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













                                   (a)  Auode-Supported Cell












                                   (b)  Cathwle-Supported Cell
               Figure I  I .8.  Schematicdiagram of(a)anode-and(b)cathode-supportedSOFCs[47].

        not negligible); however, this adds further parameters of  uncertain magnitude
        to the polarisation expressions and detracts from their original conciseness. The
        simplicity  of  the mass-transfer-based  approach makes  it  attractive as a  first-
        order  approach  in  scale-up  modelling  [5,48,49]  because  it  is  axiomatic  in
        practice that a good fuel cell electrode should have rapid kinetics. However, for
        analysis  of  transients  other  simplified  models  may  be  preferable,  and  for
        optimisation  of  electrode  microstructure  other  specialised  models  may  be
        equally suitable.


         11.8.3 One-Dimensional Porous Electrode Models Based on Complete Concentration,
        Potential, and Current Distributions
        Simplified models  that do  not make a priori  assumptions about one or more
        dominant resistances  are often  of  the 1-D macrohomogeneous type.  The  1-D
         assumption is similar to that in mass transfer-based models. The assumption of
        macrohomogeneity,  based  on work  by  Newman  and Tobias  [SO],  has proven
        useful  in  battery  and  fuel  cell  electrode  modelling.  It  implies  that  the
        microstructure of  the electrode is homogeneous  at the level of  the continuum
         equations governing mass transfer, heat transfer, and current conduction in the
         electrode (Eqs. (1)-(7)  and (33)-(37)). This type of model can exploit solutions
         available in chemical reaction engineering practice and has been elaborated by
         several researchers in that field [ 5 1-5 51.
           Mathematically,  the  three  phases,  the  solid  electrocatalyst,  the  solid
         electrolyte, and the gas, are assumed to be present simultaneously at each point.
         The microstructure of  the electrode, which produces the interface between the
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