Page 334 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

3 10 High Temperature SoIid Oxide Fuel Cells: Fundamentals, Design and Applications

balanced by heat convection and conduction to and from adjacent nodes. Thus,
all nodes in the 2-D model are thermally coupled to one another. Note, however,
that in the 2-D model, the principal variable that determines the nonuniformity
of heat generation, and therefore temperature, over the 2-D surface is the
current I through each node (perpendicular to the 2-D plane). Applying the 2-D
model to a planar stack with reasonably low in-plane electrical resistance
(compared with the impedance of the electrochemical reaction), the variable V,
the voltage at a given node, is relatively constant from node to node. Because the
term (V - Vhn) is then also relatively uniform, the nonuniformity of Iis the key to
the temperature distribution. The principal cause of the nonuniformity of I, in
turn, is the asymmetry of utilisation (hence of the local driving force, the local
Eeq) imposed by the flow configuration of the planar cell.
In the 2-D cell simulation, as well as in simplified (quasi-2-D) stack-level
simulations, it is usually assumed that each side of the electrode/interconnect is
at equal potential over the whole 2-D plane of the cell. As mentioned above, this
is justified because the ohmic voltage drop in the plane of the electrodes and
interconnect layer is usually much smaller than the ohmic voltage drop across
the electrolyte and the combined polarisation of the two electrodes.
Nevertheless, in such a quasi-2-D stack model, individual fuel cells in the stack
may have different celI voltages due to different temperature, fuel distribution,
and other factors. However, the total current flow through each cell (integrated
over the plane of the PEN elements and the gas flows) must be the same. The total
stack output voltage is the sum of each individual cell voltage.
A true three-dimensional model [28-321 is necessary for a more accurate
thermal analysis of a stack or for a detailed analysis of the temperature profile at
the contact regions between PEN element, current collector/gas channel
profiles. and the interconnect layer. In those cases, a more detailed heat source
calculation is also needed. It is necessary to distinguish three different types of
heat effects acting in specific components of the fuel cell: chemical, electrical, and
electrochemical.
Chemical reactions (reforming and shift reactions) take place at the anode
side, and chemical heat effects represent an important heat source (sink) term for
the anode and the fuel channel.
The electrical heat effects are caused by resistance to current flow, which
yields ohmic heating (also called Joule heating). Ohmic heating takes place
throughout the solid structure wherever electrical current flows, for instance,
from PEN element to interconnect layer. The total ohmic resistance can be
decomposed into contributions from various cell components. If the component
material has an ohmic resistivity yi (expressed in S2 m), the ohmic heat generated
per unit volume of that computational region can be calculated from

where i is the local current density.
The electrochemical heat effect has two components: reversible or entro$c
heat effect (positive or negative, endothermic or exothermic), and irreversible