = T(iS~o2 - rb - 2g!)i/2F (284

while that at the cathode is given by Eq. (28b). In that case, the overall reversible
heat effect due to hydrogen oxidation (Eq. 28c) must be accounted for separately
in the anode fuel gas channel. The advantage of introducing such a symmetric
expression for the reversible heat effect is that in principle it allows taking
into account heat development due to diffusion effects in the solid electrolyte
upon current passage. However, in an SOFC these effects are minor compared
with the Joule heating due to the ohmic resistance of the electrolyte included in
Qohm (Eq. 2 7).
Irreversible heat generation due to the electrochemical reaction can be
concisely represented by the local planar heat source for a two-electron reaction:

Qirr = -(~a + ~c)i/2F (29)

Using an approximate electrochemical performance model, as discussed in
Section 11.2, or a more detailed electrode-level model, as will be discussed
in Section 11.8, the polarisation components can be estimated and the heat