2。2。  Thermo-fluid model

In the simulation, the solid and fluid domains were pided into some discrete meshes, and in each computational mesh, the conservation equations of species, mass, momentum and energy were solved using the finite volume method。

The species conservation equation:

∇(ρCk U) = ∇(Dk,eff∇ Ck ) + Ik, k = H2, O2, H2O (1) where Ik  is the rate of production or the consumption of specie

k, and given by [27]:

I (skj) (2)

k = ± (2F )

The diffusion coefficients of hydrogen and oxygen are obtained as follow [27]:

2。1。Geometry of MOLB-type SOFC

As shown in Fig。 1, a typical MOLB-type SOFC [13] is sym- metric about the mid-planes of the air and fuel channels。 For the sake of simplicity in the simulation, the calculation domain includes the region between these two mid-planes [21]。 The

The mass conservation equation:

∇· (ερU) = 0 (4)

The gas was considered as ideal gas mixtures with the densities given by:

thicknesses of anode, cathode, electrolyte and inter-connector were 0。5, 0。25, 0。05 and 1。0 mm, respectively。

where mk is the mass fraction of specie k with molecular weight

Mk。

The momentum conservation equation:

Table 1

Coefficients of the specific heats of gas

where a, b and c are relevant coefficients, as listed in Table  1。

where SM is momentum source, and SM = 0 in the flow chan- nels。 However, in the porous electrodes, Darcy law with constant porosity and permeability is applied to the model and the momentum source is obtained by [27]:

Solid material properties used in this simulation are listed in Table 2。

2。3。  Electrochemical model

The oxidant reduction reaction occurring at the cathode    is

expressed as follows:

where ueff  is the effective viscosity of the mixture gas and isgiven by [27]:

The oxygen ions transfer through the electrolyte and then  into

the active reaction areas of anode。 The electrochemical reaction of fuel at the anode is:

。[1 + (μk/μj )1/2(Mj/Mk )1/4]  。

where Xk is the molar percent of the specie k, μj and μk are kinematical viscosities of specie j and k, respectively。

The energy conservation equation:

∇· (U(ρfEf + p)) +∇ · (τU) +∇ · (keff∇ T ) + SE  = 0 (10)

So the overall reaction is:

H2 + 0。5O2 → H2O (16)

According to the Faraday law, the reaction rates depend on the current density i [15]:

Heat transfer between the fluid and the solid materials was lim- ited to conduction and convection, and the effect of   radiation

was neglected in this calculation because it is very small rela- tive to the other kinds of heat transfer。 Additionally, the effective thermal conductivities of porous electrodes are calculated by the Eq。 (11) [28]:

keff  = εkf + (1 − ε)ks (11)

where kf  and ks  are thermal conductivities of fluid and   solid,

where df/dt, dO2/dt are the molar consumption rates of fuel and

oxygen at the anode and the cathode, respectively。

During the process of energy conversion, when the charge transfer reactions at the interfaces of electrolyte and electrode are too slow to provide ions at the rate required by the demands of current, the activation polarization occurs and is defined by the Butler–Volmer equation [28]: