Page 320 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

296 High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications

neglected for SOFC flows. A user-defined source term, Qk, can be used to represent
in- and outflows due to electrode reactions at the boundary of the flow field.
Equation (3) provides details of gas flow movements. The full treatment
requires a rigorous computational fluid dynamics (CFD) tool. Startup and
transient processes as well as variations in certain operating parameters may
have a sizeable effect on flow and concentration profiles, but the effect on overall
electrochemical performance of the cell is not necessarily of the same order.
Sometimes it is desirable to make a simplification such as assuming laminar
flow to reduce the computation cost and allow quick estimates of certain flow
properties. For example, the pressure drop of a laminar flow through a channel
can be estimated as

AP = (1/2)pv2fl/(ReDh) (4)

where Re is the Dh-based Reynolds number, Dh is the hydraulic diameter, I is
the length of the flow path, andfdepends on the shape of the cross section of the
channel, e.g.,f= 56.8 and 64 for a square and a round channel, respectively [3].
Such simplification can reduce the computation cost significantly [4].

11.23 Energy Balance
The temperature field and local heat fluxes in the gas phase are governed by the
energy balance:

Here cp is specific heat, h is thermal conductivity, Q is the nonviscous volumetric
heat generation term, Qvis is the viscous heat-generation term, Wv is viscous
work, and Ek is turbulent kinetic energy. The volumetric heat source Q
represents heat generation by the electrochemical reactions (planar heat sources
being expressed on volumetric basis), chemical reactions (e.g., hydrocarbon
reforming and CO water shift reaction), and Joule heating (due to ohmic
resistance of electrolyte and electrodes). Without the last four terms, Eq. (5) also
applies to the solid components of the fuel cell. These components consist of the
Eositive electrode, the electrolyte, and the negative electrode (PEN) elements and
the interconnect (IC) or bipolar plate. The PEN is sometimes assigned lumped
properties for heat transfer modelling.
Heat transfer between cell components must also be accounted for, either as
boundary conditions of Eq. (5) (boundary heat flows) or as a volumetric heat
source (contributing to Q in Eq. (5)). These heat source terms due to interfacial
heat transfer occur mainly in two ways [ 51:

0 Between cell component layers and flowing gas streams, e.g., between the
anode or anode side of the PEN and the fuel gas stream or between
the interconnect and the oxidant gas stream. This type of heat transfer is
best described in terms of convective heat transfer coefficient h.