A mathematical model has been developed to simulate the electrochemistry and thermal hydraulics in a monolithic solid oxide fuel cell (MSOFC). Dividing a single cell layer into a number of nodes, the model sets up the steady-state heat and mass transfer equations for each node in a cell layer. Based on the average thermal and compositional conditions at each node and a specified cell voltage, the model calculates the Nernst potential and the resultant current, heat generation, and heat removal rates at each node. These calculations yield the temperature and the fuel and oxidant compositions and partial pressure matrices for the entire cell. The simulation also provides related performance data for the fuel cell stack, such as energy efficiency, fuel utilization, and power density. The model can be used to simulate operation with different fuel gases, such as hydrogen, coal gas, and methanol reformate. A mathematical model such as this can be used to examine the effects of changing one or more of the various design variables and to evaluate the effectiveness of fabrication improvements in technology development. In the design phase, the model can be used to determine the size of the stack that will be required for a given power rating and to make design decisions regarding structure-specific parameters, such as the thicknesses of the anode, electrolyte, cathode, and interconnect layers and dimensions of the flow channels in the anode and the cathode. The model can also be helpful to the fuel cell system operator. For example, given a particular stack, the most favorable operating conditions can be determined by determining a priori the effects of altering process variables, such as flow rates and feed conditions. 6 refs., 12 figs., 3 tabs.