Mathematical description effective conductivity

The initial emphasis on evaluation and modeling of losses in the membrane electrolyte was required because this unique component of the PEFC is quite different from the electrolytes employed in other, low-temperature, fuel cell systems. One very important element which determines the performance of the PEFC is the water-content dependence of the protonic conductivity in the ionomeric membrane. The water profile established across and along [106]) the membrane at steady state is thus an important performance-determining element. The water profile in the membrane is determined, in turn, by the eombined effects of several flux elements presented schematically in Fig. 27. Under some conditions (typically, Pcath > Pan), an additional flux component due to hydraulic permeability has to be considered (see Eq. (16)). A mathematical description of water transport in the membrane requires knowledge of the detailed dependencies on water content of (1) the electroosmotic drag coefficient (water transport coupled to proton transport) and (2) the water diffusion coefficient. Experimental evaluation of these parameters is described in detail in Section 5.3.2. 

Thermal energy at T > 0 K can excite electrons from the valence to conduction band. The excited conduction band electron leaves behind an empty state in the valence band often termed a hole. When such a transition occurs, both bands are now partially filled and conduction can take place. It is important to note that charge carrier motion in a semiconductor is strongly influenced by scattering events at atomic centers and by the electric fields that exist between those points. To simplify the mathematical description of these phenomena, the masses of the electrons and holes are often described within the effective mass approximation where the free electron mass, is replaced with the effective mass (w for electrons or m for holes). 

The calculation of drying processes requires a knowledge of a number of characteristics of drying techniques, such as the characteristics of the material, the coefficients of conductivity and transfer, and the characteristics of shrinkage. In most cases these characteristics cannot be calculated by analysis, and it is emphasized in the description of mathematical models of the physical process that the so-called global conductivity and transfer coefficients, which reflect the total effect on the partial processes, must frequently be interpreted as experimental characteristics. Consequently, these characteristics can be determined only by adequate experiments. With experimental data it is possible to apply analytical or numerical solutions of simultaneous heat and mass transfer to practical calculations. 

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