where 0

is  the  electronic  conductivity  of  the  pure  material,  is  the porosity,

el     is the

volume fraction of electronic conductor phase, B is the Bruggeman factor used to include the effects of

tortuous  conduction paths  (B  is  set  as  3。5 [30]) and

pelis  the probability for electronic   conductor

particles to belong to the percolated clusters of electronic (ionic) conductor particles。

for Ni and LSM may be estimated as [26, 31],

 

The ionic conductivity of electrolyte  may be estimated as

where T is the temperature。

2。1。2。Momentum Transport

Momentum transport in the fuel or air channel can be modeled by applying the Navier–Stokes equation in conjunction with the continuity equation。

where is the density, I is the identity matrix, is the viscosity coefficient of fluid, p is the pressure and u is the velocity of fluid。

2。1。3。Mass Transport

Mass transport mechanism in channel is simple, which can be described by Fick's model associated with the mass continuity equation。

Ni  (DiCi  Ciu) 0 (9)

whereNi   is the molar flux of species i , Ci

is the molar concentration of species i ,

diffusion coefficient of species i , which equates to binary diffusion coefficient

compose of two species (H2, H2O) and the air compose of two species (O2, N2)。

by following equation。

Dijcan be evaluated

3。198108 T1。75  1 1

is diffusion volume for specie i  ( 6。1210

, 13。110

, 16。310

and 18。510

m3 mol-1  for  H  ,  H  O ,  O  and

N  , respectively [32]) and M   ( M  ) denotes molecular mass of species

2 2 2 2 i j

i  ( j ) (kg mol-1)。

Mass transport mechanisms in the porous electrodes are complex, molecular diffusion and Knudsen diffusion are taken into account。

where Deff is the equivalent diffusion coefficient of species i , which can be written as

wherexi  ( x j ) is the molar fraction of species i ( j ),

diffusion coefficient and the effective Knudsen diffusion coefficient of species  i respectively。

can be evaluated by following equations respectively [29, 33]。

where R is the universal gas constant,

r   is the pore radii and is the tortuosity factor。

2。1。4。Heat Transport

Temperature is one of the most critical factors, which significantly affects SOFC performance, because many properties of the SOFC components are temperature dependent such as the electrical and ionic conductivity, the electrochemical reaction rate, fluid properties。 For a 3D model, it is essential to take into account heat transport。

In the fluid domain, heat conduction and heat convection are must considered together。

is  the  thermal  conductivity  of  the   fluid,

NT     is  the  heat  flux,

Cf   is  the  molar

concentration of the fluid,  C   is the molar heat capacity of the fluid, which can be written as [32]