High-current regime

Note that Equation 4.291 approximates f only close to the membrane. However, this is exactly what is needed for the heat transport problem outside the conversion domain, the proton current and the reaction rate are small. This region, therefore, is of no interest as it does not contribute to heat production. 

Using Equation 4.291 in Equation 4.284 yields an equation for the heat balance  

Integrating this equation from 0 to x and taking into account Equation 4.285 gives 

Setting X = Icl and taking into account that ( cl) = 0 results in the heat flux 

In the HC regime, Ich/la 1 and the exponent e ]) —lcL/la) is vanishingly small. Neglecting this exponent, one finds heat flux leaving the CCL 

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Any model of PEFC must cover at least the three basic processes (1) transport of reactants to/from the catalyst sites, (2) charged particles production or consumption at these sites, and (3) transport of charged particles (electron and proton currents). The simplest realistic model of PEFC must take into account these processes. (More sophisticated models, particularly important for high current regimes, ought to take into account on the same footing the production of water at the cathode side and dynamic liquid-vapor phase balance.)... 

The low- and high-current regimes are separated by the transition region (Figure 23.2). In this region, the exact solution for the shapes of local parameters in the CL does not exist However, Eq. (23.11) approximates well the exact numerical curve in this region. 

Figure 23.2 The general polarization curve of the catalyst layer with ideal feed transport. Solid lines, analytical solutions for the low- and high-current regimes points, the exact numerical solution to the system [Eqs.(23.6) and (23.7)] dashed line, the approximate analytical curve, Eq. (23.11),...

The critical current density [Eqs. (23.15) and (23.16)] indicates the left (low-current) boundary of the transition region (/o/jcrit = ) For the estimate, we may neglect the finite width of the transition region and assume thatj crit separates the low- and high-current regimes of CL operation. 

In this section, we are interested in the high-current regime of CL operation. In this regime, the second exponent in Eq. (23.6) can be neglected and the equation takes the form... 

This figure shows the physical origin of the Tafel slope doubling in the high-current regime (see the next page). Poor proton transport induces a... 

The function (3.7) is shown in Figure 3.2. The parameters for this plot are listed in Table 3.1. As can be seen, the characteristic current density is small (the last column in Table 3.1) and hence this set of parameters prescribes the high-current regime of cell operation. 

This result differs from (4.141) by a constant factor 1 — J/jo in the denominator. However, after normalization (4.134) this factor vanishes and we again arrive at (4.143). A similar procedure for the high-current regime leads to (4.148). Thus, accounting for oxygen transport loss in the GDL does not affect the optimal shape of catalyst loading along the channel. 

Figure 4.22 Voltage loss due to finite hydrogen utilization u in the high-current regime 2 In (2 (l — y/l — u) /u). When utilization is above 80%, the voltage loss grows dramatically.

The model allows deriving the approximate polarization curve of the CCL in the supercritical (high-current) regime. In this regime, Coxfi — 0 and hence... 

Heat flux from the catalyst layer (W cm ). Equation 4.298 Heat flux from the CL in the high-current regime (W Equation 4.294... 

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