A mathematical model of a single unit solid oxide fuel cell (SOFC) based on partial differential equations is presented in this paper. The model consists of mass, momentum and charge conservation equations, relating gas concentration to voltage, current density, and other relevant fuel cell parameters. The model is applied and validated on a planar disk-shape anode-supported cell. Data regarding materials' properties and kinetic parameters are taken from the open literature or derived from experimental results. A commercial tool using the finite element method is used to solve the set of equations. The simulated steady state performance of the fuel cell, for different operating conditions and current densities, is further investigated. (C) 2011 Elsevier By. All rights reserved.