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Fundamental and phenomenological models for cells, stacks, and complete systems of PEFC and SOFC are reviewed and their predictive power is assessed by comparing model simulations against experiments. Computationally efficient models suited for engineering design include the (1+1) dimensionality approach, which decouples the membrane in-plane and through-plane processes, and the volume-averaged-method (VAM) that considers only the lumped effect of pre-selected system components. The former model was shown to capture the measured lateral current density inhomogeneities in a PEFC and the latter was used for the optimization of commercial SOFC systems. State Space Modeling (SSM) was used to identify the main reaction pathways in SOFC and, in conjunction with the implementation of geometrically well-defined electrodes, has opened a new direction for the understanding of electrochemical reactions. Furthermore, SSM has advanced the understanding of the COpoisoning-induced anode impedance in PEFC. Detailed numerical models such as the Lattice Boltzmann (LB) method for transport in porous media and the full 3-D Computational Fluid Dynamics (CFD) Navier-Stokes simulations are addressed. These models contain all components of the relevant physics and they can improve the understanding of the related phenomena, a necessary condition for the development of both appropriate simplified models as well as reliable technologies. Within the LB framework, a technique for the characterization and computer-reconstruction of the porous electrode structure was developed using advanced pattern recognition algorithms. In CFD modeling, 3-D simulations were used to investigate SOFC with internal methane steam reforming and have exemplified the significance of porous and novel fractal channel distributors for the fuel and oxidant delivery, as well as for the cooling of PEFC. As importantly, the novel concept has been put forth of functionally designed, fractal-shaped fuel cells, showing promise of significant performance improvements over the conventional rectangular shaped units. Thermo-economic modeling for the optimization of PEFC is finally addressed.

A solid oxide fuel cell (SOFC) is a solid-state energy conversion system that converts chemical energy into electrical energy and heat at elevated temperatures. Its bipolar cells are electrochemical devices with an anode, electrolyte, and cathode that can be arranged in a planar or tubular design with separated gas chambers for fuel and oxidant. Single chamber setups have bipolar cells with reaction selective electrodes and no separation between anode and cathode compartments. A nickel/yttria-stabilized-zirconia (YSZ) cermet is the most investigated and currently most widespread anode material for the use with hydrogen as fuel. In recent years, however, doped ceria cermet anodes with nickel or copper and ceria as the ceramic phase have been introduced together with ceria as electrolyte material for the use with hydrocarbon fuels. The state-of-the-art electrolyte material is YSZ of high ionic and nearly no electronic conductivity at temperatures between 800–1000°C. In order to reduce SOFC system costs, a reduction of operation temperatures to 600–800°C is desirable and electrolytes with higher ionic conductivities than YSZ are aimed for such as bismuth oxide, lanthanum gallate or mixed conducting ceria and the use of thin electrolytes. Proton conducting perovskites are researched as alternatives to conventional oxygen conducting electrolyte materials. At the cathode, the reduction of molecular oxygen takes place predominantly on the surface. Today's state-of-the-art cathodes are LaxSr1–xMnO3–? for SOFC operating at high temperature i.e. 800–1000°C, or mixed conducting LaxSr1–xCoyFe1–yO3–? for intermediate temperature operation, i.e. 600-800°C. Among the variety of alternative materials, SmxSr1–xCoO3–? and BaxSr1–xCoxFe1–xO3–? are perovskites that show very good oxygen reduction properties. This paper reviews the materials that are used in solid oxide fuel cells and their properties as well as novel materials that are potentially applied in the near future. The possible designs of single bipolar cells are also reviewed.