respectively。 SE is the energy source expressed by the Eq。 (12) and mainly consists of reaction and Ohmic heats [27]。

Properties of the solid material

Cell component Density (kg m−3) Effect thermal conductivity (W m−1 K−1) Specific heat (J kg−1 K−1) Porosity (%) Permeability coefficient (m2)

Inter-connector 7700 13 0。8 – –

Anode 6200 6。23 0。65 35 1。0E−12

Cathode 6000 9。6 0。9 35 1。0E−12

Electrolyte 5560 2。7 0。3 – –

where β is the transmission coefficient and β = 0。5 in this simula- tion, ηact,a and ηact,c are the activation potentials at the anode and the cathode, respectively。 i0,a and i0,c are the exchange current densities at the anode and the cathode, respectively。

A simple semi-empirical formula is used to obtained the Nernst voltage:

where E0 is the standard voltage of the cell,PH2O,PO2 and PH2 are the partial pressures of water gas, oxygen and hydrogen, respectively。

3。Numerical implementation

The cell unit analyzed in the paper represented a repeating unit in the middle of a large stack, and external walls of the cell unit were assumed to be adiabatic。 Constant temperature, delivery rate, and gaseous composition were imposed at the inlet boundaries for the fuel and air。

In the calculations, the modeling tool coupled a thermal-fluid model with an electrochemical model。 The thermal-fluid model was implemented via the commercial CFD simulation code。 First, the finite-volume Navier-Stokes and transport equations were solved to obtain the gas species concentrations and tem- peratures at each position in the cell。 Then, the information was passed to the electrochemical model, which was called via the subroutine。 Using this solution, the Nernst voltage and the cur- rent density distribution were calculated and applied to obtain heat source and species source。 Finally, gas species concentra- tions and temperature distributions were then calculated again and provide for the next iteration。 The models were coupled time after time until convergence of solution was achieved。

Fig。 2。 PEN temperature distributions in the co-flow case (a) and counter-flow case and (b) under first working conditions。

4。Simulation results and discussions

4。1。Thermo-fluid analysis

Fig。 2 shows the PEN temperature distributions in the MOLB- type SOFC under the first working conditions illustrated in Table 3。 As comparing Fig。 2(a) with Fig。 2(b), two characteris- tic features can be seen。 One is that the PEN average temperature is 1014 K with maximum and minimum temperatures of  1063

Table 3

The cell operating conditions and parameters used for simulation

Sample number Fuel Air Flow pattern

Delivery rate (v1) (m s−1)