A multi-physics model coupling electrochemical kinetics with fluid dynamics has been developed to simulate the transport phenomena in a single-chamber solid oxide fuel cell (SC-SOFC). A typical SC-SOFC is composed of a rectangular duct, planar positive electrode-electrolyte-negative electrode (PEN) assembly and planar inter-connecters. The finite element method is employed for calculation, which is based on the conservation of mass, momentum, energy, species, and electrical charge. In the gas chamber, flow is modelled by considering convective-diffusive transport and in porous electrodes the flow is governed by Darcy' s law. Ohm's law accounts for ionic and electrical potential inside the cell. The model is tested for various ratios of air-hydrogen gas mixtures at different levels of operating voltages. The effect of over-potential on the fluid flow, mass transport and electrochemistry is examined. Detailed electrochemical/mass characteristics such as flow velocities, species mass fraction and current density distributions are presented. The results can provide a good basis for optimizing the geometry of the SC-SOFC stack.