## Related Physical Laws

In order to derive the equations the structure of a fuel cell stack has been simplified. A stack is represented by a series of cells. Each cell contains a unit (including electrolyte, anode and cathode), two half-separators, a layer of fuel gas, and a layer of oxidant gas.

The time constant which is of interest for dynamic modeling should be specified. The time constant for the slowest process, which is significant to stack safe operation under load-following modes, is estimated to be in the range of a few 101 to l(r seconds (He, 1994). Those processes, with time constants much smaller than a chosen fraction of the slowest process, should preferably be eliminated from the dynamic equations. The time limit selected is 1 second, so the processes with a time constant estimated to be larger than one second are modelled in the form of dynamic equations; other processes are modelled in the form of static equations.

The current density or species concentrations distribution-in the fuel and oxidant gas channels is determined by the mass balance equation, including the cell and water-shift reactions. The temperature distribution is determined by the energy balance, including heat transfer, heat generation from both electrochemical cell and water-shift reactions, and heat generated due to losses in electrodes power generation. Furthermore, the equations of mass balance and heat balance are related to that of momentum. The major differential equations describing the dynamic processes, in a fuel cell stack use a series of mass, energy and momentum equations applying to the cell unit, separator, fuel gas and oxidant gas. In addition, auxiliary algebraic and differential equations are provided to calculate the cell electrochemical performance (e.g., cell working voltage), chemical reaction rates, heat-transfer coefficient, the mixture gas physical properties, and also the initial and the boundary conditions.

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