## Equations

The relation between operating cell voltage and current can be simply expressed by Ohm's law.

where, Za, Zc, Zir are anode polarization, cathode polarization and internal resistance, respectively.

Za, Zc are the function of the gas composition and temperature.

_ A p za = Ci • (P„,) " • (PcoJ " ■ (P O c • (Pco) * • Exp( ) (2)

Where, Ci and C2 are constants, AE is the activation energy. The power index a, b, c, d, e and f were estimated empirically'21. And Zm is the function of the gas

temperature .

E is the equilibrium potential obtained from Nernst equation.

Where, E° is the standard potential, F is Faraday constant. The equilibrium partial pressure of the anode gases were obtained from the thermodynamic equilibrium constant considering the water-gas shift reaction'4'.

By the assumption of the steady state and uniform current in differential element, material balance can be expressed as follows.

dx nFù>x where, Mi is the mole flow rate of each gas, Ax is the length of unit grid. Energy balance considering mass transfer and heat loss is,

KjArg1 - MACi • & — H ha = — (E — V) ■ 1 (6)

where, Kj, Aj are the thermal conductivity and the heat conduction area of each direction, G is the heat capacity of each gas, Hioss is the heat loss from the stack.

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