The objective of this work is to develop a detailed dynamic mathematical SOFC model capable of describing the fundamental electrochemical and transport phenomena taking place in the SOFC. This will enable more accurate prediction of its performance under a wide range of operating conditions for design and optimisation purposes. Moreover, it will be used to construct efficient model-based control strategies since during their operation SOFCs undergo frequent changes which make the implementation of a robust control scheme imperative. In order to simulate the chemically reacting flow, a multidimensional, multicomponent, non-isothermal, dynamic model has been developed. It simulates the mass, momentum, energy and charge transport as well as the electrochemical phenomena taking place in the fuel/air channel, the porous electrodes (diffusion & catalyst layer) and the electrolyte of a single planar SOFC. Furthermore, the methane reforming as well as the water gas shift reaction kinetics are taken into account in the fuel channel and the diffusion layer of the anode electrode.
For the mass transport in the fuel/air channels as well as the porous electrodes, the Dusty-Gas model (DGM) , which is considered the most accurate of the existing mass transfer models in porous media, has been used. Recently,  the capability of multi-dimensional DGM formulations has been compared with other mass transport models used in the literature, and has been validated with experimental data . The multi-dimensional DGM exhibits superior performance in predicting the experimental results, when compared to other mass transport models at high fuel utilisation operating conditions . The Navier-Stokes equations have been used for the simulation of the momentum transport. The energy conservation equation has been used for the simulation of the energy transport, taking into account convection and conduction in the channels as well as the solid areas of the SOFC. The charge conservation equation, coupled with Ohm's law and the Butler-Volmer equation, has been used for the simulation of the electrostatic and the electrochemical phenomena taking place in the solid parts of the SOFC.
The model is implemented in a two-dimensional computational domain; however, the underlying theory is independent of the geometry used. The active catalyst layers in the electrodes are treated as finite subdomains, rather than boundaries. For the numerical solution of the highly nonlinear and strongly coupled model equations the software package COMSOL Multiphysics, which is based on the Finite Element Method (FEM), was used. Within the solution algorithm the set of PDEs are solved simultaneously.
The developed model allows prediction of the species composition profiles, as well as, ionic and electronic current density and overpotentials distribution throughout the SOFC Temperature profiles in the SOFC are also computed since the temperature gradients that arise in high temperature fuel cells, such as the SOFCs, especially when internal reforming takes place, are significantly large and cannot be neglected. Furthermore, the effect of various operating conditions as well as design parameters on the system behaviour is investigated through the polarisation curves that the model generates. It is inferred that the SOFC operates more efficiently at high operating temperatures and pressures. Detailed SOFC models can aid in the study of alternative designs and operating conditions, in order to enhance SOFC performance by providing better interpretation of the relevant physico-chemical phenomena.
Open loop dynamic responses of the average current density as well as the average power density to step changes in the SOFC operating voltage and the fuel and air inlet temperatures are computed.
Model reduction technologies, both off-line  and on-line  are exploited in order to obtain computationally amenable SOFC models for model-predictive control applications. Optimal feedback control studies are then performed using these low-order models.
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