A COMPREHENSIVE FRACTAL APPROACH IN DETERMINATION OF THE
EFFECTIVE THERMAL CONDUCTIVITY OF GAS DIFFUSION LAYERS IN
POLYMER ELECTROLYTE MEMBRANE FUEL CELLS
MOHD FIKRI BIN AZIZAN
A project report submitted in partial fulfillment of the requirement for the award of
the Degree of Master of Mechanical Engineering
Faculty of Mechanical and Manufacturing Engineering
Universiti Tun Hussein Onn Malaysia
JUN 2017
iii
Special dedication to my beloved mother and father
(Azizan bin Saad and Norsyakimah Lee binti Abdullah), and all family members for
their love and encouragement
Special thanks to my friends, my lecturer and faculty members for all your care,
support and endless best wishes
iv
ACKNOWLEDGMENT
In the name of Allah S.W.T, The Most Gracious and Merciful.
Alhamdulillah, praise to Allah S.W.T. for giving me the strength to complete my Master
Research project with successfully. First and foremost, I would like to give my deepest
thanks to both my parents (Azizan bin Saad and Norsyakimah Lee binti Abdullah), and
also to family members (Mohd Faizal bin Azizan, Intan Syafinaz binti Azizan,
Muhammad Fauzi bin Azizan and Intan Diyana binti Azizan) for their continuing
support and encouragement in completing this project.
I would like to express my deepest gratitude to my supervisor, Prof Madya Dr.
Bukhari bin Mansoor and also to Dr. Hamidon bin Salleh, as the co-supervisors for
constantly guiding and encouraging me throughout this study. I would like to convey my
greatest appreciation to him for giving me the professional training, advice, motivation
and suggestion to carry this project to its final form.
In particular, my sincere thanks are also extended to all my friends and others
who have provided assistance at various occasions especially to all members
Automotive Laboratory, and Principal, Fellows and Assistance Fellows of Tun Fatimah
Resident Collage. With my heartfelt would like to say thanks to each and every one of
them. Their views and tips are useful indeed. Regrettably, it is not possible to list all of
them in this limited space.
Thank you. May Allah S.W.T. bless upon all of you.
v
ABSTRACT
The challenges in the fuel cell industry is to produce the efficient thermal and water
management for accurate determination of the effectiveness thermal conductivity of
gas diffusion layers (GDL) used in polymer electrolyte membrane fuel cells
(PEMFC‟s). This is one of the factors affecting the durability of a fuel cell and need
to get a solution to minimize costs and optimize the use of electrodes and cells. The
main objectives of this research focus on the capability of the fractal approach for
estimation the effectiveness of thermal conductivity of gas diffusion layer. Moreover,
on this research also to propose modified fractal equations in determination of the
effective thermal conductivity of GDL in PEMFCs based on previous study. Other
objectives in this study are demonstrated the thermal conductivity of GDL treated
with PTFE contents by using through-plane thermal conductivity experiment
method. The through-plane measurement (experiment method) has been used in
estimating through-plane thermal conductivity of the GDL. Thermal resistance for
GDL also has been investigated under compression pressure 0.1 MPa until 1.0 MPa.
In fractal equation, the determination of tortuous and pore fractal dimension can be
done by using Scanning Electron Microscopy (SEM) method. Determination of
effectiveness thermal conductivity using of fractal equation with slightly modified.
In findings, it was found that fractal equation have been modified and measured on
the GDL parameter characteristics. It was shown that the value of the effectiveness
thermal conductivity of the sample using fractal approach is in good agreement with
the experimental value. Finally, all the effective thermal conductivity measured by
experimental and fractal approach have been determined with the variant temperature
and compression pressure to show the validation result between of this two methods.
vi
ABSTRAK
Cabaran dalam industri fuel cell adalah untuk pengurusan haba dan air yang cekap
dan juga penentuan tepat secara keberkesanan bagi keberaliran haba pada lapisan
resapan gas (GDL) yang digunakan dalam membran elektrolit polimer fuel cell
(PEMFCs). Ini adalah merupakan salah faktor-faktor yang mempengaruhi ketahanan
pada fuel cell dan hal ini perlu mendapat penyelesaian yang terbaik untuk
mengurangkan kos dan mengoptimumkan penggunaan elektrod dan sel-sel. Objektif
utama fokus penyelidikan ini adalah untuk mengetahui keupayaan pendekatan fraktal
untuk anggaran keberkesanan kekonduksian haba pada PEM dan GDL. Selain itu,
kajian ini juga untuk mencadangkan pengubahsuaian terhadap persamaan fraktal
dalam penentuan kekonduksian haba yang berkesan GDL di PEMFCs berdasarkan
kajian sebelumnya. Objektif lain dalam kajian ini menunjukkan keberaliran haba
pada GDL dengan kandungan PTFE berbeza dengan menggunakan kaedah
eksperimen kekonduksian haba melalui ujian pelantar. Pengukuran ujian pelantar
(kaedah eksperimen) telah digunakan dalam menganggarkan kekonduksian haba
daripada GDL. Rintangan haba untuk GDL juga telah dijalankan di bawah tekanan
mampatan 0.1 sehingga 1.0 MPa. Dalam persamaan fraktal, penentuan kelikuan dan
liang dimensi fraktal boleh dilakukan dengan menggunakan kaedah Scanning
Electron Microscopy (SEM). Penentuan keberkesanan kekonduksian haba
menggunakan persamaan fraktal dengan sedikit pengubahsuaian telah dijalankan.
Hasilnya telah didapati bahawa nilai keberkesanan keberaliran haba terhadap bahan
ujikaji dengan menggunakan kaedah pendekatan fraktal adalah bersamaan dengan
nilai yang diperoleh dengan menggunakan kaedah eksperimen. Akhir sekali,
kesemua nilai keberkesanan kadar aliran haba telah diukur dengan kaedah
eksperimen dan fractal telah ditunjukkan debgan berlainan suhu pemanasan dan
tekanan mampatan yang berbeza bagi menunjukkan pengesahan keputusan bagi
kedua-dua kaedah ini.
vii
TABLE OF CONTENTS
TITLE i
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENT vii
LIST OF FIGURES ix
LIST OF TABLES xiiii
LIST OF SYMBOLS AND ABBREVIATIONS xiv
LIST OF APPENDICES xvi
CHAPTER 1 INTRODUCTION 1
1.1 Research background 1
1.2 Problem statement 3
1.3 Significance 5
1.4 Objective 5
1.5 Scope of study 6
CHAPTER 2 LITERATURE REVIEW 7
2.1 Introduction 7
2.2 Application of fuel cell 8
2.3 Proton exchange membrane fuel cell 9
2.4 Gas diffusion layer in PEMFCs 11
2.5 Fractal model of effective thermal conductivity of gas diffusion layer in
polymer electrode membrane fuel cells 13
2.6 Determination of the required fractal dimension 19
2.7 Determination of tortuous fractal dimension 20
2.8 The modified algorithm for the generation of random multi-fractal media 21
viii
2.9 Measurement the through plane thermal conductivity of the PEM and GDL 22
2.10 Summary 25
CHAPTER 3 METHODOLOGY 26
3.1 Introduction 26
3.2 Experimental setup 28
3.3 Measurement and uncertainty analysis 30
3.4 Calculation of heat flux, Q and thermal conductivity, k of PEM and GDL 35
3.5 Scanning of electron microscope 35
3.6 Fractal approach to thermal conductivity 36
3.7 Summary 39
CHAPTER 4 RESULTS AND DISCUSSION 40
4.1 Thermal conductivity of the PEM and GDL 40
4.2 Temperature profile of PEM and GDL 41
4.3 Determination of the PEM and GDL fractal dimension 42
4.4 Effect of the temperature on the through-plane thermal conductivity of
PEM and GDL 46
4.5 Thermal conductivity by fractal approach 55
4.6 Summary 57
CHAPTER 5 CONCLUSION AND RECOMMENDATION 59
5.1 Introduction 59
5.2 Conclusion 59
5.3 Recommendation 60
REFERENCES 62
ix
LIST OF FIGURES
1.1 A functionally description of fuel cells 2
1.2 Schematic of Membrane Electrode Assembly
(MEA) in PEMFCs
4
2.1 The illustration movements of hydrogen atom
cross-over the membrane
10
2.2 Nafion ® Du Pont membrane fuel cell 10
2.3 (a) The reconstructed microporous layer 13
2.3 (b) SEM image of a microporous layer 13
2.4 Microstructure and material parameter for the
fractal model
14
2.5 The series-parallel model 15
2.6 A comparison of the effective thermal
conductivity between the fractal parallel
models, series model and the series-parallel
layer models of thermal conductivity
19
2.7 (a) Scanning electron microscope picture of
typical carbon fiber paper sheets use in fuel
cell - Toray TGPH-060 CFP with no PTFE
20
2.7 (b) Scanning electron microscope picture of
typical carbon fiber paper sheets use in fuel
cell - close-up view of the TGPH-060 CFP
with no PTFE
20
2.7 (c) Scanning electron microscope picture of
typical carbon fiber paper sheets use in fuel
20
x
cell - Toray TGPH-060 CFP with 20% PTFE
2.7 (d) Scanning electron microscope picture of
typical carbon fiber paper sheets use in fuel
cell - close-up view of the TGPH-060 CFP
with 20% PTFE
20
2.8 Measured thermal conductivity of the GDLs
at different compression loads
23
2.9 Measured thermal conductivity of the
membrane as a function of the temperature for
dry Nafion ® membrane (N112 and N117),
error bar calculated at 15%
24
2.10 Measured thermal conductivity as a function
of temperature for GDL- Toray carbon paper
(TGP-H-060), error bar calculated at 15%
25
3.1 A methodology flow chart 27
3.2 Schematic diagram of the test setup to
measure
29
3.3 (a) Schematic diagram thermocouple location 32
3.3 (b) Actual through-plane test rig for location
along the aluminum bronze
32
3.4 A typical steady state temperature profile
through the GDL
33
3.5 Schematics thermal resistance network of the
upper and lower standard material and
specimen of PEM
34
4.1 Steady state temperature profile at
thermocouple location for Nafion
N117 Catalyst Coated Membrane at variants
ambient temperature
42
4.2 (a) SEM Image cross-sections TGP-H-060 44
4.2 (b) SEM Image cross-sections TGP-H-090 44
4.2 (c) SEM Image cross-sections ELAT LT1400W 44
xi
4.2 (d) SEM Image cross-sections Untreated N117
Membrane
44
4.2 (e) SEM Image cross-sections Coated N117
Membrane
44
4.2 (f) SEM Image cross-sections CT 44
4.2 (g) SEM Image cross-sections Sigracet 35 AA 44
4.2 (h) SEM Image cross-sections Sigracet 35 BA 44
4.3 (a) SEM Image surface TGP-H-060 45
4.3 (b) SEM Image surface TGP-H-090 45
4.3 (c) SEM Image surface ELAT LT1400W 45
4.3 (d) SEM image surface untreated N117
membrane
45
4.3 (e) SEM image surface coated N117 membrane 45
4.3 (f) SEM image surface CT 45
4.3 (g) SEM image surface Sigracet 35 AA 45
4.3 (h) SEM image surface Sigracet 35 BA 45
4.4 Measured thermal conductivity as function
temperature for samples of PEM and GDL
48
4.5 Measured thermal resistance for the tested
PEM Coated N117
50
4.6 Measured thermal resistance for the tested
PEM Untreated N117
50
4.7 Measured thermal resistance for the tested
GDL Toray Carbon Paper TGP-H-060
51
4.8 Measured thermal resistance for the tested
GDL Toray Carbon Paper TGP-H-090
51
4.9 Measured thermal resistance for the tested
GDL CT
52
4.10 Measured thermal resistance for the tested
GDL ELAT
52
4.11 Measured thermal resistance for the tested
GDL Sigracet 35 AA
53
xii
4.12 Measured thermal resistance for the tested
GDL Sigracet 35 BA
53
4.13 Hysteresis in thickness of the GDL under the
external compression for TGP-H-060
(increase and decrease in pressure)
54
4.14 Hysteresis in thickness of the GDL under the
external compression for TGP-H-090
(increase and decrease in pressure
55
4.15 Comparison of thermal conductivity using
experimental and fractal approach between
each sample of GDL on the Room
Temperature
57
4.16 The effect of compression pressure with the
thermal conductivity by using experimental
and fractal approach between each sample of
GDL
57
xiii
LIST OF TABLES
2.1 Properties of two type GDL material 8
2.2 Specifications of Nafion membrane
within the membrane electrode
assemblies for N117 catalyst coated
membrane
11
2.3 Estimated thermal conductivities of
GDL sample at 20°C
12
2.4 Various specific values of thermal
conductivity
12
2.5 Microstructure and material parameter
of the sample „a‟ and „b‟
18
3.1 The specification of the PEM and GDL 28
4.1 Characteristics of the GDL sample for
pore fractal dimension, tortuous fractal
dimension and thermal conductivity
56
4.2 Comparison of the experimental thermal
conductivity at room temperature with
measured using fractal approach
57
xiv
LIST OF SYMBOLS AND ABBREVIATIONS
ΔT - Temperature drop across thin film
- Ratio of the number of perpendicular channels to the
total number of channels
λ - Size of the path
λmin, λmax - The minimum and maximum pore diameters
τ - Tortuous pathways
Ɛ, Ø - Porosity
A - Total area of a structural size
As - Area of heat transfer
C - Intercept of the line constant to the data in a log-log plot
Cph Phonon heat capacity
DAQ - Data Acquisition
Df - Fractal dimension
Dp - Specific pore fractal dimension
Dt - Tortuous fractal dimension
f() - The effects of anisotropy and structure in the in-plane
and through plane directions
FC - Fuel Cell
GDL, DM - Gas Diffusion Layer and Diffusion Media
k - Thermal conductivity
kg - Thermal conductivity of the occupied gas
ks1 - Thermal conductivity of the carbon fiber
ks2 - Thermal conductivity of the PTFE
Keff - Effective thermal conductivity
Keff,s - Effective thermal conductivity of solid phase
xv
Keff,p - Effective thermal conductivity of gas phase
kmem - Thermal conductivity of PEM and GDL
L(λ) - Corresponding path of length
Lo - Linear length of capillary pathway in the flow direction
Ls - Thickness of PEM and GDL
M(L) - Fractal structure
MEA - Membrane Electrode Assembly
MPL - Microporous layer
N - The cumulative pore size distribution
P - Pressure
PEM - Polymer Eletrolyte Membrane
PEMFCs - Polymer Eletrolyte Membrane Fuel Cells
PTFE - Polytetrafluoroethylene
Q - Heat flow rate
R - Pore size
r - Pore radius
R - Thermal resistance
RH-sample - Contact resistance between the sample and the holder
RL - Lower resistance
rmax - Maximum pore radius
Rsample - Thermal of sample
Rtotal - Total thermal resistance
RU - Upper resistance
SEM - Scanning Electron Microscope
T - Temperature
Tc - Temperature of the cold plate
Th - Temperature of the hot plate
Vp - Pore volume related with a certain pressure
vph - phonon velocity
Iph - Phonon mean free path
xvi
LIST OF APPENDICES
APPENDIX TITLE PAGE
1 Steady state temperature profile for
through-plane thermal conductivity
experimental
65
2 Example calculation value of Q and k
for through-plane thermal conductivity
Experimental and fractal of TGP-H-060
69
3 Image of sample and image of SEM for
PEM and GDL
73
4 Design and development through-plane
thermal conductivity test rig
88
5 Published paper 104
CHAPTER 1
INTRODUCTION
1.1 Research background
The renewal and cleanest energy sources become more serious attention in nowadays
due to the depletion of petroleum resources and potential to reduce emission
pollution. In current high demand on that, the one of the most efficient
environmental-friendly generation of energy is called fuel cell technology. Fuel Cell
technology have received more attention in recent years is due to the high efficiency
and low emissions. There are several categories of fuel cell which is Polymer
Electrolyte Membrane (PEM) fuel cells or PEMFC, Solid Oxide Fuel Cells (SOFC),
Phosphoric Acid Fuel Cells (PAFC), Alkaline Fuel Cells (AFC) and Molten
Carbonate Fuel Cells (MCFC). The focusing on this research is Polymer electrolyte
membrane fuel cells (PEMFC), where constructed from membrane electrode
assembly (MEA) including electrodes, electrolytes, catalysts, and gas diffusion
layers. The polytetrafluoroethylene (PTFE) Nafion® membrane acting as proton
conductor and (Pt)-based material as catalyst. PEMFCs convert chemical energy
stored in hydrogen (as a fuel) and oxygen directly and efficiently into electrical
energy with water as the only byproduct, have the ability to reduce energy
consumption, pollutant emissions and dependence to generation of electric energy
using fossil fuels. Figure 1.1 Efficiency of PEMFC can reach as high as 60 % in the
overall conversion of electrical energy and 80 % in cogeneration of electricity and
heat with a reduction of more than 90 % in the primary pollutants (in United State of
America).
2
The main applications of PEMFCs not only focusing on transportation, but it
does include of portable and stationary power generation. In automotive industries,
the well-known company as Honda, Toyota, General Motor and Hyundai has been
developed and demonstrated their product based on technology fuel cell (Fuel Cell
Vehicle) not only to fuel energy consumption saving but because of the potential
impact on the environment, such as emissions control greenhouse gases (Wang et al.,
2011) (Wu et al., 2014) (You et al., 2017).
Figure 1.1: A functionally description of fuel cells (Energy Design Resources, 2013)
Since PEMFCs is a renewable energy source of the cleanest, and fuel
(hydrogen and oxygen) are abundant in the earth, there are many researchers are
racing to make fuel cells are much more efficient and low cost. Recently,
considerable progress has been in improving power density, stability operations and
design structure PEMFCs. However, there are still many challenges to overcome for
profitable commercial applications. The challenges in fuel cell are its durability of
life time while operating. Among the factors that predispose to failure of PEMFCs is
the membrane manufacturing process, the material properties of the cell components,
installation of the fuel cell, and fuel cell system operating conditions. In application
fuel cell in transport, the frequency starting up and shutting down or nearly power
3
random cycle load are effect the humidity condition of Nafion membrane and also to
GDL. (Wu et al., 2014)
The main challenge in the design of fuel cells is to transfer heat from the gas
diffusion layer (GDL) in the polymer electrolyte membrane due to the result of a
chemical reaction to produce electricity. Analysis of this process requires the
determination of the effective thermal conductivity and thermal contact resistance is
also associated with the interface between the GDL and the adjacent surface or
coating. However, thermal conductivity of diffusion media or GDL is more difficult
to estimate due it porosity structure. GDL porosity makes it necessary to use
effective thermal conductivity to describe heat transfer in solid and liquid phases.
Because of GDL is anisotropic and having high porosities, there are widely dispersed
in literature thermal conductivity values.
In measuring thermal conductivity, there are several methods can be used.
The prediction methods for effective thermal conductivity of porous media can be
predicted by empirical formulas, numerical simulations, or theoretical models. The
empirical formulas and numerical simulation have several issues where empirical
method only based on simplifying assumption and empirical constants didn‟t indicate
any specific physical meanings. For numerical simulation method, the difficult to
analyst detail of GDL geometry model of porosity structure. (Nikooee et al., 2011)
Fractal approach can be used to estimate the thermal conductivity of diffusion media.
Fractal theory can analyze complex structure such as high porosities characteristic.
Fractal theory widely used in diverse engineering application which is involve
physical phenomena in disordered structures and over multiple scales.
1.2 Problem statement
The main objectives for all researchers in the development of novel membrane
materials are to improve the performance and durability of the fuel cells and reduce
the overall cost of fuel cells. Thermal conductivity of the PEM components must be
estimated accurately for better understanding the process of heat transfer in proton
exchange membrane fuel cells. The electrochemical reaction and irreversibility
4
associated in proton exchange membrane fuel cells generate large amounts of heat
which produces a temperature gradient in the various components of the cell.
In literary studies, Nafion commonly used as the thermal conductivity of the
membrane. GDL is one of the main components in MEA. The center part in MEA is
Proton Exchange Membrane or Polymer Electrolyte Membrane (PEM). Figure 1.2
shows the schematic of MEA and their components. However, it is difficult to
estimate the thermal conductivity of thermal diffusion media or gas diffusion layer
because of GDL is anisotropic and having high porosities. However GDL porosity
makes it necessary to use an effective thermal conductivity to describe heat transfer
in solid and liquid phases. As mentioned before, in having high porosity materials
and also anisotropic of GDL, which is probably be the reason why the thermal
conductivity are widely scattered in the literature (Zakil et al., 2016).
Among the methods used including of empirical formulas, numerical
simulations, or theoretical models to in determine the thermal conductivity, it‟s
experiencing one of the following three things: analytical methods are usually based
on very simplifying assumptions. Numerical solution with realistic assumptions that
can capture details GDL as heterogeneous porous media usually takes time using
simulations. The Empirical relationships including significant physical constants. In
Figure 1.2: Schematic of Membrane Electrode Assembly
(MEA) in PEMFCs (Iranzo, 2017)
5
that case, fractal methods have been recommended by Nikoee et al., (2011) as the
successful method to estimate the thermal conductivity of diffusion media.
Fractal geometry has been widely used in recent years to characterize the
complex, heterogeneous porous media. The main idea behind fractal geometry is the
scale parameter extraction invariant, which can describe the structure of complex
geometry. Physics phenomena that occur in such media can be associated with this
parameter. The main role of fractal geometry, in this case, is to simplify the structure
of porous media complex diffusion into the fractal dimension and the physical basis
for the derivation of the targeted phenomena.
There are different fractal dimensions that describe the characteristics of the
pores in the porous medium. Among the various fractal dimension, fractal dimension
and tortuous pore fractal dimension (called pores or areas based on the number of
fractal dimension calculation method) is the most important. Parameters that can be
measured by simple experiment can be used to develop the thermal conductivity
equation. To overcome these weaknesses, fractal geometry will be proposed as an
approach that will help to estimate the effective thermal conductivity of the polymer
electrolyte membrane.
1.3 Significance
This study aim to contributed regarding the temperature and heat transfer mechanism
to determine the thermal conductivity of the components of the membrane electrode
assembly and gas diffusion layer in order to approach of fractal method.
1.4 Objectives
This study embarks on the following objectives:
i. To investigate the capability of fractal approach in order to determine
thermal conductivity in GDL and propose a new approach (fractal
6
equation) in determination of the effective thermal conductivity of GDL
in polymer electrolyte membrane fuel cells.
ii. To validate by varying temperature, pressure and thermal conductivity of
GDL by using experimental method (through-plane method).
1.5 Scopes of study
The scopes of this study are listed as below:
i. An experimental study to determine the thermal conductivity
(experimental) of the PEM samples; coated Nafion® 117 and untreated
Nafion 117, the GDL samples; CT, ELAT® LT1400W, Sigracet 35 AA
(0 % PTFE) and Sigracet® 35 BA (50 % PTFE) and additional of thermal
contact resistance experiment between PEM and GDL samples with a
metal plate as a function of temperature and pressure.
ii. Comparisons have been made between the fractal methods and the
existing experimental results measured by one dimensional through-plane
thermal conductivity.
iii. Using equation of effective thermal conductivity in series and parallel
model to obtain pore fractal dimension from GDL pore size distribution.
iv. Scanning Electron Microscope (SEM) images of diffusion media also had
been used, and conventional methods of fractal image processing such as
box counting can be used to determine the pore fractal dimension.
v. The effect of the temperature on the through-plane thermal conductivity
of all the components in the PEM and GDL was investigated in the
temperature range 27 ºC - 90 ºC.
vi. The measurements temperature along the standard material and
specimens were performed under camber in order to eliminate the heat
transfer by convection.
vii. The compression pressure ranges between of 0.1 to 1 MPa.
CHAPTER 2
LITERATURE REVIEW
2.1 Introduction
In Polymer Electrolyte Membrane Fuel Cell (PEMFC) the membrane and catalyst
layer (consisting of the MEA), both of which require further research is essential to
identify and develop cost-effective material alternatives. Correlation properties of the
membrane for the performance of polymer electrolyte materials generally are more in
need. The process of heat transfer in porous GDL has been investigated and
appropriate predictive model of effective thermal conductivity by using fractal
theoretical characterization of the actual microstructure of GDL (Wang et al., 2011).
In general, the heat transfer mechanism is controlled by convection, radiation
and conduction. When the flow of liquid happen in pores the convection heat transfer
were occurs. Generally, the effect of convection is more pronounced in the case of
large pore size, while it is negligible for small pore size less than 100 μm at a lower
temperature (below 373 K) due to lack of intensive fluid- circulation in the pores. In
PEMFC, the GDL operating temperature produce in system is below than 375 K due
to its pore sizes which is 100 µm and in this scenario the convection or radiation can
neglected. (Shi et al., 2008) (Kantorovich et al., 1999).
8
Radiation heat transfer occurs through the release or absorption of heat
radiation pore walls. From studies on the type of coal, it has been found that radiation
mechanism has a significant effect on heat transfer through large pore size (> 10 μm)
at high temperatures (>1000 K), while foremost carbon material, the effect of
radiation heat transfer is negligible for temperatures below 1000 K (Shi et al., 2008).
Table 2.1 show summarizes properties of two type GDL materials. According to
table, its show that the pore size of GDL is less than 100 µm (Wang et al., 2016).
Table 2.1: Properties of two type GDL material (Wang et al., 2016)
Material PTFE loading (%) Porosity Pore size (µm)
sssCarbon cloth 0 0.78 97
Carbon paper TGP-H-120 0 0.81 32
Carbon paper TGP-H-120 20 0.74 32
Carbon paper TGP-H-120 70 0.61 31
Carbon paper TGP-H-120 97 0.57 32
Carbon paper TGP-H-120 120 0.52 30
Carbon paper TGP-H-120 150 0.43 32
2.2 Application of fuel cell
Technologies of fuel cells have got an attention in the transportation industry
including public transport and private vehicles. This is because the potential energy
produced by the fuel cell is capable of producing high efficiency, economical used
and the ability to reduce the environmental pollution caused by carbon monoxide gas
(Wang et al., 2011).
System Proton exchange membrane fuel cells operating on hydrogen and has a
power density as high as 1:35 kW / liter have been shown. This system has been
integrated into the vehicle concept by a number of manufacturers. Specific design
features of the fuel cell system 60 kW and operate on hydrogen supplied from a
cryogenic liquid hydrogen tank. This vehicle has a range of 400 km, a top speed of
135 km/h, and can be accelerate 0 - 100 km/h in less than 16 s (Ellis et al., 2001).
9
Development of fuel cell technology not only focusing on transportation, but
there are many of manufacturer working on other application for example, vending
machine, vacuum cleaners machines and traffic light. The growing of fuel cell
technologies also involved of power generation for hospital, police station and the
bank because of the advantages its-self (Segura et al., 2009).
2.3 Proton exchange membrane fuel cell
There are many types of fuel cell as explained in Chapter 1. As PEMFC were
selected, by using proton (hydrogen ion) conducting membrane will remain squeezed
between two porous platinum-catalyzed electrodes. At first, this membrane is based
on polystyrene, but currently Teflon-based products namely "Nafion" is used. It
offers high stability, high oxygen solubility, good thermal and high mechanical
stability. Nafion membrane is widely used for PEMFCs and have variety thickness
and specific application. These membrane are proton-conductive polymer film, also
as known as electrolyte or ionomer. The membrane functions are to allow only
protons to through-pass to cathode (Oxygen) from anode (Hydrogen) as shown in
Figure 2.1. Others are to spate the anode and cathode compartment of PEMFCs.
PEMFCs are low temperature fuel cell and operating temperature is relatively low
(between 60 – 100 °C). Hydrogen fuel cells require oxygen for humidified and
operations. Pressure, in general, remains the same on both sides of the membrane.
Operating at high pressure is necessary to achieve high power density, especially
when the air is selected as the anodic reactants. The PEMFC meets the demands of
rapid startup, acceleration, high power density and reliability. PEMFC will be best
for light-duty vehicle applications (T-raissi et al., 1992) (Mekhilef et al., 2012).
As known the mechanical strength very important for membrane since the
activities of the proton conductivity of the membrane. Figure 2.1 shows the
illustration movement of hydrogen proton cross-over the membrane. Membranes, for
example, need to carry protons, but not electrons. It is as thin as possible, so that
proton current is affected as little as possible and the voltage drop across the
10
membrane is reduced. The PEM must have durability in an acidic environment at
high temperatures for thousands of hours. It should also have a reasonable low
permeability to fuel. Nafion‟s developed by Du Pont as showed in Figure 2.2 is the
most PEM used widely known and used because it can resistant of temperature
below 100 ºC. Nafion‟s also become benchmark for comparison with other material
to develop new material for low cost to produce fuel cells. In the Table 2.2, the
Nafion N117 measurements are taken with membrane conditioned to 23 ºC, 50 %
relative humidity (Khandelwal et al., 2006) (Vishnyakov, 2006).
Figure 2.2: Nafion ® Du Pont membrane fuel cell
(Stripe et al., 2011)
Figure 2.1: The illustration movements of Hydrogen atom cross-over
the membrane (Scramlin et al., 2015)
H+
H+
H+
H+ H
+
H+
Permeate H+
11
Table 2.2: Specifications of Nafion membrane within the membrane electrode
assemblies for N117 catalyst coated membrane
Specifications
Dimension 300 mm x 300 mm
Thickness 0.183 mm
Basis weight 360 g/m2
2.4 Gas diffusion layer in PEMFCs
Gas Diffusion layer as kwon as Diffusion Media (DM), have a play roles as: (1)
electronic connection between the electrode and bipolar plate with channel, (2)
transit for reactant transport and heat/water removal, (3) mechanical support to the
membrane electrode assembly (MEA), and (4) protection of the catalyst layer from
corrosion or erosion caused by flows or other factors. (Wang et al., 2011). GDL
structural are very important for transport inside of GDLs for fuel cell conversion.
There are Carbon-based GDL such as carbon paper and carbon cloth where are
commonly used in PEMFC due to its porosity, electronic conductivity, and
flexibility. The better performance for GDL material is carbon cloth than carbon
paper as mention by Ralph et al at high current more than 0.5A cm-2
with internal
humidification (Stacks, 1997) (Park et al., 2012).
Large differences in the thermal conductivity of solid and liquid phases and
high porosity micro-structure GDL makes it necessary to define the effective thermal
conductivity, which transport parameters that play an important role in the analysis
of the performance of the fuel cell and is required in computing model. Several
studies in the literature have focused on the analysis model producing experimental
measurements of conductivity values lower than most values reported in the
literature (Wang et al., 2016). By using the concept of unit cells, the authors have
recently presented a solid model analysis to determine the effective thermal
conductivity GDLs (Sadeghi et al., 2011). A review from the previous study by
Ramousse et. al., (2008) shows that thermal conductivity of Nafion membrane
(Table 2.3) is well known where the thermal conductivity of GDLs is more difficult
to estimate (Ramousse et al., 2008). The porosity of the GDLs makes it necessary to
12
use effective thermal conductivities for describing heat transfer in the solid and fluid
phases (Yu et al., 2002). In Table 2.4, it‟s estimated from the thermal conductivities
of each phase and their volumetric fraction in the medium.
Table 2.3: Estimated thermal conductivities of GDL sample at 20 °C.
(Ramousse et al., 2008)
Sample
(A = 16 cm2)
Rmeasured
(KW-1
) 𝑅𝑚𝑀𝑎𝑥
(Km2 W
-1)
𝑘𝑒𝑓𝑓𝑀𝑖𝑛
(Km-1
W-1
)
𝑅𝑚𝑀𝑖𝑛
(Km2 W
-1)
𝑘𝑒𝑓𝑓𝑀𝑎𝑥
(Km-1
W-1
)
Quintech (190 µm) 0.327 5.23E-04 0.36 1.39E-04 1.36
Quintech (190 µm) 0.537 8.59E-04 0.33 4.75E-04 0.59
Quintech (190 µm) 0.727 1.16E-03 0.20 7.79E-04 0.30
SGL Carbon (420 µm) 1.008 1.61E-03 0.26 1.23E-03 0.34
Table 2.4 Various specific values of thermal conductivity (Shi et al., 2008)
Material Thermal conductivity
(Wm-1
K-1
) Material
Thermal conductivity
(Wm-1
K-1
)
Silver 4.186 x 102 Hydrogen 0.167
Aluminum 2.093 x 102 Oxygen 0.025
Quartz 8.392 Air 0.026
Sandstone 3.767 benzene 0.159
Clay 0.837 – 1.256 Petroleum 0.147
Water 0.461 Glass 0.502 – 1.088
In the previous studies by Zamel et al., (2012), the three dimensional
reconstruction of the layer in Figure 2.3 (a) and 2.3 (b) have been used to estimate
the diffusion coefficient and thermal conductivity of the microporous layer. The
parameters on the transport properties on these studies involve the effect of MPL
porosity, thickness and penetration.
13
2.5 Fractal model of effective thermal conductivity of gas diffusion layer in
polymer electrode membrane fuel cells
The model accounts for the actual microstructures of the GDL in terms of two fractal
dimensions, one relating the size of the capillary flow pathways to their population
and the other describing the tortuosity of the capillary pathways have been discussed
in previous study. The fractal permeability model is found to be a function of the
tortuosity fractal dimension, pore area fractal dimension, sizes of pore and the
effective porosity of porous medium without any empirical constants. A large
number of reports show that the microstructure and pore size distribution of porous
media have fractal characteristics. Therefore, it is possible to get through porous
media permeability pore structure fractal analysis (Shi et al., 2006).
Figure 2.3: (a) The reconstructed microporous layer : (b) SEM image of a
microporous layer (Zamel et al., 2012)
14
2.5.1 Fractal parallel model
In a porous medium having fractal characteristics, surface area, pore volume and the
length of capillary pathways follow a power law (Nikooee et al., 2011) (Shi et al.,
2012). Figure 2.4 shows the microstructure and material parameters for the fractal
model. The length L(λ) of the capillary pathway equation (1) can be considered as
below:
𝐿(𝜆)
𝐿0=
𝐿𝑜
𝜆 𝐷𝑡−1
(1)
Where, Lo represents the linear length of these capillary pathways in the flow
direction, λ denotes the diameter of the path, L(λ) is its corresponding length and Dt
is the tortuous fractal dimension (Shi et al., 2008). From the equation (2), the
tortuous pathways can be obtained by:
𝜏 = 𝐿(𝜆)
𝐿0
2=
𝐿𝑜
𝜆
2𝐷𝑡−2
(2)
For porous media have fractal characteristics, the cumulative pore size
distribution N can be attributed with the maximum pore size as equation (3) follows:
λ Lo
λ(x)
Figure 2.4: Microstructure and material parameter for the fractal model
15
𝑁 𝑅 ≥ 𝑟 = 𝑟𝑚𝑎𝑥
𝑟 𝐷𝑝
(3)
Where, R denotes an arbitrary pore size for which pores with the larger than
radii, r have been counted, rmax is the maximum pore radius and Dp specifies pore
fractal dimension. Based on the method of fractal analysis the pore fractal dimension
can vary, for instance, if the image of the GDL cross section is used, the pore fractal
dimension would vary between 1 and 2 and if the pore size distribution (example as
obtained by porosimetry methods) is employed the dimension would be between 2
and 3 (Nikooee et al., 2011) (Zheng et al., 2012).
The series–parallel model (Figure 2.5), Nikooee et al.,(2011) claimed that Shi
et al., (2012), was proposed a fractal model for estimation of thermal conductivity
(Nikooee et al., 2011) (Shi et al., 2012). The effective thermal conductivity of the
medium can be obtained as equation (4) :
𝑘𝑒𝑓𝑓 =1
1−𝜉
𝑘𝑒𝑓𝑓 ,𝑝+
𝜉
𝑘𝑒𝑓𝑓 ,𝑠
(4)
Where, keff is effective thermal conductivity, keef,p represents effective thermal
conductivity of the gas phase in parallel and keef,s is the effective thermal conductivity
if the gas and solid phases in perpendicular pore channel . ξ is the ratio of the number
Figure 2.5: The series-parallel model
16
of perpendicular channels to the total number of channels, with values range from 0
to 1.
The effective thermal conductivity through of parallel and perpendicular to
the heat direction can be described by using equation (5) and (6) :
𝑘𝑒𝑓𝑓 ,𝑠 = 1
휀
𝑘𝑔+
0.22
𝑘𝑠1+
0.78−휀
𝑘𝑠2
(5)
𝑘𝑒𝑓𝑓 ,𝑝 =𝑘𝑔 2−𝐷𝑝 휀𝜆𝑚𝑎𝑥
𝐷𝑡−1 1− 𝜆𝑚𝑖𝑛𝜆𝑚𝑎𝑥
𝐷𝑡−𝐷𝑝+1
𝐿0𝐷𝑡−1 𝐷𝑡−𝐷𝑝+1 1−
𝜆𝑚𝑖𝑛𝜆𝑚𝑎𝑥
2−𝐷𝑝
+ 0.22𝑘𝑠1 + 0.78− 휀 𝑘𝑠2 (6)
Where kg, ks1 and ks2 are the thermal conductivities of the occupied gas carbon
fiber and PTFE, respectively. ε donate the specifies porosity and λmin and λmax denote
the minimum and maximum pore diameters respectively.
The modified equations for parallel and series claimed by Shi et al.,(2008) are
suitable for the prediction of the effective thermal conductivity of a GDL. The
proposed of combination with the contribution of parallel and series tubes by a series
scheme based on the equation (4) will reach the effective thermal conductivity (Shi
et al., 2008). Such series scheme is suitable to determine through plane conductivity.
The equation (7) is suitable to determine of in-plane thermal conductivity
contribution with combination of parallel scheme.
𝑘𝑒𝑓𝑓 = 1− 𝜉𝑖𝑛 𝑘𝑒𝑓𝑓 ,𝑝 + 𝜉𝑖𝑛𝑘𝑒𝑓𝑓 ,𝑠 (7)
Where, ξin is the ratio of the number of channels perpendicular to the in-plane
flow direction to the total number of channels. The ξin, is related in the through plane
heat conduction, ξ. As on the geometrical parallel–perpendicular tubes scheme
presented previously (Figure 2.4), the equation (8) is the ratio of the number of
channels:
𝜉𝑖𝑛 = 1 − 𝜉 (8)
17
By using simplifying assumption on equation (8) to obtained suitable
configuration of channels in through-plane condition. Based on Nikooee et al.,
(2011) this simplifying assumption and for practical applications is suitable used for
two parameters can be related using a more general function, f(ξ)as equation (9)
below:
𝜉𝑖𝑛 = 𝑓 (9)
Where f(ξ) represents to the effects of anisotropy and structural differences in
the in-plane and through plane directions. To get the length of Lo can be calculated in
the mathematical equation (11) as proposed by Nikooee et al., (2011). The A can be
expressed as the total area of a structural size and determine using equation (10). The
pore area fractal dimension Dp can be calculated if the parameter such as ε, λmin and
λmax are determined by the equation (12) (Zheng et al., 2012). The distribution size
can be measured as the solid part as well as of all pores of different size between λmin
and λmax. It is can be describes using fractal geometry as equation (12) below:
𝐿𝑜 = 𝐴 (10)
𝐴 =𝜋𝐷𝑝𝑑
2𝑚𝑎𝑥
4휀 2−𝐷𝑝 1−
𝜆𝑚𝑖𝑛
𝜆𝑚𝑎𝑥
2−𝐷𝑝 (11)
And the general equation of Lo can be estimated as below:
𝐿𝑜 = 𝜋𝐷𝑝𝑑2
𝑚𝑎𝑥
4휀 2−𝐷𝑝 1−
𝜆𝑚𝑖𝑛
𝜆𝑚𝑎𝑥
2−𝐷𝑝 (12)
In the in-plane condition, the equation (12) can be used for considering of Lo as GDL
thickness.
18
2.5.2 Fractal prediction of effective thermal conductivities
Shi et al., (2008) using the effective thermal conductivities keff by modification of fhe
fractal parallel model equation used air through the samples GDL: TGP-H-060
carbon paper „a‟ and TGP-H-060 carbon paper treated with PTFE „b‟(Shi et al.,
2008). A comparison is made between different theoretical models. In this study, the
parameters of GDL used are listed in Table 2.5; the values of fractal dimension are
derived from scanning electron microscopic micrographs of the two samples.
Comparison between the results of both samples showed that the sample keff 'b' is
greater than the sample 'a‟ according to Table 2.5. The increase is due to the filling of
keff PTFE, which has high thermal conductivity, in the pore space of carbon paper.
Figure 2.6 shows the comparison of the effective thermal conductivity between the
fractal parallel models, series model and the series-parallel layer models of thermal
conductivity. It was showed that for each model giving different results.
Table 2.5: Microstructure and material parameters of the sample „a‟ and „b‟
(Shi et al., 2008)
Parameter Sample „a‟ Sample „b‟ Description
λmax 8 x 10-5
m 7 x 10-5
m Maximum pore diameter
λmin 3.079 x 10-8
m 1.487 x 10-8
m Minimum pore diameter
Ø 0.78 0.55 Porosity
Lo 1.9 x 10-4
m 1.9 x 10-4
m Thickness of the GDL
Ks1 8 Wm-1
K-1
8 Wm-1
K-1
Thermal conductivity of
carbon fiber
Kg 0.02624 Wm-1
K-1
0.02624 Wm-1
K-1
Thermal conductivity of
gas
Ks2 0.25 Wm-1
K-1
0.25 Wm-1
K-1
Thermal conductivity of
PTFE
Dp 1.9669 1.9276 Pore area dimension
Dt 1.1447 1.1447 Tortuous dimension
19
2.6 Determination of the required fractal dimension
To define the pore fractal dimension, it can be calculated by various techniques
which are obtained from GDL pore size distribution by using equation (3). Mercury
porosimetry are recommended by Nikooee et al., (2011) to obtain the pore size
distribution. The other techniques is using Scanning Electron Microscope (SEM)
images of diffusion media and fractal image processing conventional methods which
is counting the box can be utilized in the determine of pore fractal dimension (Rama
et al., 2008). The last technique is measured the GDL capillary pressure is curve by
using this equation (13):
𝐼𝑛 𝑑𝑉𝑝
𝑑𝑃 = 𝐷𝑝 − 4 𝐼𝑛𝑃 + 𝐶 (13)
Figure 2.6: A comparison of the effective thermal conductivity between
the fractal parallel models, series model and the series-parallel layer
models of thermal conductivity (Shi et al., 2008)
20
Where Vp can be defined as pore volume related with a certain pressure, P
and C is intercept of the line constant to the data in a log-log plot.
The fractal dimensions of pore size distribution of the GDL material have
been introduced by using a porosimetry technique. In this method, it can be
determine the hydrophilic and hydrophobic pore size distribution (Nikooee et al.,
2011). The equation (3) and SEM method are been used for this fractal analysis.
Figure 2.7 shows the SEM image of a carbon fiber without any coating.
2.7 Determination of tortuous fractal dimension
In the previous study by Nikooee et al., (2011) introduced a new method in the
determination of tortuous fractal dimension in the absence of SEM images. In this
method, the ideas generated by the most representative medium based on the
available data on the pore size distribution and porosity of GDL layer. In advance for
(a) (c)
(b) (d)
Figure 2.7: Scanning electron microscope picture of typical carbon fiber
paper sheets use in fuel cell (a) Toray TGPH-060 CFP with no PTFE;
(b) close-up view of the TGPH-060 CFP with no PTFE; (c) Toray
TGPH-060 CFP with 20% PTFE ; (d) close-up view of the TGPH-060
CFP with 20% (David et al., 2010)
21
construction, the selection of the type of artificial medium must be selected. The
multi-fractal has been used as the representative of the real porous media. A proper
depiction of the real GDL layer will come out from the random multi-fractal model
which can be considered as generalization of simple mono-fractal models. The
similar to the real porous medium in basic characteristics of the generated medium
such as pore size distribution and porosity can produce the most representative multi-
fractal medium. Though, the common algorithms for the generation of multi-fractal
media do not usually match the required pore size distribution and/or porosity, they
have recently been used to shed light into physical characteristics of porous media
such as hydraulic permeability and water retention characteristics (Shi et al., 2012).
Nikooee et al., (2011) used the counting box technique for determination of
tortuous fractal dimension. In the description, it will use the different size of boxes to
cover the tortuous curves. The non-empty boxes needed to accommodate curves
which are then calculated. Finally, the numbers of numbers of boxes versus to the
size of the box are drawn on a log-log and the slope of the line that best fitted to give
the tortuous fractal dimension (Yu et al., 2004) (Nikooee, et al., 2011).
2.8 The modified algorithm for the generation of random multi-fractal
media
At the beginning, the platform on which the pores and solid parts distributed, divided
into cells of different sizes based on known samples GDL pore size. In descending
order, the pore sizes produced. For example, in the first step, the largest pores in the
solid parts of the pores with smaller sizes produced. A similar procedure by Nikooee
et al., (2011) is followed to make the pores of each size (Zamel et al., 2012)
(Nikooee et al., 2011).
The iteration step is the best way for the matching threshold probability so
that the number of the generated pores can reach the actual number of pores in
determining of pore size distribution. The initial value for threshold probability is
considered to be equal to the porosity of GDL.
22
In the next step, the solid parts are divided into cells with specific size smaller
pore size equal to certain smaller are present in the GDL medium. This algorithm is
repeated to generate pore size of the GDL and to match the pore size distribution as
much as possible. Due to the number of pores and solid parts together with the
porosity that can be used to determine the field of initiator, the final generated
medium will have a porosity and pore size distribution in real samples.
Nikooee et al., (2011) mention that to get the distribution of tortuous fractal
dimension, the algorithm was coded and run 100 times for each of three used of
samples which is pure GDL, 12.8% PTFE coated GDL and 32.2% PTFE coated
GDL (Nikooee et al., 2011).
2.9 Measurement the through plane thermal conductivity of the PEM and
GDL
In better understanding of heat transfer in proton exchange membrane fuel cells, the
thermal conductivity of the PEM and GDL must be accurately estimated in both
direction, namely the in-plane and through-plane direction. The steady state method
using through-plane directions for measured the thermal conductivity of gas
diffusion layers GDLs. The temperature measured by using thermocouple in different
level in fuel cell which is the temperature gradient can be define and plotted in graph.
Alhazmi et. al., (2014) have conducted the experiment setup using steady state
method, developing the measure the through-plane thermal conductivity of the
components in PEM and GDL at the different operating temperature. The thermal
conductivities of the GDLs are investigated as a function of the PTFE loading,
temperature and compression pressure (Alhazmi et al., 2014).
23
2.9.1 Effect of compression pressure on the through-plane thermal
conductivity of the gas diffusion layer
When applying the compression pressure, it will have the reduction in the thickness
on the GDL and PTFE. Then, the variation in thickness is almost negligible after
increasing the pressure which indicates that the deformation of the GDL has
„saturated‟. Alhazmi et al., (2014) claimed that there is a hysteresis effect in the
compression curves which signals that there has been a permanent deformation in the
compressed GDL sample. In Figure 2.8, shows the investigated effect of the applied
load on the thermal resistance. It is clear that the thermal resistance values of the
treated GDLs are higher than that of the untreated GDL. This is due to the increase in
the contact resistance between the fibers of the GDL after adding the PTFE
(Khandelwal et al., 2006) (Alhazmi et al., 2014).
Figure 2.8: Measured thermal conductivity of the GDLs at different
compression loads (Alhazmi et al., 2014)
24
2.9.2 Effect of the temperature on the through-plane thermal conductivity in
the PEM
Figure 2.9 shows that the thermal conductivity of Nafion® decreases with increasing
temperature, where the test temperature is defined as the average temperature across
the test specimen. Although the downward trend in thermal conductivity is nearly
within the error bar limit, this behavior of Nafion® may be explained on the basis of
its structure and morphology (Chun et al., 1998) (Zhang et al., 2006).
2.9.3 Effect of the temperature on the through-plane thermal conductivity of
the GDL
The through-plane thermal conductivity of the GDL was found to be significantly
lower than its in-plane thermal conductivity. The through-plane thermal conductivity
of the GDL increasing with the temperature (Nikooee et al., 2011). Figure 2.10
shows the variation of the thermal conductivity for Toray carbon paper (TGP-H-060)
as a function with increasing of temperature
Figure 2.9. Measured thermal conductivity of the membrane as a
function of the temperature for dry Nafion ® membrane (N112 and
N117), error bar calculated at 15% (Alhazmi et al., 2014)
62
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