are the activation energies for the anode and cathode electrochemical reactions,  respectively。

p0 are the partial pressure of H2 and the partial pressure of H2O at the fuel channel inlet,

2respectively,

0    is the partial pressure of O  at the air channel inlet,

pressure of H2  and the partial pressure of H2O at the anode three phase boundaries (TPBs), respectively

is the partial pressure of O2  at the cathode TPBs,

are  the  exchange transfer

current density of anode and cathode respectively。

are the anode and cathode activation loss respectively, defined as

) is the anode (cathode) concentration loss。

2。2。2。Boundary Setting for the Mass Transport Equation

At the channel inlets, the concentration of gaseous species are imposed, whereas,  the convective fluxes are considered at the channel outlets, which mean diffusive component across the channel outlets is zero。 The boundaries B5 and B9 represent the interfaces between channel and electrode, where species fluxes are continuous。 As there is electrochemical reaction at boundaries B6

and  B7,  the  normal  molar  flux  of  hydrogen,  water  and  oxygen     are

/ (4F) , respectively。 The insulation condition is set at all other boundaries, which implies the

molar flux of species is zero。

2。2。3。Boundary Setting for the Momentum Transport Equation

At the channel inlets, the uniform inlet velocity are applied, whereas, pressure and the normal flow are imposed at the channel outlets。 The no slip condition is considered at all others boundaries, which means  u  0 。

2。2。4。Boundary Setting for the Heat Transport Equation

At the channel inlets, the uniform temperature are applied, whereas, the convective fluxes are considered  at  the  channel  outlets。  The  boundary  condition  at  boundary  B4  and  B8  become    as

n NT  Qohm  due to contact resistance。 The boundary condition at boundary B6 and B7 are specified as

n NT  Qact  Qentr

due to the reaction。 Boundary B2, B3, B10 and B11 are the interfaces between rib

and channel, where the convection heat between rib and channel is considered。

For rib, convection heat transfer rate is given as

n NT  h(Tchan/rib  Trib/chan )

(29)

For fluid in channel, convection heat transfer rate is given as

n NT   h(Tchan/rib  Trib/chan )

(30)where Tchan/ rib

channel (rib) side。

( Trib/chan ) is the temperature at the interfaces between rib and the channel on

Adiabatic boundary condition is employed at all other boundaries since the simulation region is the half of one repeating unit located at the center of stack。

2。3。 Numerical Implementation

The model was implemented in the finite element commercial software COMSOL MULTIPHYSICS。 The COMSOL stationary nonlinear solver uses an affine invariant form of the damped Newton method to solve the discretized PDEs with a relative convergence tolerance of 1×10-6。 The mesh is composed of 6,540 elements with 117,279 degrees of freedom。 The values of input parameters for the base case are summarized in Table 1 and Table 2 unless otherwise stated。

Table 1。 Model parameters。

Parameter Value

Fuel channel inlet velocity,  u fuel  (m s-1)

0