Heat Flux from the Catalyst Layer

The parameters -qoRR, j, and Rqrr in Equations 1.45 and 1.46 are functions of the distance through the catalyst layer. The total heat flux from the CCL should be calculated based on the solution of the CCL performance problem this will be done in the section Heat Flux from the Catalyst Layer. ... 

In general. Equation 1.50 is nonlinear, as Rqrr and j, which appear in the source terms (1.45) and (1.46), exponentially depend on temperature. However, the CCL is thin, and the temperature variation along x is usually very small. To a good approximation, the CCL temperature in the source terms can be taken to be constant. This leads to a simple general expression for the heat flux produced in the CCL, which will be derived in the section Heat Flux from the Catalyst Layer in Chapter 4. This expression can be used in the modeling of application-relevant cells and stacks, in which quite significant in-plane temperature gradients may arise based on a nonuniform distribution of reactants. 

Kulikovsky, A. A., and McIntyre, J. 2011. Heat flux from the catalyst layer of a fuel cell. 

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... 

The right-hand side of Equation 4.282 includes the dominant sources of heat in catalyst layers of low-temperature fuel cells. Note that part of the heat flux from the CCL is transported with liquid water produced in the ORR. Being not represented explicitly, this flux is taken into account in the equations of this section (see below). 

The generation of current induces fluxes of gases, liquid water, heat and charged particles in a cell. The distribution of the respective parameters (concentrations, fields etc.) is usually very non-uniform. Furthermore, the characteristic scale of parameters variation ranges from several micrometres (the thickness of the catalyst layer) to several metres (the length of the channel). In general, the problem of fuel cell modeling is multi-scale and multi-dimensional. 

FIGURE 1.11 The dimensionless heat flux due to liquid water evaporation in the catalyst layer. The curve is obtained with the data from Table 1.3 and Py = 0, which corresponds to zero pressure of water vapor in the CCL (the limit of fast vapor removal). The heat flux is normalized to that flux at 100°C. 

Example 5.17 Estimated Temperature Gradient inside a PEFC Consider a typical PEFC operating at 0.6 V generating around 0.6 W/cm waste heat flux. Determine the expected temperature gradient from the 400-pm-thick cloth DM to the cathode catalyst layer, assuming 50% of the waste heat is removed from the cathode side. 

In applications, the reduced system is embedded in a 1 + ID computational scheme for the overall fuel cell. This includes a model of the membrane s water content and temperature, the anode GDL, and the variation of the oxygen and water vapor contents in the flow field channels in the along-the-channel direction, providing the channel conditions and fluxes which were taken as prescribed in the analysis. To present numerical results from the reduced system, we simulate this coupling by providing along-the-channel data for the oxygen and water vapor concentrations, temperature, current density, and catalyst layer production of heat and total water from a previous 1 + ID computation reported in [3]. These values vary in the y direction but are constant in time and do not couple back to the reduced simulations. 

If the efficient reaction rate is high enough, the reactant concentration drops significantly across the external boundary layer as indicated in Figure 2.18. In this case the surface concentration is lower compared to the bulk of the fluid phase (cj s < Cj i). First we will neglect eventual heat effects and assume equal temperatures in the fluid and the catalyst particle T=T = Tj). To determine the concentration profile in the particle, we first have to calculate the concentration at the external surface. This will be done based on the mass balance for the reactant Aj. At steady state, the molar flux of from the bulk to the external surface must be equal to the effective rate of transformation (see Equation 2.137). 

Consider, as a specific example, a flat catalytic surface at x = 0, with an adjacent film layer. A chemical reaction takes place at this surface at a rate r. The surface is a good heat conductor and has the temperature T°. A diffusion layer develops in front of the surface with thickness d. The reactants enter with temperature T. The concentrations of the reactants and products as well as the temperature in x = —d are known. We consider a stationary state in which the total heat flux fq, as well as the mass fluxes Jj, are independent of position and directed in the x-direction. Other variables depend on x only. On the o-side of the catalyst the mass fluxes are zero. It follows from eq 14.31 that fg = J = J g in a stationary state. The mass fluxes become proportional to the reaction rate, eq 14.32, giving J)= — n/. All chemical potential gradient terms in eq 14.15 can then be contracted, and we obtain for the entropy production in the i-phase ... 

Mass and heat flux during evaporation are strongly coupled by the heat of vaporization of water from phosphoric acid. Kablukov and Zagwosdkin [185] and Brown and Whitt [173] published data for the heat of vaporization for acid concentrations up to 100 wt%. Very little is known about the vapor-liquid interphase area within the catalytic layer, which is needed for the calculation of the evaporation mass flux. The interphase area within the porous medium depends on the acid holdup and the wetting behavior of the catalyst surface which both also... 

Since the reaction is exothermic, heat must be conducted through the catalyst particle to the external surface, and then transported through the boundary layer. Temperature gradients must be present in order for these fluxes to exist. The temperature declines from the interior of the particle through the boundary layer and to the bulk fluid stream. 

Equation (6-45) may be solved numerically for a variety of boundary conditions, such as constant T at the walls, or constant or prescribed beat flux. Because of complicated three-dimensional heat transfer pathways (shown in Figure 6-23), calculation of heat fluxes and temperature profiles in a fuel cell stack requires 3-D numerical simulation. Figure 6-25 shows temperature distribution in a representative cross-section of a fuel cell obtained by 3-D numerical simulation [28]. From Figure 6-25, it is obvious that there are significant temperature variations inside a fuel cell stack. Because most heat in a fuel cell stack is produced in the cathode catalyst layer, that layer expectedly has the highest temperature. 

---