Page 321 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Cell, Stack and System Modelling 29 7

0 Between adjacent solid layers with different thermal conductivities, hi
(where i = cathode, anode, electrolyte, or interconnect). This type of heat
transfer may be folded into a lumped effective conductivity, for example,
for the PEN.

Alternatively, the heat transfer from the fuel gas stream to the oxidant gas
stream via a solid layer such as the PEN element or the interconnect may be
described in terms of an overall heat transfer coefficient.
For convective heat transfer at the boundary between a solid layer and a fluid,
the following continuity condition may be imposed [6]:

i(x)VTs(x).n = h[Tf(x) - Ts(x)] (6)

where n is the unit vector normal to the boundary, h is the heat transfer
coefficient, and T,(x) and TAX) are the temperatures of the solid and fluid,
respectively, at location x on the boundary. Heat transfer may also take place by
radiation from solid to gas phase or from solid to solid across a gas phase. This
can usually be represented by variants of Eq. (6). Radiative heat transfer is
especially important in higher temperature (900-1000°C) SOFC systems, for
example, the tubular design SOPC generator [ 7,8].
For steady-state simulation, the equations above are simplified by deleting the
time-dependent terms. However, the general forms are necessary for simulating
transient operating conditions such as startup and ‘load’ variation. i.e., change
in electrical output.
The combined ff ow and thermal models can be a powerful tool for addressing
various SOFC design issues. For example, during fast startup or fast cool-down,
which may be needed in automotive applications, thermal stresses that develop
within the fuel-cell stack must not exceed acceptable levels. It is therefore
necessary to model in detail the gas flows as well as heat and mass transfer
throughout the fuel-cell stack to analyse the transient temperature distribution.
The latter, in turn, may be used to predict the thermal stresses.
As an example, Figure 11.1 shows a typical planar cell stack model geometry
[9]. The upper-left portion ofthe figure shows the full stack geometry. Preheated
air is introduced at the bottom left side of the stack. The air travels across the
interconnect channels, is further heated in contact with the PEN, and exits
downward at right. In the fuel electrode (anode) side manifolds, as in the air
electrode manifold, the outlet manifold is wider than that at the inlet. The ’zoom’
view of the stack at the upper right in Figure 11.1 shows more detail of the grid.
Details of the individual flow channels are simulated using a porous media model
in the active area.
Obtained using the commercial computational fluid dynamics (CFD) software,
STAR-CD, Figure 11.2 shows the temperature distribution within the
interconnect which is subject to the largest temperature gradient, 5 minutes
after startup.
Predictions of the stress created by thermal gradients within the stack can be
used to establish control parameters for transient operations and to minimise