Page 298 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Testing of Electrodes, Cells and Short Stacks 275

where

Here X is the molar fraction, Pa is the air pressure and superscripts i, o signify
inlet and outlet, respectively. Nfand N, are the molar flows of fuel and air.
The assumption of a position-independent local area specific resistance is an
approximation, which is not always justifiable. Part of the anode polarisation
resistance is dependent on fuel composition. However, often this part is small. If
the cell is not isothermal, the local resistance will vary with position due to its
temperature dependence. Also the actual flow pattern may be much more
complex than just co-flow. Even so, if the fuel utilisation is large, ASR,,, derived
from Eqs. (4) and (5) will always be a better characteristic of a cell than a value
derived neglecting the fuel utilisation (Eq. (1)). More precise evaluation of ASR,,,
requires a rigorous 3-D modelling of the cell test.
For purposes of evaluating Eq. (4), the integral may be approximated by a
sum [44]:

where Emf(XH2(j)) is given by Eq. (4) with

The more terms are included in the sum, the better the approximation.
A ‘first-order’ correction for the effects of finite fuel and air utilisations may be
obtained taking only one term in the sum in which case ASR,,, should
be evaluated from Eq. (3) with

where the bar indicates ‘average’, i.e.

If there are no significant leaks in the cell or the test equipment, then both fuel
and air utilisation, and from this the compositions, may be calculated from the
flow rates and the current using Faraday’s law. Alternatively, the composition of