The Gas Diffusion Layer in High Temperature Polymer Electrolyte Membrane Fuel Cells

31
0.10.20.30.40.50.60.70.80.91.01.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
without MPL
10% Teflon in the MPL
20% Teflon in the MPL
40% Teflon in the MPL
60% Teflon in the MPL
-Z'' / ohm cm
2
Z' / ohm cm
2

Fig. 13. Impedance spectra of the cell when electrodes with different Teflon percentage in
the MPL were used

0 200 400 600 800 1000 1200
0
100

the catalytic layer plays a more important role in terms of global performance (lower
performance in almost the whole range of current densities). Therefore, in terms of global
performance, it is also advisable to use a MPL with a low Teflon percentage.

Heat and Mass Transfer – Modeling and Simulation

32
PTFE content / % j
HL,h
y
dro
g
en
/ mA cm
-2
Without MPL 1.000,8
10 1,000.4
20 990.2
40 980.9
60 964.9
Table 6. Limiting current density for the hydrogen oxidation for the different Teflon
percentages of the MPL
3.2.2 Influence of the carbon content in the microporous layer
For this study, microporous layers with a Teflon percentage of 10% were prepared, on a
total weight base, varying the carbon loading (0.5, 1, 2 and 4 mg cm
-2
).
a) Physical characterisation
Figure 15 shows the pore size distribution of the gas diffusion layer for the different carbon
loadings in the MPL, along with the carbon support. Results are shown focusing on the

0.4
0.5
0.6
Specific pore volume /
ml g
-1
m
-1
Pore size / m
(a) (b)

Fig. 15. Specific pore volume for the GDLs with different carbon loadings in the MPL in: (a)
the macroporous region, and (b) in the microporous layer (Lobato et al., 2010, with
permission of Wiley Interscience)
As it can be observed, the macroporosity of the GDL diminishes with the addition of more
carbon to the MPL. As previously commented for the Teflon percentage, part of the MPL
will penetrate inside the macroporous carbon support, and therefore, will occlude part of
the macropores. Macroporosity decreases until a carbon loading of 2 mg cm
-2
. Above this
value, no more MPL carbon particles seem to penetrate into the carbon support, and
therefore, the MPL is fully fulfilling its protective role since it is expected that no catalytic
particle will penetrate inside the carbon support. Contrarily, the microporous region
increases with the carbon content of the MPL. Logically, more microporosity is introduced
in the system the higher is the carbon content (Park et al., 2006).
Overall porosity, mean pore size and tortuosity of the GDL with different carbon loading in the
MPL can be estimated from the pore size distribution. The corresponding values are
collected in Table 7.

The Gas Diffusion Layer in High Temperature Polymer Electrolyte Membrane Fuel Cells

10
12
10
12
permeability / m
2
Carbon loading in the MPL / mg cm
-2
H2
O2
Air
Water vapour

Fig. 16. Gases and water vapour permeability of the GDLs with different carbon loadings in
the MPL (horizontal lines represent the carbon support permeability)
As it can be seen, gases/water vapour permeability decreases with the carbon loading in the
GDL. This is an effect of the reduction of the macroporosity, and the increase in the
microporosity, which makes more difficult the transport of the gases reactant, and the water
vapour through the GDL (Wang et al., 2006). On the other hand, the decay in the
permeability becomes less noticeable the higher is the carbon loading in the MPL. This
agrees with the previously mentioned fact that a lower amount of carbon particles from the
MPL penetrates in the carbon support, so that the results reflect the effect of the increase in
the microporosity. As in the previous cases, the molecular size of the gases determines the
values of the gas permeability, except for the case of the extensively commented water
vapour.
As in the case of the influence of the Teflon percentage in the MPL, the simplest GDL,
without microporous layer, seems to be the most adequate disposition in terms of mass

Heat and Mass Transfer – Modeling and Simulation


-2
C in the MPL
4 mg cm
-2
C in the MPL
Cell voltage / mV
Current density / mA cm
-2
0 200 400 600 800 1000 1200
0
100
200
300
400
500
600
700
800
900
Cell voltage / mV
Current density / mA cm
-2

Fig. 17. Cell performance of the electrodes prepared with different carbon loading in the
MPL, (a) Oxygen stoichometry at 1 A cm
-2
= 1,5, (b) Air stoichometry at 1 A cm
-2
= 4 (Lobato
et al., 2010b, with permission of Wiley Interscience)


35
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
without MPL
10% Teflon in the MPL
20% Teflon in the MPL
40% Teflon in the MPL
60% Teflon in the MPL
-Z'' / ohm cm
2
Z' / ohm cm
2

Fig. 18. Impedance spectra of the cell when electrodes with different carbon loading in the
MPL were used (Lobato et al., 2010b, with permission of Wiley Interscience)

Carbon loading / mg cm
-2
j
OL,ox

MPL to the electrode design. Protection of the catalytic layer is fundamental in order to
maximize the cell performance, and indeed, and according to the experimental results, it
plays even a more important role than mass transfer characteristics of the GDL. However, if
an excessive amount of carbon is added to the MPL, significant mass transport limitations
appear, leading to an optimum carbon loading of 2 mg cm
-2
.
b.ii) The Teflon percentage in the anodic MPL
Figure 19 shows the influence of the Teflon percentage of the MPL in different GDLs.
As it can be observed, the influence of the carbon loading in the anodic MPL is more
notorious than in the case of the cathode. However, it is visible the beneficial effect of the
inclusion of the MPL, despite being at the anode. The carbon loading, in this case, slightly
improves the global cell performance with an increase of the carbon loading, showing the
best performances for 1 and 2 mg cm
-2
, and a decrease when the carbon loading was

Heat and Mass Transfer – Modeling and Simulation

36
4 mg cm
-2
. Table 9 collects the values of the hydrogen limiting current density for the
different carbon loaded MPL in the gas diffusion layer.

0 200 400 600 800 1000 1200
0
100
200
300

mass transport. Nevertheless, in the case of the carbon loading of 2 and 4 mg cm
-2
, the
limiting current density decreases, due to the more impeded access of the hydrogen gas.
However, as in the case of the study focused on the cathode, the optimum protective role of
the MPL prescribes the use of a carbon loading of 2 mg cm
-2
, since hydrogen mass transfer
limitations will only appear in case of the use of a very restricted stoichometry.

Carbon loading / mg cm
-2
j
HL,h
y
dro
g
en
/ mA cm
-2
Without MPL 1.000,8
0.5 1,000.1
1 1,000.4
2 990.2
4 975.3
Table 9. Limiting current density for the hydrogen oxidation for the different carbon loading
in the MPL
4. Conclusions
The gas diffusion layer plays an important role for High Temperature PBI-based PEMFC in
terms of cell performance. Thus, it is desirable to have a carbonaceous support with a low


P
pressure different observed
across the carbon support
C
R
S

reactant concentration at the
external surface of the electrode
E cell voltage
C
P
S

product concentration at the
external surface of the electrode
E
0
open circuit voltage
C
R
C

reactant concentration at the
catalytic layer
b Tafel slope
C
P
C

impedance measurement
K permeability R
ct
resistance for the charge
transfer process
Q flow of gas (CPE)
ct
constant phase element for the
charge transfer process
µ gas viscosity R
mt
resistance for the mass transfer
process
L thickness of the porous medium (CPE)
mt
constant phase element for the
mass transfer process
7. References
Antolini, E.; Passos, R.R. & Ticianelli, E.A. (2002). Effects of the cathode gas diffusion layer
characteristics on the performance of polymer electrolyte fuel cells. Journal of The
Applied Electrochemistry, Vol. 32, No. 4, pp. 383-388, ISSN : 0021-891X.

Heat and Mass Transfer – Modeling and Simulation

38
Appleby, A.J. & Foulkes F.R. (1993). Fuel cell handbook, Krieger Publishing Company (Ed.),
ISBN: 0-89464-733-4, Malabar, Florida, United State.
Benziger, J.; Nehlsen, J.; Blackwell, D.; Brennan, T. & Itescu, J. (2005). Water flow in the gas
diffusion layer of PEM fuel cells. Journal of Membrane Science, Vol. 261, No. 1-2,
(September 2005), pp. 98-106, ISSN: 0376-7388.

membrane fuel cells. Journal of Power Sources, Vol. 160, No. 2, (October 2006), pp. 1096-
1103, ISSN: 0378-7753.
Lai, C M.; Lin, J C.; Ting F P.; Chyou, S D. & Hsueh K L. (2008). Contribution of Nafion
loading to the activity of catalysts and the performance of PEMFC. International
Journal of Hydrogen Energy, Vol. 33, No. 15, (August 2008) pp. 4132-4137, ISSN: 0360-
3199.
Li, Q.; He, R.; Jensen, J.O. & Bjerrum, N.J. (2003a). Review Approaches and Recent
Development of Polymer Electrolyte Membranes for Fuel Cells Operating above 100
°C. Chemistry of Materials, Vol. 15, No. 26, (December 2003), pp 4896–4915, ISSN: 0897-
4756.
Li, Q.; He, R.; Gao, J A.; Jensen, J.O. & Bjerrum, N.J. (2003b). The CO Poisoning Effect in
PEMFCs Operational at Temperatures up to 200°C. Journal of The Electrochemical
Society, Vol. 150, No. 12, (November 2003), pp.A1599-A1605, ISSN: 0013-4651.

The Gas Diffusion Layer in High Temperature Polymer Electrolyte Membrane Fuel Cells

39
Li, Q.; He, R.; Jensen, J.O. & Bjerrum, N.J. (2004). PBI-Based Polymer Membranes for High
Temperature Fuel Cells – Preparation, Characterization and Fuel Cell Demonstration.
Fuel Cells, Vol. 4, No. 3, (August 2004), pp. 147–159, ISSN: 1615-6854.
Linares, J.J. (2010). Celdas de combustible de membrana polimérica de alta temperatura
basadas en polibencimidazol impregnado con ácido fosfórico. PhD Thesis Dissertation,
(January 2010), Ciudad Real, Spain.
Liu, Z.; Wainright, J.S.; Litt, M.H. & Savinell R.F. (2006). Study of the oxygen reduction reaction
(ORR) at Pt interfaced with phosphoric acid doped polybenzimidazole at elevated
temperature and low relative humidity. Electrochimica Acta, Vol. 51, No. 19, (May
2006), pp. 3914-3923, ISSN: 0013-4686.
Lobato, J.; Cañizares, P.; Rodrigo, M.A.; Linares, J.J. & Manjavacas G. (2006). Synthesis and
characterisation of poly[2,2-(m-phenylene)-5,5-bibenzimidazole] as polymer
electrolyte membrane for high temperature PEMFCs. Journal of Membrane Science, Vol.

357-363, ISSN: 0378-7753.
Park, G G.; Sohn, Y J.; Yang T H.; Yoon, Y G.; Lee, W Y. et al. (2004). Effect of PTFE contents
in the gas diffusion media on the performance of PEMFC. Journal of Power Sources,
Vol. 131, No. 1-2, (May 2004), pp. 182-187, ISSN: 0378-7753.

Heat and Mass Transfer – Modeling and Simulation

40
Prasanna, M.; Ha, H.Y. & Cho, E.A. (2004a). Influence of cathode gas diffusion media on the
performance of the PEMFCs. Journal of Power Sources, Vol. 131, No. 1-2, (May 2004),
pp. 147-154, ISSN: 0378-7753.
Prasanna, M.; Ha, H.Y.; Cho, E.A.; Hong, S A.; Oh, I H. (2004b). Investigation of oxygen gain
in polymer electrolyte membrane fuel cells. Journal of Power Sources, Vol. 137, No. 1,
(October 2004), pp. 1-8, ISSN: 0378-7753.
Quingfeng, L.; Hjuler, H.A. & Bjerrum, N.J. (2000). Oxygen reduction on carbon supported
platinum catalysts in high temperature polymer electrolytes. Electrochimica Acta, Vol.
45, No. 25-26, (August 2000), pp. 4219-4226, ISSN: 0013-4686.
Samms, S.R.; Wasmus, S.; Savinell, R.F. (1996). Thermal Stability of Proton Conducting Acid
Doped Polybenzimidazole in Simulated Fuel Cell Environments. Journal of The
Electrochemical Society, Vol. 143, No. 4, (April 1996), pp. 1225-1232, ISSN: 0013-4651.
Savadogo, O. (2004). Emerging membranes for electrochemical systems: Part II. High
temperature composite membranes for polymer electrolyte fuel cell (PEFC). Journal of
Power Sources, Vol. 127, No. 1-2, (March 2004), pp. 135-161, ISSN: 0378-7753.
Seland, F.; Berning, T.; Børresen, B. & Tunold R. (2006). Improving the performance of high-
temperature PEM fuel cells based on PBI electrolyte. Journal of Power Sources, Vol. 160,
No. 1, (September 2006), pp. 27-36, ISSN: 0378-7753.
Soler, J.; Hontañón, E. & Daza, L. (2003). Electrode permeability and flow-field configuration:
influence on the performance of a PEMFC. Journal of Power Sources, Vol. 118, No. 1-2,
(May 2003), pp. 172-178, ISSN: 0378-7753.
Song, J.M.; Cha, S.Y. & Lee, W.M. (2001). Optimal composition of polymer electrolyte fuel cell

University Henri Poincaré - Nancy I
France
1. Introduction
Heat exchangers are commonly used in industrial fields such as air conditioning,
petrochemical and agriculture-food industries. The design and utilization of a heat
exchanger should fulfill some conditions of performance, economy and space requirement.
The most widely operated heat exchangers make use of fin-and-tube configuration in
association with the application of heating, ventilating, air-conditioning and refrigeration
systems (Khalfi & Benelmir, 2001). With regard to the fin temperature and dew point
temperature of surrounding air, three situations on a fin surface can be distinguished (Lin &
Jang, 2002, Benelmir et al., 2009). The fin surface is fully dry if the temperature of the whole
fin is higher than the air dew point temperature. It is partially wet when the air dew point
temperature is lower than the fin top temperature and is higher than the fin base
temperature. Finally, the fully wet surface occurs if the temperature of the whole fin is lower
than the dew point temperature. A reliable determination of the fin efficiency must account
for the simultaneous heat and mass transfer on the cooling surface. Many experimental, and
few numerical, studies have been carried out to study the heat and mass transfer
characteristics of the fin-and-tube heat exchangers under dehumidifying conditions. It was
stated by Liang et al. (2000) that the condensation of the moist air along the fin surface
causes reduction of the fin efficiency. They found also that measured fin efficiency was less
than the calculated one assuming a uniform heat transfer coefficient. The calculated results
of Saboya & Sparrow (1974), Chen et al. (2005), Chen & Hsu (2007), and Chen & Chou (2007)
concluded that the heat transfer coefficient was non-uniform under dry conditions. Due to
the difficulty of considering a variable sensible heat transfer coefficient (Choukairi et al.,
2006), this later was often assumed to be uniform by many investigators in the calculation of
fin efficiency. Liang et al. (2000) used one-dimensional and two-dimensional models to
determine the humid fin efficiency of a plate-fin-tube heat exchanger: The results obtained
show comparable efficiencies with both 1-D and 2-D models. Chen (1991) analyses the fin
performance under dehumidifying conditions and shows, through a 2-D model, that the
humid fin efficiency was sensitive to the moist air relative humidity value. As mentioned

a
, along a cold surface at a fixed temperature T
w
, which is lower
than the dew point temperature of the air (T
dew,a
), condensation occurs on the wall. At the
air-condensate interface, the saturated air is characterized by the condensate-film
temperature T
c
and the saturated humidity ratio W
S,c
, at T
c
. The total wall heat flux includes
the sensible part due to convection, spent by cooling air, resulting from the temperature
differences between air and condensate-film, and the latent part due to the vapor phase
transition heat leading to the partially condensation of the vapor contained in the moist air. Fig. 1. Air dehumidification by a cold wall
T
a
, W
a
Moist air
Inlet
T
a,i
W

m"
a,dry
Outlet
T
a,o
W
a,o
m"
a,dry
Condensate-film
W
S,c
(T
c
)
T
c
Cold wall T
w
Numerical Analysis of Heat and Mass Transfer in a Fin-and-Tube
Air Heat Exchanger under Full and Partial Dehumidification Conditions
43
The total heat transfer rate through the wall can be expressed as:



,,,tadryaiao cc
q
mii mi


(2)
According to the mass transfer law, the mass flux of the condensate is expressed as:



,cma Sc
mWW



(3)
As reported by Lin et al. (2001), most of the investigators applied the Chilton-Colburn
analogy to set a relationship between the mass transfer coefficient and the sensitive heat
transfer coefficient, hence; the following relation is reported and used in our work:

,
2/3
,
.
sen hum
m
p
a
Le c



(4)
Combining equations (2), (3), and (4), the following equation is obtained:




(6)
Thus, we obtain the expression bellow for the overall heat transfer coefficient:

,
,,
2/3
,
1
.
aSc
O hum sen hum
ac
pa
WW
Lv
TT
Le c












fin
tube
P
t
2h
2l
P
l
2h
2l
P
l
P
t
air
fin
tube
P
t
2h
2l
P
l
2h
2l
P
l
P
t
Air flow



;
cc
Vdxd
y


;


afc
V
p
dxd
y


;


tff
V
p
dxd
y



2.3 Governing equations

*
,,
ff
b
f
ai
f
b
TT
T
TT



(8)

,,
*
,,,
aS
f
b
a
ai S
f
b
WW
W
WW


f
δ
c
2δ
f
δ
c
δ
c
δ
f
δ
f
δ
c
air (T
a
, W
a
)
fin
(T
f
,W
S,f
)
fin
(T
f
,W

c
δ
f
δ
f
δ
c
air (T
a
, W
a
)
fin
(T
f
,W
S,f
)
fin
(T
f
,W
S,f
)
fin
(T
f
,W
S,f
)



*
1
r
r
r


(10)

*
f
P
P
r


*
c
c
r




*
x
x
i

22
22
xx xx
xya
uu uu
uu
xy
xy


 
 





(13)

22
22
y
yyy
xya
uu uu
uu
xy
xy



2
Re
xx xx
xy
D
uu uu
uu
xy xy

 
 


 

(16)

** 2*2*
**
** *2*2
2
Re
y
yyy
xy
D
uu uu
uu
xy xy


,
*
1
x
u

,
*
0
y
u

(19)
The upper and lower edges of the fin are subject to the following boundary conditions:

**
y
h

 ,
*
x

,
*
0
y
u

(20)

condensate-film. Fig. 5. Vapor flow rate variation in an elementary air volume
According to Fig. 5, the variation of the vapor mass flow is written as:

,
aa
vx
y
adr
y
a
WW
mu u V
xy



 




(23)
Using Eqs. (3), (22) and (23) yields to the following equation:



,

,,

sen hum
aa
x
y
ac
cpaiadry
WW
uu WW
xy
pLecu



 


(25)
And the corresponding boundary conditions are:
y
z
Elementary air volume
p
f
-δ
c
x
dy
dx

**
y
h

 ,
*
x

,
*
*
0
a
W
y




(26)

2.3.3 Energy balance equation for air flow
Referring to Fig. 5, the energy balance equation held the same form as Eq. (22):

"0
asen
E q dxdy




,
2/3
,

sen hum
aa
x
y
ac
fc paa
TT
uu TT
xy
pLec



 


(29)
After introducing the dimensionless variables, we get :



**
,
** **
**
**2/3

1
a
T

(31)

**
y
h

 ,
*
x

,
*
*
0
a
T
y



(32)
2.3.4 Energy balance equation for the condensate-film
As mentioned above, heat transfer through the condensate-film is assumed to be purely
conductive. Using the fact that the temperature of the condensate-film internal surface is the
same as that of the fin surface, the heat flux transferred from the condensate-film to the fin
is:


(34)
From this equation, the condensate-film temperature is deduced:

,
1
af
ca
c
Ohum
c
TT
TT






(35)
2.3.5 Mass balance equation for condensate-film
The film-wise condensation of a stationary saturated vapor on a plane vertical surface has
been analyzed by Nusselt (1916) by means of some assumptions. The expression of the
condensate-film thickness given by Nusselt is:




1/4
4

c
vc c v c Ohumc
hyT T
gL



    







(37)
2.3.6 Energy balance equation for the fin surface
The energy balance equation for the fin is obtained from the heat conduction equation
within the fin surface, thus, the subsequent equation is obtained:

22
22
0
ff
ff
TT
E
xy



  


(39)
Combining these equations yields:



22
,
22
,
0
ff
Ohum c
af
ff c OhumC
TT
TT
xy

   
















(41)
Using the adiabatic condition in the inlet and the outlet as well as the symmetry condition in
both upper and lower, of the fin wall, the following boundary conditions holds:

**
xl

 ,
*
y

,
*
*
0
f
T
x



(42)



(44)
2.4 Solving equations
The two-dimensional model developed above is based on the following equations: the
continuity and momentum equation (Eqs. 15 to 17), the mass balance equation for water
vapor (Eq. 25), the energy balance equation for air stream (Eq. 30), the heat transfer equation
in the fin surface (Eq. 41) and the heat and mass transfer equations for the condensate-film
(Eqs. 35 and 37). In our model, the simultaneous influence of the local speed and heat
transfer coefficient is considered for solving heat and mass transfer within the air flow
(Eqs.25 and 30). Moreover, equation (30) uses in its expression the mass flow of moist air
(

a
u
i
), while in Eq. (25), the dry air mass flow is used. This allows the consideration of the
effect of condensation on heat and mass transfer only once.
2.4.1 Solving continuity and momentum equations
The problem described by Eqs (15) to (17) is a classical fluid flow problem, as the flow
around a cylinder. However, in our case, the fluid flows inside a rectangular channel. In
order to analyze the heat and mass transfer fin performance, it is necessary to know the
airflow pattern, particularly the distribution of the airflow velocities. The investigation of air
velocity field has been carried out either by using the analytical approaches given by
Johnson (1998) or by a numerical analysis using the finite-volume method. In the completion
of this work, as the Reynolds number based on fin length is less than 2000 (laminar case)
and as the air thermo-physical properties are weakly temperature dependent, except the
kinetic viscosity, the following expressions of the dimensionless velocities found by Johnson
(1998) are approved:

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