This Study examines the performance of a ten-cell solid oxide fuel cell (SOFC) stack with a non-uniform flow rate in the stacking direction. The author develops a two-dimensional numerical method to solve the electrochemical, mass and energy equations one stack at a time. The energy equations couple the heat exchange between the interconnector and both the cell and the flowing gas of adjacent cells. Moreover, this paper considers two boundary conditions, adiabatic and constant temperature, on the top and bottom faces of the SOFC. The results show that the non-uniform inlet flow rate of the fuel dominates the current density distribution; it causes the cell voltage to vary by over 13% for both boundary conditions. In addition, the constant temperature condition in this study can produce 3% more power than with the adiabatic condition. On the other hand, the air dominates the temperature field of a SOFC, and the non-uniform inlet flow rate of the air produces a variation of 3% in the average cell temperature of the cells when the boundary condition is adiabatic. This non-uniform effect on the electrical performance of each stack is apparently larger than in the transverse direction, which has been examined in our previous research. (C) 2008 Published by Elsevier B.V.