Page 333 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Cell, Stack and System Modelling 309

The cell- and stack-level models can improve understanding of the complex
interactions between fluid dynamic, thermal, chemical, and electrochemical
phenomena. The combined models can therefore help maximise efficiency or
power density by optimising PEN element design, cell configuration, and stack
architecture for a given set of operating conditions. Most SOFC modeIIing focuses
on cell- and stack-level performance for exactly this purpose.
Cell-level models simulate the performance of a single cell, also called a unit
cell. This is the repeating unit of a stack and consists basically of a PEN element,
an interconnect layer, and a gas channeI/current collector structure. The
desired output is the current-voltage relationship, the temperature distribution,
and the heat production in the cell. Cell-level models frequently treat the
major cell components, the PEN element, the interconnect layer, and the gas
flow, as two-dimensional (2-D) - having negligible thickness compared with
the dimensions of the flow direction [12,25-271. When the continuum
flow/thermal/electrochemical model is treated as a 2-D model, calculations of
heat production at any point of the cell plane (node of the 2-D model) can be
simplified substantially. In such a 2-D cell model (or quasi-2-D stack model), heat
generation may be determined by evaluating the change in gas composition
between the inlet and exit conditions. The total energy (heat and work) delivered
per unit time at each control volume (node) is simply

Etotal = (AH/nF)I (264

where AH is the enthalpy of formation, representing the maximum chemical
energy for the simplest H2 + 1/202 + H20 reaction. Note that Etotal is negative,
in agreement with thermodynamic sign conventions for heat and work (heat
positive when absorbed by, and work positive when performed on, the system).
The heat generation, Qgen, is then determined by subtracting from the total
energy generation the electrical work delivered per unit time externally, i.e., the
electric power:
P,, = -l.v (26b)

Therefore, the heat generated per unit time at each node is
Q,,, = (AH/nF).I + V.1 (2 64

which is sometimes expressed in terms of the 'thermoneutral voltage' Vh" =
-( AH/nF) as
thn I
Qgen = (V - V )- (264

The expressions (26c) and (26d) for Qgent because they are derived from the
overall change in thermodynamic state, account for all the various kinds of heat
generation, including Joule (or ohmic) heating, heating due to polarisation, and
entropic (TAS) heat effects. The heat development at each node, Qgen(i,j), is