Mass and Heat transfer processes in Solid oxide fuel cell (SOFC)

Project Report
2012 MVK160 Heat and Mass Transport
May 7, 2012, Lund, Sweden
Mass and Heat transfer processes in Solid oxide fuel cell (SOFC)
Chao Yang
Dept. of Energy Sciences, Faculty of Engineering,
Lund University, Box 118, 22100 Lund, Sweden
ABSTRACT
SOFC is one of the prominent fuel cell which
can convert chemical energy of hydrocarbon fuel
into electrical energy with heat change. This
process includes mass transfer of various reactant
gases (CH 4 , H 2 , H 2 O, CO, CO 2 , O 2 in this work)
and heat transfer between different reaction
processes referring to endothermic methane steam
reforming reactions (MSR) and exothermic
electrochemical reactions between different parts of
the SOFC components. There is a balance of mass
and heat transfer between different species,
different reactions and also in different parts of the
SOFC. It is important to evaluate the mass and heat
transfer processes as talked above to research the
reaction mechanism and transport process
occurring in SOFC, which will be benefit to give an
advice for design and optimization of SOFC.
1 INTRODUCTION
Solid oxide fuel cell (SOFC) is one of the
prominent fuel cell, it works in high temperature
conditions, SOFC has a relative higher
performance and fuel utilization due to its
endothermic internal reforming occurring in anode
porous layer. Tubular SOFC and planar SOFC are
two basic types of SOFC. In this work, planar
SOFC is chosen for work as shown in Fig.1. The
SOFC cell includes porous anode/cathode,
electrolyte, fuel and air channel, solid connector,
etc. The porous electrode structure is an important
character in SOFC, gas species can penetrate
through the porous layer from gas channel, then
occurring reforming and electrochemical reactions
near the interface between gas and solid phases.
Mass and energy changes are also occurring in the
processes of reactions. High temperature has high
performance and more kinds of fuel can be used in
SOFC, but high temperature also causes thermal
stress, catalyst degradation (carbon deposition),
materials thermal stability problems, etc. How to
decrease the temperature is a big issue for the
development of SOFC [1], evaluate the various
transfer processes coupled with reaction
mechanism is benefit to achieve the target.
Regarding to the transfer processes in SOFC, it
includes mass, energy, momentum and also charge
(electron and ion) transfers. The transfer processes
are affected by the reaction occurring in electrode
layer (diffusion and active layer in Fig.2a and 2b),
porous characteristics, fuel composition, etc.
Referring to the heat transfer, many researchers
assumed an isothermal system in their models[2-6],
in the other hand, many work focus on the heat
transfer modeling to evaluate the more accuracy
physical processes occurring in SOFC [7-12]. The
heat transfer mainly refers to the heat generation
due to electrochemical reactions, overpotential
losses and joule effects of conductor and heat
consumption due to reforming. As mentioned
above, decreasing the temperature is one of the
most important issues in the development of SOFC,
It is a good approach to increase the thickness of
anode (called anode-supported SOFC) in order to
reduce the temperature, and there is a large amount
of heat transfer between anode active layer (with
exothermic electrochemical reactions) and anode
support layer (with reforming reactions), it affects
MSR strongly, higher temperature increase the
reaction rate of MSR to improve the performance
of SOFC. The conductivities of ion and electron
also depend on the temperature distribution. But
too high temperature leads to thermal stress and
material thermostabilization problem which are the
major reasons of low working life. Evaluate the
physical processes to help understand how it works
in energy balance between different components
and how to keep balance between temperature
reduction, meanwhile avoiding performance losses.
In recent work, many literatures have focused on
the small scale of function materials in porous layer
and surface elementary reactions on and inside
catalyst species [13-17]. In consideration of the
porous structure and catalytic elementary reaction
mechanism, more accuracy models have been
developed to evaluate the true physical processes in
SOFC.
Mass transfer in SOFC is coupling with other
transfer, MSR and electrochemical reactions
occurring in anode porous layer are the most

important factors to affect the mass transfer
processes. Due to internal reforming can occur in
SOFC’s anode, mixture hydrocarbon fuel
(CH 4 ,H 2 ,H 2 O,CO and CO 2 in this work) is usually
used, H 2 and CO are generated by MSR and
WGSR, then provide to take part in the
electrochemical reactions in anode active layer.
H 2 O and CO 2 will be produced in anode active
layer, amount of H 2 O can be reused by MSR in
anode which improve the fuel usage obviously. In
the other hand, O 2 will be consumed in the cathode
side. Diffusion of mixture species (especially in
porous layer) has been worked in many literature to
evaluate the physical processes. Fick model (FM) is
a simple approach to describe the diffusion between
different gas species, to extend the FM, Stefan-
Maxwell Model (SMM) has been used more and
more to evaluate the mixture gas diffusion.
Knudsen diffusion is also in consideration to fit for
the gas diffusion in porous structure. In summary,
FM with Knudsen diffusion (EFM) and SMM with
Knudsen diffusion (Dusty-Gas Model DGM) are
most common in mixture gas diffusion model in
SOFC. There are both many literatures to use EFM
and DGM.
process occurring in the anode layer, in anodesupported
planar SOFC, MSR reaction occurring in
the thick anode can reduce the temperature of
SOFC. The heat consumption by MSR reaction is
mainly provided by the heat production from
electrochemical reactions and water-gas shift
reaction(WGSR), exothermic electrochemical
reactions occurring in the active anode layer is the
major heat source. There is a heat transfer between
exothermic electrochemical reaction in active layer
and endothermic reaction in diffusion layer.
Regarding to the model describing the heat transfer
processes, local temperature equilibrium (LTE)
approach is the most common way to be used,
which assume the same temperature for fluid and
solid materials in SOFC. Accordingly, local
temperature non-equilibrium (LTNE) approach
which assumes the temperature difference between
solid and fluid materials in SOFC is also used in
many references. It will be discussed later.
Table I . GEOMETRY OF SOFC COMPONENT
Component
Geometry Size (m)
Cell length 20
Cell width (half) 1
Duct width (half) 0.5
Anode support layer thickness 0.48
Anode/Cathode active layer thickness 0.02
Cathode support layer thickness 0.05
Electrolyte layer thickness 0.01
Fig. 1 The sketch of 3D anode-supported SOFC
cell
2. HEAT TRANSFER IN SOFC
Heat transfer in SOFC mainly includes the
transfer processes due to the production and
consumption of reactions, joule, overpotential and
ohmic effects in electronic and ion conductor, heat
conductivity, convection and heat radiation in solid
and fluid materials, energy change due to species
diffusion is also in consideration in some models.
Energy change due to the reactions is the most
important part of heat transfer in SOFC. Methane
steam reforming reaction (MSR) is an endothermic
Fig. 2 The drawing of (a) structure of porous, (b)
mass and heat transfer in SOFC
2.1 LTE approach model
Assume the same temperature between fluid and
solid materials in SOFC, energy balance in SOFC
can been evaluated as:
n
eff
cp,eff
T
eff cp,eff UT = ( keff T mh
i i
) S
(1)
T
i1
As shown above, the energy balance equation
includes unsteady term, convection term, diffusion
term and source term. The first two terms on the
right-hand side of equation represent energy
transfer due to conduction and species diffusion,
respectively. And k eff , c p,eff represents effective

conductivity and specific heat capacity which equal
to:
keff
k
f
(1
) ks
(2)
cp, eff
cp, f
(1
) cp,
s
(3)
where ε is the porosity.
S T in equation (1) is source term which can be
represented as:
2
ST hreact Ran , cat
an,
cat
I Rohm
(4)
where R an,cat η an,cat is heat change due to
overpotential by active current, I 2 R ohm is joule heat
production due to ohmic effects, h react is the
enthalpy change caused by reactions, MSR, WGSR
and electrochemical reactions which should be in
consideration, then h react can be represented as:
S Rh
T i reaction,
i
i
(5)
where R i are reaction rates of MSR, MGSR and
electrochemical reactions, i is the reaction index,
Δh reaction,i are enthalpy changes of those reactions.
2.2 LTNE approach model
In consideration of the temperature distribution
between solid and fluid phase, the temperature
distribution can be calculated separately for the gas
and solid phase as shown below:
( ks
Ts)
Q
s
(6)
( kg Tg)
Qg g cp,
g
uT g
(7)
where k s and k g are conductivity of solid and gas
phase, Q s and Q g are source terms in solid and gas
phase. It should be noted that, the source term Q s in
solid phase includes heat transfer between two
phase, heat production of electrochemical reaction,
ohmic effects and overpotential losses in active
layer. Q g in gas phase includes heat transfer
between two phase and enthalpy changes of MSR
and WGSR. The heat source is similar with LTE
approach model discussed above. But there is a
heat transfer between solid and gas phase which
can be evaluated by:
Qg hv( Tg Ts) SAhs, g,
por
( Tg Ts)
(8)
where h s,g,por is the heat transfer coefficient which
can be evaluated in [18]. SA is the surface area ratio
which means the surface area per volume.
2.3 Radiation effects
Due to the high temperature of SOFC (800-
1100K), thermal radiation has been in evaluated in
many work, In general, heat radiation in SOFC is
between the surface of gas and solid phase, as
shown below:
' 4
qnet Ak
s
( gTg gT
4 s
) (9)
where A s is the active surface area, ε g is the
emissivity and the α g is absorptivity.
2.4 Enthalpy change in energy equation
As mentioned above, the energy change of MSR
and WGSR can be evaluated by enthalpy change of
global way as shown below:
CH
4+H2O CO+ 3H2 ΔH (1000 K)
= 226 kJ/mol (10)
COH2O CO2 H2 H ( 1000K) 35 kJ / mol (11)
the electrochemical reaction can be formulated
globally as well:
2
H
2
O
H2O2e H( 1000K) 248 kJ / mol (12)
More and more work has been done in the
elementary surface reactions mechanism in Ni/YSZ
materials, It describes the elementary reactions of
adsorption, desorption and surface reaction in
catalyst, there are multi-step mechanisms to
describe the methane steam occurring reforming
reaction and electrochemical reactions in the
Ni/YSZ anode materials respectively.
Table II. HETEROGENEOUS REACTION MECHANISM
FOR METHANE REFORMING REACTIONS ON NI/YSZ
Reaction
Reaction
1. H 2 +Ni s +Ni s →H s +H s 22. CO2s+Nis→Os+COs
2. O 2 +Ni s +Ni s →O s +O s 23. HCO s +Ni s →Hs+CO s
3. Nis+CH4→CH4s 24. H s +CO s →HCO s +Ni s
4. H2O+Nis→H2Os 25. HCO s +Ni s →CH s +O s
5. CO2+Nis→CO2s 26. CH s +O s →HCO s +Ni s
6. CO+Nis→COs 27. CH 4s +Ni s →CH 3s +H s
7. Hs+Hs→H2+Nis+Nis 28. CH 3s +H s →CH 4s +Ni s
8. Os+Os→O2+Nis+Nis 29. CH 3s +Ni s →CH 2s +H s
9. CH4s→Nis+CH4 30. CH 2s +H s →CH 3s +Ni s
10. H2Os→H2O+Nis 31. CH 2s +Ni s →CH s +H s
11. CO2s→CO2+Nis 32. CH s +H s →CH 2s +Ni s
12. COs→CO+Nis 33. CH s +Ni s →C s +H s
13. Os+Hs→OHs+Nis 34. C s +H s →CH s +Ni s
14. OHs+Nis→Os+Hs 35. O s +CH 4s →CH 3s +OH s
15. OHs+Hs→H2Os+Nis 36. OH s +CH3 s →O s +CH 4s
16. H2Os+Nis→OHs+Hs 37. O s +CH3 s →CH2 s +OH s
17. OHs+OHs→Os+H2Os 38. OH s +CH2 s →CH3 s +O s
18. Os+H2Os→OHs+OHs 39. O s +CH 2s →CH s +OH s
19. Os+Cs→COs+Nis 40. OH s +CH s →CH 2s +O s
20. COs+Nis→Os+Cs 41. O s +CH s →C s +OH s
21. Os+COs→CO2s+Nis 42. C s +OH s →O s +CH s
For example, there is a 42-step elementary
reactions mechanism including several gases and
surface species participating in the elementary
reaction processes as shown in Table II, and the
enthalpy changes of each species which can be
used to calculate the heat change in each reaction
has also been evaluated in Table III.
Table III. ENTHALPIES OF SPECIES IN NI/YSZ
MATERIALS IN 973K
Species
Molar
Enthalpies
J/mol Species
Molar
Enthalpies
J/mol Species
Molar
Enthalpies
J/mol
H2 1,987E+04 H2Os -2,816E+05 CO2s -3,915E+05
H2O 2,169E+05 Hs -3,274E+04 HCOs -1,136E+05
O2 2,176E+04 OHs -1,997E+05 CH4s -8,022E+04
CH4 3,860E+04 COs -2,051E+05 CH3s -5,135E+04

CO 8,974E+04 Cs -3,275E+04 CH2s 2,607E+04
CO2 3,616E+05 Os -2,287E+05 CHs 7,675E+04
2.5 Further improvement discussion
More and more work has been focused on the
small scale of SOFC involving the meso-scale and
micro-scale models of porous electrode and
electrolyte, elementary reactions on catalytic
surface species, etc. It has improved the heat
transfer model more accurate and reasonable in
some aspects.
2.5.1 Effect heat conductivity
More and more work has been focused on the
heat analysis and model development based on the
smaller scale of porous electrode structure. As
mentioned before, the heat conductivity in porous
layer can been evaluated as equation (13), but it can
not define the different solid connect materials (Ni
and YSZ) in porous layer. Due to low velocity of
gas transfer in porous layer, convection can be
omitted in comparison with heat conduct in some
degree, and conduct through solid structure
dominates the heat transfer process. Evaluate the
conductivity of Ni and YSZ separately is necessary
to improve the accuracy of heat transfer and
temperature distribution, as shown in equation (13):
k 1
eff
( ) k V s,
i
eff
i
(13)
where ε is porosity, τ is tortuosity, k s,i is
conductivity of Ni or YSZ, and V eff is volume
fraction of each species in solid part. Table IV is
porous properties in SOFC.
Table IV. POROUS PROPERTIES IN SOFC
Anode Electrolyte Cathode
ε 0.4 0 0.3
τ 10 None 10
Veff YSZ:0.6, Ni:0.4 YSZ:1 YSZ:0.6, Ni:0.4
2.5.3 Heat transfer in rarefied gases region.
As mentioned above, the scale of signal SOFC
cell is on mm order, the component (channel,
electrode, electrolyte, etc.) of cell unit is less than
mm order, and the function layer (active layer,
porous pore, etc.) is under μm order. In the micro
structure in SOFC, continuum model is not
adequately to describe the low pressure or low
density in small scales. It is supposed to develop a
new approach to characterize the transfer processes
in smaller scales. Compare with conventional
approach used in continuum model, kinetic gas
theory with important parameters (wavelength of
the molecular, mean velocity, etc.) is a good tool to
evaluate the conditions. There is a reasonable
approach to evaluate the flow type of boundary
layer between solid surface and gas flow in SOFC.
As shown in equation (16)-(17), Knudsen number
represent the ratio of free mean path wavelength λ
of the molecule and characteristic dimension L, for
boundary layer in SOFC, characteristic dimension
is thickness of boundary layer δ.
1 r
Ma
Kn
/ L
0.499 8 Re
(16)
Ma
Kn
Re
(17)
In summary, the flow can be divided into
different regimes depending on the magnitude of
the Knudsen number, and there are different
methods for different flow regimes, as shown
below.
Table V. GENERAL FLOW REGIMES DIVIDED BY
KNUDSEN NUMBER
Flow
regimes
Important
parameter
for
validation
Characteristic
conditions
Methods
2.5.2 Anisotropic heat transfer
Regarding to the particle structure of porous
layer in smaller scale as shown in Fig.2a, heat
transfer should be in consideration of anisotropic
way. Compare with isotropic materials, the thermal
conductivity in anisotropic materials is assumed to
vary with the directions. Omit the effect of
convection and heat transfer by diffusion, energy
equation for anisotropic materials can be evaluated
as:
2 2 2 2
eff
cp,eff
T T T T T
kxx k 2 xy
kxz kyx
x xy xz yx
2 2 2 2 2
T T T T T
kyy k 2 yz
kzx kzy kzz
S
2 T
y yz zx zy z
(14)
where k ij is the anisotropic conductivity in different
directions, it should be noted that k ij =k ji then the
equation can be simplified as:
2 2 2
eff
cp,eff
T T T T
kxx k 2 yy
k
2 zz 2
x y z
2 2 2
T T T
2kxy 2kyz 2kxz ST
xy yz zy
(15)
Continuum
flow
Ma Re <
0.01
Slip flow 0.01<
Ma Re <
0.1
Transition
flow
Ma Re >
0.1 and
Ma/Re

Free
molecular
flow
(Knudsen
flow)
Ma/Re>10
Molecular hit the
solid surface much
more than
intermolecular
collisions, the
boundary flow
depends on the
interaction between
fluid molecular and
solid surface.
Use kinetic
gas theory
k j can been expressed as Arrhenius expression as
below [20]:
Ks
E
j
aj
kj
kj k
k
jAT
j
exp( ) k
exp( )
RT k1
RT (25)
where A j and E aj are Arrhenius parameters, μ kj and
ε kj the parameters modeling the coverage
dependence on the rate constants, θ k is the surface
coverage.
It should be noted that, this theory is also
adequately for momentum and mass transfer.
3 MASS TRANSFER IN SOFC
Mass transfer in SOFC is very important for the
reactions and performance of fuel cell. Mass
transfer in SOFC mainly refers to diffusion of the
multi-component gas species and transport in
porous layer. Mass balance equation has been
shown below:
( eff U Yi ) ( Di,
eff
Y i
) S
(18)
g , i
where D i,eff is mass diffusion coefficient, Y i is mass
fraction of species i and S g,i is mass source term of
species i. And ρ eff is effective density of multicomponent
gas species which can be expressed as:
X
eff i i
f i
(19)
X i is molar fraction of gas species i.
3.1 Source term
According to the source term, it depends on the
reaction mechanism. In global reaction mechanism
as discussed in 2.4, source term of species i in
reforming and electrochemical reactions can be
evaluated as:
Sg , i
( mRr nRs)
M
i
(20)
Iact
Sele,
i
TPB Mi
nF
(21)
where R r and R s are reaction rate of MSR and
WGSR, I act is active current density, and TPB is
three phase boundary area per volume for
electrochemical reaction.
In surface elementary reaction mechanism of
methane on Ni/YSZ anode as discussed in Table II,
reaction rate of each gas species should be
expressed as [19]:
Kr
KgKs
R
k X
gi ,
ij j i
j1 i1
(22)
where k j is the reaction constant, K r , K g , K s
represent the number of the total reactions, gas and
surface-phase species, respectively, υ ij and υ ’ ij the
stochiometric coefficients of products and reactants.
[X i ] is gas species concentration:
X
i
p
3
X
( /
i
mol cm )
6
RT
g
10
(23)
while the surface-phase species concentration is
calculated by :
2
X
i itot ( mol / cm )
(24)
Γ tot is the total surface site density including open
catalyst surface specie Ni s .
'
ij
3.2 Diffusion coefficient
As mentioned above, diffusion of mass can be
evaluated by EFM which can be calculated D i,eff as:
Digm
,
Dik
,
Dieff
,
Digm
,
Dik
,
(26)
where ε is porosity and τ is tortuosity of porous
materials, D i,gm is the diffusion of multi-component
gas species, which can be expressed as [21]:
1
Yi
Digm
,
Y
i
i
j Di,
j
(27)
where D i,j are the binary diffusion coefficients of
gas-phase species i, as shown in Table VI.
Table VI. BINARY DIFFUSIVITY OF THE ITH GAS-
PHASE SPECIES AT T=1123.2K, P=1.013 BAR [22]
i/j D ij (m2/s) i/j D ij (m2/s)
CH 4 /CO 3.47e-05 CO/ H 2 11.92e-05
CH 4 / H 2 O 4.30e-05 CO/ CO 2 2.59e-05
CH 4 / H 2 11.04e-05 H 2 O/ H 2 14.10e-05
CH 4 /CO 2 2.88e-05 H 2 O/ CO 2 3.38e-05
CO/ H 2 O 4.15e-05 H 2 / CO 2 10.23e-05
The diffusion coefficients of gas-phase species i
in the porous layer are controlled by the pore size
and the free-path of the diffusion gas molecules. In
this work, it is assumed that the mean free-path of
the molecules is bigger than the pore size, which
means that the collisions between the molecules
and the walls are more often than the collisions
between themselves. Then, Knudsen diffusion is
evaluated as follows:
2 2 8RT
Dik ,
revi re
3 3 M
i
(28)
where r e is the effective radius and ν i is the average
molecular speed of species i.
But SMM has been used in many literatures [23-
25]. It is generally agreed that DGM is superior to
EFM to predict the fluxes inside porous materials
[26]. The model can be evaluated by [27]:
( effU Yi ) ( Jk ) S
(29)
g,
i
where J k equal to
DGM
Kg
Kg Dij
X
DGM
j
Ji Mi Dij X
(30)
j
p
e
j1 j1
D
jin ,
where D DGM kl are defined as the matrix of DGM
diffusion coefficients and can be represented as a
matrix inverse:
D
DGM
ij
1
H
where the elements of H matrix are
(31)

1 X
l
X
i
hij
ij
(
ij
1)
e
e
e
D l
j,
in
D
il Dil
(32)
D i,j and D i , k are the effective binary diffusion
coefficient and effective Knudsen diffusion
coefficient which have been given above.
4 SIMULATION RESUTLS AND
DISCUSSION
In this work, a SOFC model (discussed in Table
1) involved LTE energy model (equations (1)-(5))
with global reaction mechanisms referring to
equations (10)-(12) has been simulated by
Ansys/Fluent 12.1 with Fuel Cell Module issued by
Fluent Inc. to show the temperature and gas species
distribution in order to evaluate the heat and mass
transfer. It should be noted that, the CFD model is
also includes momentum transfer besides heat and
mass transfer but not be discussed in this paper.
Fig. 4 (a) Distribution of H 2 (molar fraction) in
anode, (b) H 2 along main flow direction at
symmetric side
Regarding to the mass distribution, it includes
the hydrocarbon fuel in anode side and oxidant (O 2 )
in cathode side. H 2 distribution is shown in Fig 4a
and b, X H2 in porous layer is big near the inlet
region, and decreases along the y direction, that is
because of the combined reforming and
electrochemical reactions. MSR and WGSR
produce large amount of H 2 especially near the
inlet region, and H 2 goes through the porous layer
then be consumed by electrochemical reaction at
TPB near the electrolyte. The H 2 distribution along
z direction is affected by channel near inlet and by
electrochemical reaction near outlet, it is in keep
with the reforming rate and H 2 drop.
Fig. 3 (a) Temperature distribution in half-cell, (b)
Temperature distribution in sectional cross near
outlet
According to Fig.3a, It shows the temperature
distribution affected by the reforming and
electrochemical reactions. As mentioned above,
there is a heat balance between endothermic RSM
with exothermic electrochemical reactions, and a
higher temperature appears in active layer near
electrolyte. Lower temperature exits in inlet side
which means bigger reaction rate of reforming
consuming more heat, it is because the higher fuel
concentration near inlet improves MSR. As shown
in Fig. 3b, the temperature of gas channel is lower
than other parts.

Fig. 5 (a) Distribution of CH 4 in anode, (b) CH 4
along main flow direction at symmetric side
Fig. 6 (a) Distribution of O 2 in cathode, (b)O 2
along main flow direction at symmetric side
As shown in Fig.5a and b, CH 4 decrease along
all directions because of consumption by reforming
in anode porous layer, X CH4 is about 11% to 17%,
which means the usage of CH 4 is only up to 45%.
The only reactant in the cathode side O 2 also
decreases as shown in Fig.6a and b. It should be
noted that, the concentration near outlet decrease
apparently, even below 1% in some part along z
direction, it means too much O 2 has been used in
the active layer and lower concentration will cause
big concentration potential losses.
In Fig.7, the distribution of H 2 , H 2 O, CH 4 , CO,
CO 2 and O 2 have been presented along main flow
direction of anode and cathode in active layer (in
Fig.7a) and diffusion layer (in Fig.7b). H 2 O and
CO 2 are main production in anode side. It should
be noted that, as reactant of MSR and WGSR, H 2 O
is still increasing, even though the electrochemical
reaction rate is much smaller than reforming. The
MSR is still insufficient, maybe due to fuel
concentration, porous diffusion, catalyst activity,
etc. CH 4 and H 2 are main reactants at anode side
and O 2 is the only reactant at cathode side,
respectively. X H2 is big near inlet because strong
reforming releases large amount of H 2 , but it
decreases apparently. CO is generated by MSR and
consumed by WGSR and electrochemical reaction,
its concentration becomes small, especially near the
outlet where the rate of reforming is smallest.
Comparing with the distribution between two
figures, it is found that less H 2 , CO and more H 2 O,
CO 2 exit in active layer (Fig.7a) due to
electrochemical reactions occurs in active layer.
Fig. 7 Averaged molar fraction of fuel and O 2
along main flow direction in (a) active layer (plane
y=1.385mm in anode and y=1.365mm in cathode)
(b) diffusion layer (plane y=1.65mm in anode and
y=1.33mm in cathode)
CONLUSION
In this work, the heat and mass transfer in SOFC
has been discussed. The heat process is based on
the exothermic and endothermic reactions
occurring in the active and diffusion layer in SOFC,
overpontential losses and ohimc effect are also
included. Heat transfer between solid and gas phase
and thermal radiation are supposed to be in
consideration in the future work. Mass transfer
model referring to multi-component fuel and air
has been developed, there are EFM and SMM to
evaluate the mass transfer processes in the porous
layer, mass transfer is coupled with heat transfer
due to the reactions which consume and produce
the mass and heat simultaneously. The further
discussion should be taken in the smaller scale, the
mechanism of heat and mass transfer will be
different in the smaller scale model, improvements
for the method to evaluate the micro-scale transfer
processes (such as gas species and heat transfer in
the pore structure, or in the catalyst surface, etc. )
are supposed to be develop in the future work.
REFERENCE
[1] D. Wachsman, Kang Taek Lee, 2011,
“Lowering the Temperature of Solid Oxide
Fuel Cells”, Science 18 November, pp.
935-939.
[2] Jin X, Xue X. 2010, “Mathematical
modeling analysis of regenerative solid
oxide fuel cells in swithching mode
conditions”. Journal of Power Sources
195, pp. 6652-6658

[3] Zu H, Kee Rj. 2003, “A general
mathematical model for analyzing the
performance of fuel-cell membraneelectrode
assemblies” Journal of Power
Sources, 117, pp.61-74.
[4] Suwanwarangkul R, Croiset E, Pritzker
MD, 2006, “Mechanistic modeling of a
cathode-supported tubular solid oxide fuel
cell” Journal of Power Sources, 154, pp.
74-85.
[5] Lehnert W, Meusinger J, Thom F. 2000,
“Modelling of gas transport phenomena in
SOFC anodes” Journal of Power Sources,
87, pp. 57-63.
[6] Xie Y, Xue X. 2009, “Transient modeling
of anode-supported solid oxide fuel cells”
International Journal of Hydrogen Energy,
34, pp. 6682-6691.
[7] B. Sundén and J. Yuan 2010,
“Development of Multi-scale Models for
Transport Processes Involving Catalytic
Reactions in SOFCs,” Int. J. Micro-Nano
Scale Transport, Vol.1, No.1, pp. 37-42.
[8] BA Haberman, JB Young, 2004 “Threedimensional
Simulation of Chemically
Rreacting Gas Flows in the Porous
Support Structure of an Integrated-planar
Solid Oxide Fuel Cell,” Int.J. Heat Mass
Tranfer, 47, pp. 3617-3629.
[9] A. Aguiar, C.S. Adjiman, and N.P.
Brandon. 2004 “Anode-supported
Intermediate Temperature Direct Internal
Reforming Solid Fuel Cell, I: Modelbased
Steady-state Performance”. J. Power
Sources 138, pp. 120-136,.
[10] H. Yakabe, M. Hishinuma, M. Uratani, Y.
Matsuzaki and J. Yasuda, 2000
“Evaluation and Modeling of Performance
of Anode-supported Solid Oxide Fuel
Cell,” J. Power sources 86, pp. 423-431.
[11] J. Yuan and B. Sunden, 2006 “Analysis of
Chemically Reacting Transport
Phenomena in an Anode Duct of
Intermediate Temperature SOFCs,” ASME
J.Fuel Cell Sci., Tech. and Engn., 2, pp.
89-98.
[12] J. Yuan, Y. Huang, B. Sundén and W.G.
Wang, 2009, “CFD Approach to Analyze
Parameter Effects on Chemical-Reacting
Transport Phenomena in SOFC Anodes”,
Heat and Mass Transfer, 45, pp. 471-484.
[13] U. Doraswarmi, P. Shearing, N.
Droushiotis, K. Li, N.P. Brandon, G.H.
Kelsall, 2011, “Modelling the effects of
measured anode triple-phase boundary
densities on the performance of microtubular
hollow fiber SOFCs” Solid State
Ionics, 192, pp. 494-500.
[14] K.N. Grew, A.S. Joshi, A.A. Peracchio,
W.K.S. Chiu, 2010, “Pore-scale
investigation of mass transport and
electrochemistry in a solid oxide fuel cell
anode” 195, pp. 2331-2345.
[15] V.M. Janardhanan, O. Deutschmann,
2006, “CFD analysis of a solid oxide fuel
cell with internal reforming coupled
interactions of transport, heterogeneous
catalysis and electrochemical processes”
162, pp. 1192-1202.
[16] Sangho S., Jin H.N., Dong H. J. Charn J.
K. 2010, “A micro macroscale model for
intermediate temperature solid oxide fuel
cells with prescribed fully-developed axial
velocity profiles in gas channels”
International Journal of Hydrogen Energy
35, pp. 11890-11907.
[17] Zhang, Y., Xia C., Ni M.
2012, ”Simulation of sintering kinetics
and microstructure evolution of composite
solid oxide fuel cells electrodes”,
International journal of hydrogen energy
37, pp. 3392-3402.
[18] Damm D.L., Fedorov A.G., Local Thermal
Non-Equlibrium Effects in Porous
Electrodes of the Hydrogen Fueled SOFC,
J.Power Sources, 159 1153-1157, 2006.
[19] H.Zhu, R.J. Kee, V.M. Janardhanan, O.
Deutschmann, D. Goodwin, 2005 J.
Electrochem. Soc. 152, pp. A2427-A2440.
[20] Y.X. Shi, N.S. Cai, C. Li, 2007, J.Power
Sources 164, pp. 639-648.
[21] I.L. Mostinsky, G.F. Hewitt, G.L. Shires,
and Y.V. Polezhaev, 1996, “Diffusion
coefficient”, International Encyclopedia of
Heat & Mass Transfer, CRC Press,
Florida, USA.
[22] H. Yakabe, M. Hishinuma, M. Uratani, Y.
Matsuzaki and J. Yasuda, 2000,
“Evaluation and Modeling of Performance
of Anode-supported Solid Oxide Fuel
Cell” J. Power sources 86, pp. 423-431.
[23] Y.X. Shi, N.S. Cai, C. Li, C. Bao, E.
Croiset, J.Q. Qian, Q. Hu, S.R. Wang.
2007, J. Power Sources 172, pp. 235-245.
[24] Y.X. Shi, N.S. Cai, C. Li, 2007, J.Power
Sources 164, pp. 639-648.
[25] H.Zhu, R.J.Kee, M.R.Pillai, S.A.Barnett,
2008, J. Power Sources 183, pp. 143-150.
[26] Dincer I, Hamdullahpur F.A, 2008 “review
on macro-level modelling of planar oxide
fuel cells”. Int. J. Energy Res. 32, pp. 336-
355.
[27] E.A. Mason, A.P. Malinauskas, Gas
Transport in Porous Media: The Dusty-
Gas Model, Elsevier, New York, 1983.