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STRUCTURE AND PROPERTIES OF ONE-

DIMENSIONAL FIBER-BASED

THERMOELECTRIC GENERATORS

ZHANG LISHA

PhD

The Hong Kong Polytechnic University

2019

The Hong Kong Polytechnic University

Institute of Textiles and Clothing

Structure and Properties of One-Dimensional

Fiber-Based Thermoelectric Generators

Zhang Lisha

A thesis submitted in partial fulfilment of the

requirements for the degree of Doctor of Philosophy

December 2018

CERTIFICATE OF ORIGINALITY

I hereby declare that this thesis is my own work and that, to the best of my

knowledge and belief, it reproduces no material previously published or written,

nor material that has been accepted for the award of any other degree or diploma,

except where the acknowledgement has been made in the text.

ZHANG Lisha

(Signed)

(Name of student)

To my parents

Abstract

I

Abstract

To collect scavenged energy from objects with large and three dimensional surface

like human body, it requires the energy harvesting devices to be flexible,

deformable, stretchable and light weight. Traditional rigid thermoelectric (TE)

generators cannot fulfill this purpose, although they can convert thermal energy into

electrical energy directly without any moving parts or working fluids. In the past,

very few research has been reported on flexible and conformal fiber-based TE

generators (FTEGs). Therefore, this thesis focuses on one-dimensional (1D) FTEGs,

that is, only fiber or yarn structures will be considered and they can be further

fabricated into two-or three-dimensional devices. A systematical research is

conducted on the geometric structure of 1D FTEGs and their thermoelectric

performance.

Based on a systematic literature review, the research gaps were identified. A

theoretical model of 1D FTEGs was designed analytically and numerically

simulated with COMSOL Multiphysics®, a finite element software package. From

the structure viewpoint, the 1D FTEGs were designed as a coaxial shell/core

structure: TE layer and electrodes were the shell; fiber/filament was the core.

Initially, the convergence of the numerical simulation was verified with appropriate

discretization approach. The reliability of the numerical simulation was examined

Abstract

II

and confirmed through the comparison of simulation results with those from the

previously published articles and the analytical solutions of the theoretical models.

Then, based on the appropriate mesh configuration, the output power and energy

conversion efficiency of 1D FTEGs with different geometric parameters were

derived. Their influencing factors were studied in three cases of different conditions:

(1) conduction heat transfer only; (2) conduction with thermal and electrical contact

resistance (TCR and ECR); (3) conduction and radiation heat transfer. In the first

two cases, the hot and cold side temperature were fixed as constants. In the third

case, the cold side was a free end, whose temperature was determined as the result

of radiative and conductive heat transfer. The geometric parameters included the

radius of filament, the thickness and length of TE layer. The simulations showed

that, among all these parameters, the thickness of TE layer was the primary factor,

because it brought the highest variation in the maximum output power and energy

conversion efficiency in several orders of magnitude. Besides, although the large

TCR and ECR caused the deterioration of the device’s performance, they can hardly

lead to the decrement in orders of magnitude. Finally, the influence of the radiative

heat transfer was rather complex, indicating the increment in filament radius

resulted in the increasing efficiency first and then decreasing one.

In order to verify the theoretical analysis and numerical simulation of 1D FTEGs,

experimental investigations were carried out. 1D FTEG samples were fabricated

Abstract

III

with poly(ethylene terephthalate) (PET) filament and poly(3,4-

ethylenedioxythiophene): poly(styrene sulfonic acid) (PEDOT: PSS), one polymer

thermoelectric (TE) material. The TE material was characterized by thermo-

gravimetric analysis (TGA), crystalline structure with X-ray diffraction (XRD),

Seebeck coefficient, thermal conductivity and electrical conductivity. The 1D

FTEG samples were characterized with scanning electron microscope (SEM) and

an optical microscope. The energy conversion performance of these samples were

measured with a lab-made measurement system, which was composed with a heat

source, real-time temperature measurement and output electrical potential

measurement. Finally, the experimental results were compared with the numerical

solutions. The experiment results showed good agreement with that from the model

and simulation: the variation of TE layer thickness caused the huge variation (in

serval orders of magnitude) of maximum output power.

The 1D FTEGs are commonly used in an array. The radiation influence in FTEG

arrays would be much more prominent as the 1D FTEGs were closely packed.

Therefore, an assembly unit of parallel 1D FTEGs was further considered by taking

account of the surface-to-surface radiation and the air conduction simultaneously.

This investigation has been divided into two parts: the first part was the exploration

of the necessary and limitation of considering these progress of thermal

transmission; the second part focused on the issue of the performance of the

Abstract

IV

assembly unit of parallel 1D FTEGs under the condition of various emissivity and

distance between 1D FTEGs. For the two parts of this investigations, the

temperature at the hot side was fixed as a constant. But the cold side was set as a

free end. In order to accomplish the exploration assignment, the theoretical models

were design as the 1D FTEG being encircled with a thin wall. Under distinct

thickness of TE layer conditions, the influences on output performance were

demonstrated with various distances between the adjacent surfaces of 1D FTEGs

and thin wall with a series of varied emissivity. Under this condition, the decrease

of temperature at the cold side was caused by two factors: the major one was the

increasing distance between the surfaces of 1D FTEG and thin wall; another was

the enlarged emissivity. Whereas, for the second part of the investigation, in the

assembly unit of 1D FTEG array, the decrement of temperature at free end was the

result of the increasing emissivity as the primary reason and the increment of the

distance as the second one. For all cases, if the temperature at the free end dropt

down, the output power of devices raised up.

In this study, the multi-physics models have been established and used to explain

the relationships between the performance and geometric structure of 1D FTEGs,

for the first time. The models of 1D FTEG arrays were designed, whose

performance and the influential factors were also explored. A simple and feasible

method has been developed to fabricate 1D FTEGs, which can facilitate the

Abstract

V

application of these devices. More 1D FTEGs and their arrays are expected to be

fabricated and characterized in the future. Then, the experimental results will be

compared to the simulation results of the developed models. This comparison may

help to modify the current models if necessary. The study of 1D FTEGs also

provides a solid foundation for the development of FTEGs in two- or three-

dimensions. For the long term, this study could provide engineering guidance to the

design and fabrication of FTEGs.

Publications Arising from the Thesis

VII

Publications Arising from the Thesis

Published journal paper:

Zhang L, Lin S, Hua T, Huang B, Liu S and Tao X. Fiber‐Based Thermoelectric

Generators: Materials, Device Structures, Fabrication, Characterization, and

Applications. Adv Energy Mater. 2018; 8: 1700524.

The pending journal papers:

Zhang L, Hua T and Tao X. Modeling and Experimental study of One-Dimensional

Fiber-Based Thermoelectric Generators. (To be submitted)

Zhang L, Hua T and Tao X. A Comprehensive Modeling Study of One-

Dimensional Fiber-Based Thermoelectric Generator Arrays. (To be submitted)

Acknowledgements

IX

Acknowledgements

“Love suffers long.

Love is kind; it is not jealous.

Love does not brag and is not puffed up.”

— 1 Corinthians 13:4

One of the precious gifts in my fortunes is the opportunity to pursue my Ph.D.

degree under the direction of my chief supervisor, Dr. T. Hua, and co-supervisor,

Prof. X. M. Tao. Their direction has been the lighthouse, when I navigated in the

darkness. Without their help and encouragement, I could not accomplish the

training process for Ph.D. degree. I am extremely grateful that they have inspired

me to thoroughly think problems from a global view. Besides, they have spent so

much time and energy to discuss issues with me patiently. Through the discussion,

my critical thinking has been sharpened. In addition, except that they supported me

to conduct such an interesting and meaningful investigation, their serious attitude

to research has influenced me profoundly. I really appreciate what they have done

in their daily work. Their spirit of endless expanding and updating knowledge

encourages me to learn new things. Their courage to face difficulties motivates me

to keep moving forward. Their attitude towards novelties inspires me to innovate.

Moreover, I’d like to express my gratitude to technicians and colleagues in the

Acknowledgements

X

department and research group. Thanks for the patient and clear explanation of the

application of many instruments given by Ms. Mow-nin Sun, Mr. Patrick Pang, Mr.

Kevin Hui, and Mr. Kwan-on Choi. Thanks for the help from Ms. Sicily Ho, Ms.

Lemona Kong, and Ms. Wu Chunyan Tracy. They helped me to deal with many

miscellaneous things. Besides, in the research group, I really appreciate many

useful suggestions and help that have been offered by Dr. Yang Bao and Ms. Lin

Shuping during my study. Discussion with them inspired me to solve research

problems. And I am grateful that Ms. Li Ying, Dr. Yin Rong and Mr. Liu Shirui gave

me very helpful reminders. Without the help from these persons, my research could

not proceed smoothly.

I acknowledge the financial support of the Hong Kong Polytechnic University for

a postgraduate scholarship.

Additionally, I am extremely grateful for my friends’ solicitude in these years. Dr.

Zhang Tong and Dr. Gu Weiqun are my friends of my parents’ generation. During

the past decades, they have cast in my direction the pearls of wisdom and shared

invaluable experience with me. Thus, I really appreciate their support and advice.

Besides, I’d like to express my gratitude to Ms. Wang Di, because she has always

encouraged me to do better since nine years ago. What’s more, I want to thank some

friends who I have made in Hong Kong, especially, Ms. Lin Shuping, Ms. Yang

Acknowledgements

XI

Yingqiao and Mr. Rico Cheung. If Ms. Lin did not take me in, I would have nowhere

to stay for over one month. If Ms. Yang did not keep me away from the cliff, I would

be hurt deeply in life. If Mr. Rico Cheung did not teach me how to play squash, I

would not enjoy the game and philosophy behind it. Except for them, other friends

have supported me to overcome difficulties and shared golden time with me. They

are Ms. Xiao Yelan, Ms. Dai Richen, Ms. Liang Xin, Ms. Lin Bingna, Ms. Yang

Xingxing, Dr. Wu Di.

I’d like to express my immense gratitude to my family. My aunt cultivated my

reading habit and kept me company in several summer holidays, when I was a little

girl. Reading habit is a present for my whole life. Finally, I am eternally grateful to

my parents. To teach me the importance of living has taken their great tolerance,

patience, wisdom and perseverance. Without their love and support, I could not

pursue my dreams.

Table of Contents

i

Table of Contents

Abstract .................................................................................... I

Publications Arising from the Thesis.................................. VII

Acknowledgements ............................................................... IX

Table of Contents .................................................................... i

List of Abbreviations .............................................................. v

Introduction ...................................................... 1

Background ............................................................................... 1

Research Problems .................................................................... 3

Research Objectives .................................................................. 4

Research Methodology ............................................................. 5

Research Significance ............................................................... 8

Structure of the thesis .............................................................. 10

References ............................................................................... 11

Literature Review ........................................... 16

Introduction ............................................................................. 16

Operational Principles and Performance of Fiber-based

Thermoelectric Generators (FTEGs) .................................................. 16

2.2.1. Mechanisms of thermoelectric conversion in FTEGs .......................... 17

2.2.2. Mechanisms of heat transfer in FTEGs ................................................ 19

2.2.3. Performance of FTEGs ........................................................................ 20

Finite Element Method and Its Application to Thermoelectric

Generators (TEGs) .............................................................................. 21

2.3.1. Finite element method (FEM) .............................................................. 21

Table of Contents

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2.3.2. Brief Introduction to the COMSOL Multiphysics® Software .............. 25

2.3.3. Application of FEM to TEGs ............................................................... 27

Structure of FTEG devices ...................................................... 29

2.4.1. One-dimensional (1D) structures.......................................................... 30

2.4.2. Two-dimensional (2D) structures ......................................................... 31

2.4.3. Influence of structure parameters on FTEGs performance .................. 32

Materials and Fabrication Methods of FTEGs ........................ 33

2.5.1. Thermoelectric materials ...................................................................... 34

2.5.2. Fabrication methods ............................................................................. 36

Summary ................................................................................. 37

References ............................................................................... 38

Modeling of the Performance of One-Dimensional Fiber-Based Thermoelectric Generators (1D FTEGs)…………………………………………………….............53

Introduction ............................................................................. 53

Reliability of the simulated results from COMSOL ............... 55

The 1D FTEG Model .............................................................. 63

3.3.1. Geometric and material parameters ...................................................... 63

3.3.2. Assumptions ......................................................................................... 65

3.3.3. Governing equations and boundary conditions .................................... 66

3.3.4. Performance of FTEGs ......................................................................... 70

3.3.5. Grid independence ................................................................................ 71

Results and discussion ............................................................. 75

3.4.1. Influence of geometric size on thermoelectric performance of 1D FTEGs

………………………………………………………………………...76

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3.4.2. Influence of contact resistance on thermoelectric performance of 1D

FTEGs .. ……………………………………………………………………...77

3.4.3. Influence of radiation heat transfer on thermoelectric performance of 1D

FTEGs ........................................................................................................... 102

Conclusion............................................................................. 116

Appendix: Analytical solution for the traditional π-structure

TEG .……………………………………………………………......117

References ............................................................................. 118

Fabrication and Characterization of One-Dimensional Fiber-Based Thermoelectric Generators (1D FTEGs) ..………………………………………………………….121

4.1. Introduction ........................................................................... 121

4.2. Experiment ............................................................................ 123

4.2.1. Materials ............................................................................................. 124

4.2.2. Measurement of the PEDOT: PSS ..................................................... 124

4.2.3. Fabrication of PET-based 1D FTEGs ................................................. 126

4.2.4. Performance evaluation of the PET-based 1D FTEGs ....................... 127

4.3. Results and discussion .......................................................... 127

4.3.1. Characterization of the PEDOT: PSS properties ................................ 127

4.3.2. Morphology of the 1D FTEG ............................................................. 132

4.3.3. Comparison between the experimental and the predicted values of

electrical potential ......................................................................................... 133

4.4. Conclusion............................................................................. 140

4.5. References ............................................................................. 140

Modeling of the Performance of One-Dimensional Fiber-Based Thermoelectric Generators (1D FTEGs) Arrays .................................................................... 143

Table of Contents

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Introduction ........................................................................... 143

The Physical Model of 1D FTEG Arrays.............................. 145

5.2.1. Geometric and material parameters .................................................... 145

5.2.2. Assumptions ....................................................................................... 151

5.2.3. Governing equations and boundary conditions .................................. 152

Analytical and numerical solution of traditional TEGs in

different structure .............................................................................. 156

Results and discussion ........................................................... 161

5.4.1. Influence of interaction radiation between 1D FTEG and thin wall .. 162

5.4.2. Performance of 1D FTEG array ......................................................... 181

Conclusion ............................................................................. 187

Appendix ............................................................................... 188

5.6.1. Analytical solution of traditional TEGs in different structures .......... 188

5.6.2. Radiation heat rate under different situations ..................................... 194

References ............................................................................. 198

Conclusions and Future Work .................... 200

Conclusions ........................................................................... 200

Future work ........................................................................... 203

6.2.1. Design of other arrangement forms of 1D FTEGs ............................. 203

6.2.2. Fabrication of devices composed of 1 D FTEG arrays ...................... 204

6.2.3. Verification and modification of 1D FTEG arrays model .................. 204

6.2.4. Models of two- or three-dimensional FTEGs ..................................... 204

List of Abbreviations

v


Nomenclature

𝐴 area (m2)

𝐶 the specific heat capacity (J ∙ K−1)

𝑑 thickness (m)

𝐸 emissive power

𝐹 view factor

𝐺 irradiation

ℎ convection coefficient (W ∙ m−2 ∙ K−1)

𝐼 electric current (A)

𝐽 radiosity

𝐽 electric current density (A ∙ m−2)

𝑘 thermal conductivity (W ∙ m−1 ∙ K−1)

𝐾 thermal conductance (W ∙ K−1)

𝐿 length (m)

𝑃 output power (W)

𝑞 heat rate (W)

𝑞′′ heat flux (W ∙ m−2)

𝑟 radius (m)

𝑅 electrical resistance (Ω)

𝑇 temperature (K or ℃)

𝛻𝑇 temperature difference (K or ℃)


vi

�⃗⃗� velocity vector (m ∙ s−1)

𝑈 electrical potential; thermos-electromotive force

𝑥 x-direction

𝑍𝑇 figure-of-merit

Greek letters

𝛼 Seebeck coefficient (V ∙ K−1)

𝜀 emissivity (1)

𝜂 efficiency

𝜃 thermal resistance (K ∙ W−1)

𝛱 Peltier coefficient

𝜌 density (kg ∙ m−3); reflectivity

𝜎 electrical conductivity (S ∙ m−1)

𝜎0 Stefan-Boltzmann constant, 5.670 × 10−8 W/(m2 ∙ K4)

𝛷 electric scalar potential (V)

Subscripts and superscripts

𝑎𝑏 absorptivity

𝑏 blackbody

𝑐 cold side

𝑐𝑜𝑛𝑑 conductive heat transfer

𝑐𝑜𝑛𝑣 convective heat transfer

𝑒𝑥 external


vii

𝑓 fluid; fiber/filament

ℎ hot side

𝑖𝑛 flow into

𝑚𝑎𝑥 maximum

𝑜𝑢𝑡 flow out

𝑝 constant pressure

𝑟 radiation

𝑟𝑎𝑑 radiative heat transfer

𝑠 surface

𝑠𝑢𝑟 surroundings

𝑇𝐸 thermoelectric

𝑡𝑜𝑡 total

1.1 Background

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Introduction

Background

To fulfil the requirement of collecting scavenged energy from three-dimensional

(3D) and large surface objects like human body1, energy harvesting devices should

be flexible, deformable, stretchable and light in weight. Although thermoelectric

generators (TEGs) can convert thermal energy into electrical energy directly

without any moving parts or working fluids, the traditional ones cannot be applied

to surfaces in arbitrary shape2. The primary reason is that they are usually fabricated

with rigid and bulk materials3-18. As the counterparts of TEGs, fiber-based TEGs

(FTEGs) can successfully fulfil these demands. But few research has been reported

on the flexible and conformal FTEGs19-24.

Except for the backward development of appropriate TE materials that can be

fabricated into FTEGs, research gaps also exist in the theoretical issues behind these

devices. Besides, although instruments for characterizing performance have been

more available and reliable, some experiments involving to the limitation problems

can hardly be operated to obtain accurate results. In this situation, researchers can

improve their knowledge and understand the truth behind phenomenon through

theoretical analysis25. The analysis process can be accomplished with mathematical

models by obtaining numerical solutions. Among a kind of approaches, finite

1.1 Background

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element method (FEM) is an effective way to solve sophisticated computation

problems in areas like physics and engineering. Although many efforts have been

made to conduct theoretical analysis and structure optimization of traditional

TEGs25-40, very little attention has been paid to these issues of FTEGs.

Additionally, the fabrication method is also a significant problem to inhibit the

development of FTEGs, although some one-dimensional (1D) FTEGs were

fabricated by researchers. For example, one of the pioneers was that the silica fiber

as substrate was adjacently deposited with the evaporation of nickel and silver as

TE materials19. Recently, n-type and p-type semiconductor materials, Bi2Te3 and

Sb2Te3, were deposited separately onto the surface of highly aligned

polyacrylonitrile (PAN) nanofibers20. Additionally, Ag2Te as TE material was

coated on nylon fiber, in order to fabricate FTEGs41. However, although these

conscientious reports did fabricate 1D FTEGs, potential problems constrained their

application. For example, the electrospinning method to fabricate PAN nanofibers

can hardly manufacture products. The exfoliation can be observed on the surface of

Ag2Te coating layer, implying the brittleness. Therefore, an urgent requirement of

promoting the development of FTEGs is to find a feasible fabrication method.

Hence, in order to study the theoretical issues, this thesis systematically investigates

the structure of 1D FTEGs affecting the performance with analytical and numerical

1.2 Research Problems

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solution. Besides, a feasible and reliable method is developed to fabricate 1D

FTEGs. The experiment result is compared with the numerical solution for model

validation. In addition, the investigation of 1D FTEG arrays includes two parts:

exploring the theoretical limitation and studying the performance of assembly unit

of parallel 1D FTEGs.

Research Problems

As stated in the background, the major research problems of FTEGs involve the

following aspects:

P1. No available model for FTEGs

The models of traditional TEGs can hardly describe the physical issues in the

FTEGs, because of the absence of fiber/filament as substrates. Thus, to considering

the influence of fiber-based substrates, new theoretical models of FTEGs should be

designed and established. The research starts with 1D FTEGs, which can develop

into higher dimensional FTEGs in the future.

P2. Unknown effects of geometric structure of 1D FTEGs on thermoelectric

performance

The geometric structure significantly influences the performance of 1D FTEGs,

1.3 Research Objectives

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because it affects the temperature distribution, the transmission of thermal energy

and the electrical properties. Thus, the lack of understanding the effects of

geometric structure greatly inhibits the development of 1D FTEGs.

P3. Feasible method to fabricate 1D FTEGs

As mentioned in the “Background” section, a feasible fabrication method needs to

be developed, in order to produce the reliable 1D FTEG devices.

P4. Absence of systematic studies on 1D FTEG arrays.

Compared with single 1D FTEGs, real devices are usually composed of a large

number of 1D FTEGs forming regular arrays. However, it is absent that systematic

study on the 1D FTEG arrays and their theoretical limitation.

Research Objectives

As pioneering research on TEGs, this dissertation carries out a systematical

investigation about 1D FTEGs with mathematical models which are solved to

discover and reveal the influence of the geometric structure on the device

performance. Besides, 1D FTEGs are fabricated with a feasible and reliable method.

The detailed research objectives are as follows:

1.4 Research Methodology

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Ob1. To validate the reliability of the numerical solution, and to develop multi-

physical models of 1D FTEGs;

Ob2. To investigate the theoretical issues through studying the influence of

geometric structure on the device performance by changing the parameters, under

different physical conditions;

Ob3. To fabricate and characterize 1D FTEGs with filament and polymer TE

material, to validate the models by the comparison between the experimental results

and the numerical solution, and to modify the model if necessary;

Ob4. To develop and investigate models of 1D FTEG arrays, and to explore the

theoretical limitation of 1D FTEG arrays.

Research Methodology

Based on the illustrated research problems, in order to achieve the stated objectives,

this research will be conducted with the following methodology:

M1. Development of multi-physical models of 1D FTEGs based on verification

of the reliability of numerical solution.

FEM will be applied in this research with a commercial software: COMSOL


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Multiphysics®. It is crucial to verify the reliability of FEM before conducting the

systematical research. Thus, the convergence of the numerical simulation will be

verified with appropriate discretization approach. Then, the reliability of the

simulation will be examined and confirmed through the comparison of simulation

results with the results from the previously published articles and the analytical

solutions of the theoretical models. Based on the above verification, the models of

1D FTEG will be designed and developed.

M2. Investigation of the effects of geometric parameters of 1D FTEG models

under different conditions

The1D FTEG models with distinct geometric parameters will be studied in three

cases. Firstly, the geometric parameters will include the fiber/filament radius, the

thickness and length of TE layer. Secondly, the transmission of thermal energy

under different conditions may have significant influence on the performance. Thus,

models will be investigated in three cases with different conditions: (1) conduction

heat transfer only; (2) conduction heat transfer with thermal and electrical contact

resistance at the interface between the TE material and electrode; (3) conduction

and radiation heat transfer without contact resistance. In the first two cases, the hot

and cold side temperature will be fixed as constants. In the third case, the hot side

temperature will be fixed, but the cold side one will be free and determined by the


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heat transfer. These efforts will reveal the dominant and subdominant factors of

geometry on the performance and deeply understand the mechanism of 1D FTEGs

from theoretical aspect.

M3. Fabrication, characterization and comparison of 1D FTEGs

The 1D FTEGs will be fabricated with poly(ethylene terephthalate) (PET) filament

and poly(3,4-ethylenedioxythiophene): poly(styrene sulfonic acid) (PEDOT: PSS),

one polymer TE material. Firstly, the TE material will be characterized by thermo-

gravimetric analysis (TGA), the crystalline structure with X-ray diffraction (XRD),

Seebeck coefficient, thermal conductivity and electrical conductivity. Secondly, the

morphology of 1D FTEG samples will be characterized with a scanning electron

microscope (SEM) and an optical microscope. Thirdly, the energy conversion

performance of these samples will be measured with a home-made measurement

system. Finally, the experimental results will be compared with the numerical

solutions. If the comparison result shows huge difference, it will be analyzed from

the theoretical viewpoint and the model will be revised and corrected.

M4. Design and study of models of 1D FTEG arrays

Instead of applying single 1D FTEG, the device is composed of numerous 1D

1.5 Research Significance

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FTEGs closely packed in a sealed environment. Therefore, an assembly unit model

of parallel 1D FTEGs will further consider about the surface-to-surface radiation

and the air conduction simultaneously. And the hot side temperature will be fixed;

the cold side one will be free, which is determined by the conduction and radiation

heat transfer. Before the study of 1D FTEG arrays, under the same boundary

condition, the necessary and limitation of models will be explored. These models

are composed of 1D FTEG and thin wall. Two variables – the distance between 1D

FTEGs and the emissivity – are set to reveal their influence on the performance of

the device.

Research Significance

This research conducts systematic investigation about the structure and

performance of 1D FTEGs through theoretical models and experiment. The

accomplished work has resulted in the following significance:

S1. Design of 1D FTEGs for the first time

This research designs models of 1D FTEGs, based on the verification of the

reliability and convergence of numerical simulation. It provides a reliable approach

to the following study of models of 1D FTEGs.

1.5 Research Significance

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S2. New knowledge of the effects of geometric structure on the performance of

1D FTEGs in different cases

The theoretical models of 1D FTEGs are investigated in different cases. The issue

of the influence of the geometry on the performance of devices is studied

thoroughly for the first time.

S3. A feasible method to fabricate 1D FTEGs

Samples of 1D FTEGs are fabricated in a feasible method with the commonly

commercial filament and polymer TE material. The fabrication progress is not only

easy to conduct, but also reliable and repeatable. These 1D FTEGs show uniform

morphology and stable performance. Thus, this fabrication method provides a

possible approach to the future study and even the mass fabrication of 1D FTEGs.

S4. New knowledge of the effects of geometric structure on the performance of

1D FTEG arrays

For the study of 1D FTEG arrays, the theoretical limitation of the models of 1D

FTEGs surrounded by a thin wall is investigated for the first time. Based on the

fundamental study on the limitation, the influence of different geometric parameters

on the performance of 1D FTEG arrays is investigated. To my knowledge, all these

1.6 Structure of the thesis

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work has never been reported before, which fills the research gaps and develops

new knowledge and direction to this research area and even the mass fabrication.

S5. A research method for multi-dimensional FTEGs

The method applied to 1D FTEGs in this fundamental research can be widely used

to direct the future work that FTEGs are in two- or three- dimension.

Structure of the thesis

The dissertation is organized as follows:

Chapter 1 starts with the background of the conversion of thermal energy to

electrical energy and the application of FEM to the research of traditional TEGs.

Then, the problem issues are summarized and the specific research objectives are

proposed. Lastly, the methodology and significance of this research are introduced.

Chapter 2 provides a systematical and profound review on the operational principles

of FTEGs, FEM and its application to TEG research, TEG structure, and the

materials and fabrication of FTEGs.

Chapter 3 depicts the theoretical models of 1D FTEGs by analytical calculation and

numerical simulation with the FEM software: COMSOL Multiphysics®. The

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influence of the geometry of 1D FTEG is studied in three different cases. Based on

the simulation results, the primary factor on the performance of 1D FTEG is

revealed.

Chapter 4 describes the experiment progress of the fabrication of 1D FTEG with

filament and polymer TE materials. Then, the characterization includes the TE

material properties, the morphology and the performance of 1D FTEG samples.

Finally, the performance of the experiment is compared with that of the simulation.

Chapter 5 illustrates the model of an assembly unit of parallel 1D FTEGs with the

consideration of the surface-to-surface radiation and the air conduction

simultaneously. This chapter begins with the discussion about the necessary of

studying the assembly unit model under these conditions, through comparing 1D

FTEG models under four different cases. The comparison also explores the

theoretical limitation. Numerous effort has been put into revealing the influence of

the geometry on the performance of device.

Chapter 6 summarizes primary findings and offers recommendations for future

research.

References

1. Zeng W, Shu L, Li Q, Chen S, Wang F and Tao XM. Fiber-based wearable

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electronics: A review of materials, fabrication, devices, and applications. Adv Mater.

2014; 26: 5310-36.

2. Zhang L, Lin S, Hua T, Huang B, Liu S and Tao X. Fiber‐Based Thermoelectric



3. Walia S, Balendhran S, Nili H, et al. Transition metal oxides - Thermoelectric

properties. Prog Mater Sci. 2013; 58: 1443-89.

4. He J, Liu Y and Funahashi R. Oxide thermoelectrics: The challenges, progress,

and outlook. J Mater Res. 2011; 26: 1762-72.

5. Han C, Sun Q, Li Z and Dou SX. Thermoelectric Enhancement of Different

Kinds of Metal Chalcogenides. Adv Energy Mater. 2016; 6.

6. Gao MR, Xu YF, Jiang J and Yu SH. Nanostructured metal chalcogenides:

synthesis, modification, and applications in energy conversion and storage devices.

Chem Soc Rev. 2013; 42: 2986-3017.

7. Poudel B, Hao Q, Ma Y, et al. High-thermoelectric performance of

nanostructured bismuth antimony telluride bulk alloys. Science. 2008; 320: 634-8.

8. Li JH, Tan Q, Li JF, et al. BiSbTe-Based Nanocomposites with High ZT : The

Effect of SiC Nanodispersion on Thermoelectric Properties. Adv Funct Mater. 2013;

23: 4317-23.

9. Il Kim S, Lee KH, Mun HA, et al. Dense dislocation arrays embedded in grain

boundaries for high-performance bulk thermoelectrics. Science. 2015; 348: 109-14.

10. Xie DW, Xu JT, Liu GQ, et al. Synergistic Optimization of Thermoelectric

Performance in P-Type Bi0.48Sb1.52Te3/Graphene Composite. Energies. 2016; 9.

11. Hu LP, Wu HJ, Zhu TJ, et al. Tuning Multiscale Microstructures to Enhance

Thermoelectric Performance of n-Type Bismuth-Telluride-Based Solid Solutions.

Adv Energy Mater. 2015; 5.

12. Huang BL and Kaviany M. Ab initio and molecular dynamics predictions for

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electron and phonon transport in bismuth telluride. Phys Rev B. 2008; 77.

13. Fu CG, Bai SQ, Liu YT, et al. Realizing high figure of merit in heavy-band p-

type half-Heusler thermoelectric materials. Nat Commun. 2015; 6.

14. Li W, Yang GF and Zhang JW. Optimization of the thermoelectric properties of

FeNbSb-based half-Heusler materials. J Phys D: Appl Phys. 2016; 49.

15. Xue QY, Liu HJ, Fan DD, Cheng L, Zhao BY and Shi J. LaPtSb: a half-Heusler

compound with high thermoelectric performance. Phys Chem Chem Phys. 2016; 18:

17912-6.

16. Gao P, Berkun I, Schmidt RD, et al. Transport and mechanical properties of

high-ZT Mg2.08Si 0.4-x Sn0.6Sb x thermoelectric materials. J Electron Mater.

2014; 43: 1790-803.

17. Bashir MBA, Mohd Said S, Sabri MFM, Shnawah DA and Elsheikh MH.

Recent advances on Mg2Si1-xSnx materials for thermoelectric generation.

Renewable Sustainable Energy Rev. 2014; 37: 569-84.

18. Zhao LD, Lo SH, Zhang Y, et al. Ultralow thermal conductivity and high

thermoelectric figure of merit in SnSe crystals. Nature. 2014; 508: 373-7.

19. Yadav A, Pipe KP and Shtein M. Fiber-based flexible thermoelectric power

generator. J Power Sources. 2008; 175: 909-13.

20. Lee JA, Aliev AE, Bykova JS, et al. Woven-Yarn Thermoelectric Textiles. Adv

Mater. 2016; 28: 5038-44.

21. Kim MK, Kim MS, Lee S, Kim C and Kim YJ. Wearable thermoelectric

generator for harvesting human body heat energy. Smart Mater Struct. 2014; 23.

22. Lu ZS, Zhang HH, Mao CP and Li CM. Silk fabric-based wearable

thermoelectric generator for energy harvesting from the human body. Appl Energy.

2016; 164: 57-63.

23. Du Y, Cai K, Chen S, et al. Thermoelectric fabrics: Toward power generating

clothing. Sci Rep. 2015; 5.

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24. Yamamoto N and Takai H. Electrical power generation from a knitted wire panel

using the thermoelectric effect. Electr Eng JPN. 2002; 140: 16-21.

25. Turenne S, Clin T, Vasilevskiy D and Masut RA. Finite element

thermomechanical modeling of large area thermoelectric generators based on

bismuth telluride alloys. J Electron Mater. 2010; 39: 1926-33.

26. Shimizu K, Takase Y and Takeda M. Performance improvement of flexible

thermoelectric device: FEM-based simulation. J Electron Mater. 2009; 38: 1371-4.

27. Ebling D, Jaegle M, Bartel M, Jacquot A and Bottner H. Multiphysics

Simulation of Thermoelectric Systems for Comparison with Experimental Device

Performance. J Electron Mater. 2009; 38: 1456-61.

28. Ebling D, Bartholome K, Bartel M and Jagle M. Module Geometry and Contact

Resistance of Thermoelectric Generators Analyzed by Multiphysics Simulation. J

Electron Mater. 2010; 39: 1376-80.

29. Jang B, Han S and Kim JY. Optimal design for micro-thermoelectric generators

using finite element analysis. Microelectron Eng. 2011; 88: 775-8.

30. Wang CC, Hung CI and Chen WH. Design of heat sink for improving the

performance of thermoelectric generator using two-stage optimization. Energy.

2012; 39: 236-45.

31. Xiao JS, Yang TQ, Li P, Zhai PC and Zhang QJ. Thermal design and

management for performance optimization of solar thermoelectric generator. Appl

Energy. 2012; 93: 33-8.

32. Deng Y, Zhu W, Wang Y and Shi YM. Enhanced performance of solar-driven

photovoltaic-thermoelectric hybrid system in an integrated design. Sol Energy.

2013; 88: 182-91.

33. Rezania A, Rosendahl LA and Yin H. Parametric optimization of thermoelectric

elements footprint for maximum power generation. J Power Sources. 2014; 255:

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34. Ziolkowski P, Poinas P, Leszczynski J, Karpinski G and Muller E. Estimation

of Thermoelectric Generator Performance by Finite Element Modeling. J Electron

Mater. 2010; 39: 1934-43.

35. Bjork R, Christensen DV, Eriksen D and Pryds N. Analysis of the internal heat

losses in a thermoelectric generator. Int J Therm Sci. 2014; 85: 12-20.

36. Al-Merbati AS, Yilbas BS and Sahin AZ. Thermodynamics and thermal stress

analysis of thermoelectric power generator: Influence of pin geometry on device

performance. Appl Therm Eng. 2013; 50: 683-92.

37. Picard M, Turenne S, Vasilevskiy D and Masut RA. Numerical Simulation of

Performance and Thermomechanical Behavior of Thermoelectric Modules with

Segmented Bismuth-Telluride-Based Legs. J Electron Mater. 2013; 42: 2343-9.

38. Jia XD and Gao YW. Estimation of thermoelectric and mechanical

performances of segmented thermoelectric generators under optimal operating

conditions. Appl Therm Eng. 2014; 73: 335-42.

39. Wu YJ, Ming TZ, Li XH, Pan T, Peng KY and Luo XB. Numerical simulations

on the temperature gradient and thermal stress of a thermoelectric power generator.

Energy Convers Manage. 2014; 88: 915-27.

40. Erturun U, Erermis K and Mossi K. Influence of leg sizing and spacing on power

generation and thermal stresses of thermoelectric devices. Appl Energy. 2015; 159:

19-27.

41. Finefrock SW, Zhu XQ, Sun YM and Wu Y. Flexible prototype thermoelectric

devices based on Ag2Te and PEDOT:PSS coated nylon fibre. Nanoscale. 2015; 7:

5598-602.

2.1 Introduction

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Literature Review

Introduction

This chapter is separated into four parts. It begins with the review of fundamental

theory of FTEGs, illustrating the primary equations for depicting the conversion of

thermal energy into electrical energy. Based on this description, FEM is introduced

briefly, which is used as one of the solution methods in this research. Analytical

solution is another method applied to solve problems in this investigation. Then,

structure of FTEG devices is summarized, which has a significant influence on the

performance. Finally, it is reviewed that the development of materials and

fabrication methods of thermoelectric devices.

Operational Principles and Performance of Fiber-based Thermoelectric Generators (FTEGs)

FTEGs are devices that can accomplish the conversion of thermal energy into

electrical energy without any moving part or working fluid, which are composed of

fiber-based substrate or shown in quasi-fiber shape. The energy conversion in

FTEGs is achieved by taking the advantages from the properties of TE materials.

As shown in Figure 2.1(a), being perfectly flexible and deformable, FTEGs consist

mainly of thermoelectric (TE) materials, fiber-based substrate/conductive yarn, and

fabric electrodes1, 2. The difference between FTEGs and traditional TEGs happens

2.2 Operational Principles and Performance of Fiber-based Thermoelectric Generators (FTEGs)

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in the process of heat transfer in the devices. The reason is that the fiber-based

substrate/conductive yarn has effects on the temperature distribution. Therefore,

this section depicts the mechanisms of TE conversion and heat transfer in FTEGs.

It follows by the introduction to the standard of the performance of FTEGs.

2.2.1. Mechanisms of thermoelectric conversion in FTEGs

The fundamental mechanisms of TE conversion in FTEGs are Seebeck effect,

Peltier effect and Thomson effect. These mechanisms are same to those in

traditional TEGs, because the effective part to accomplish the energy conversion is

the TE material in all these devices. As shown in Figure 2.1(b), Seebeck effect is

the movement of holes in p-type TE material from the hot side to the cold side,

which is driven by the temperature difference. Similarly, if the TE material is a n-

type one, the temperature difference between two ends causes the movement of

electrons. The movement of holes or electrons generates the electrical potential

difference between the two sides. If the TE materials are connected with conductive

fabric or flexible electrodes and loads, the electrical current flows in the loop, under

temperature difference condition. The magnitude of thermos-electromotive force

due to the Seebeck effect can be given by:

𝛻𝑈 = 𝛼𝛻𝑇 (2-1)

where 𝛼 is the Seebeck coefficient of the TE material; 𝛻𝑇 is the temperature


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difference. Seebeck effect is the primary mechanism of FTEGs for the conversion

of thermal energy into electrical energy.

Figure 2.1 (a) A typical FTEG draped on a sphere; (b) enlarged view of the device

structure.1

In addition, apart from Seebeck effect, Peltier effect and Thomson effect also exist

in the energy conversion process. As the basic mechanism for the TE coolers, Peltier

effect can be regard as the reversible process of Seebeck effect, because it converts

electrical energy into thermal energy with endothermic or exothermic phenomenon

when the current flows in a loop. Besides, except that Joule heat is generated due

to the internal resistance, when the electrical current flows in TE material, some

heat can be absorbed or exuded as the result of the temperature gradient. This

phenomenon is called Thomson effect.

(a)

(b)


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2.2.2. Mechanisms of heat transfer in FTEGs

Temperature difference leads to the transition of thermal energy with three methods:

conductive, convective or radiative heat transfer. When the two sides of FTEGs

have different temperature, the thermal energy from the hot side is transported to

the cold side through the device by conductive heat transfer due to the particle

activity. For 1D conduction, the heat flux, 𝑞𝑐𝑜𝑛𝑑′′ (W ∙ m−2), can be given by:

𝑞𝑐𝑜𝑛𝑑′′ = −𝑘

𝑑𝑇(𝑥)

𝑑𝑥 (2-2)

where 𝑘 is the thermal conductivity (W ∙ m−1 ∙ K−1 ); 𝑇(𝑥) is the temperature

distribution along x-direction.

Additionally, except for the thermal energy transmitted through random molecular

motion, the convective heat transfer happens between the device surface and the

fluid mass, if the surface has different temperature with its fluid circumstance. The

convective heat flux, 𝑞𝑐𝑜𝑛𝑣′′ (W ∙ m−2), can be given by:

𝑞𝑐𝑜𝑛𝑣′′ = ℎ(𝑇𝑠 − 𝑇𝑓) (2-3)

where ℎ is the convection coefficient (W ∙ m−2 ∙ K−1); 𝑇𝑠 is the temperature of

object surface; 𝑇𝑓 is the fluid temperature.

Being different from the conduction and convection, the radiative heat transfer is


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thermal energy emitted by electromagnetic wave from object’s surface whose

temperature is above the absolute zero. The surface properties directly affect the

transmission of radiation. For a grey surface whose absorptivity is equal to its

emissivity, the radiative heat flux, 𝑞𝑟𝑎𝑑′′ (W ∙ m−2), can be given by:

𝑞𝑟𝑎𝑑′′ = 𝜀𝜎0(𝑇𝑠

4 − 𝑇𝑠𝑢𝑟4 ) (2-4)

where 𝜀 is the emissivity; 𝜎0 is the Stefan-Boltzmann constant, 5.670 ×

10−8 W/(m2 ∙ K4); 𝑇𝑠 is the temperature of the body surface (SI unit: K); 𝑇𝑠𝑢𝑟

is the temperature of the surroundings (SI unit: K).

2.2.3. Performance of FTEGs

The performance of a FTEG device is commonly evaluated by its output power and

efficiency. The output power is given by:

𝑃 = 𝐼𝑈 (2-5)

where 𝐼 and 𝑈 represent the current and electrical potential, respectively. When

the external resistance (𝑅𝑒𝑥) is equal to the resistance of TE material (𝑅𝑇𝐸), the

device obtains the maximum of power, which is given by:

𝑃𝑚𝑎𝑥 =𝑈2

4𝑅𝑇𝐸 (2-6)

The efficiency is given by:

2.3 Finite Element Method and Its Application to Thermoelectric Generators (TEGs)

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𝜂 =𝑃

𝑞𝑖𝑛 (2-7)

where 𝑞𝑖𝑛 is the heat rate flows into the device, (SI unit: W).

Finite Element Method and Its Application to Thermoelectric Generators (TEGs)

Generally, the analytical and numerical methods take advantages from the

emergence of computing science and electronic industry, as the accelerated

computation speed saves time and cost. Based on the operational principles of

different physical process, these methods render scientists and researchers powerful

assist to discover the essential problem from the theoretical viewpoint. This section

provides an introduction to one of numerical methods: FEM. Then, the commercial

software: COMSOL Multiphysics®, which is used in the following research, is

introduced briefly. Finally, this section reviewed the applications of FEM to the

study of TEGs.

2.3.1. Finite element method (FEM)

Although instruments for characterizing performance are more available and

reliable than several decades ago, some experiments involving to the limitation

issues can hardly be operated to obtain accurate results. In this situation, researchers

can improve their knowledge and understand the truth through theoretical analysis3.

Theoretical analysis allows researchers to focus on specific problems under ideal


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situation. For example, researchers investigated the influence of the composite of

several TE materials on the performance of device4. They assumed thermal stress

between different materials was negligible, although the stress may lead the failure

of the device due to the difference of thermal expansion coefficients in reality.

Although this research results did not depict the real situation, they provided

extremely important reference to the real lab experiment.

To revealing the essential nature from the physical phenomenon can be

accomplished by the basic processes with the following steps5: (1) to conceptualize

the physical phenomenon with mathematical model; (2) to solve the model and

obtain solutions like analytical or numerical ones; (3) to apply the model to make

prediction; (4) to validate the prediction model with experiment; (5) to correct and

optimize the model with the experiment results. Through these steps, the nature of

phenomenon can be learnt and the model can be used to make prediction and

decision in the future. The second step in the progress can be accomplished with

FEM which is one kind of numerical methods to solve sophisticated computation

problems in areas like physics and engineering.

In the mid-20th century, scientists and researchers began to use FEM for dealing

with complexed situation, such as the analysis of stress and structure6, 7, and the

solution of equilibrium and vibrations8. Then, FEM has gradually and widely been


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applied to engineering computation due to its effectiveness and general usefulness.

The fast development and broad application of FEM has benefited enormously from

the rapid growth of the computing science, which saves the calculation time and

illustrates the results visually.

Another approach to solve mathematical models is analytical method. This method

is much suitable for computing simple problems and providing exact results.

However, when the problem is complex or the exact results can hardly be obtained,

the analytical method is time consuming or the mathematic problems may not be

solved with this method. Accordingly, in order to apply the analytical method, some

complex problems have to be simplified. For example, some articles have reported

the analytical solution about the performance of TEG device, which only emphasize

the conductive heat transfer in one dimention9-14. Another example is that a common

approach to solve the problems about finite-time or/and non-equilibrium

thermodynamics is to obtain the analytical solution, based on Newton heat transfer

law9-11. This law simplifies the problem, through treating the convection or/and

radiation with the total heat transfer coefficient. Besides, when equations and

functions are used to describe real application, they are usually too complicated to

obtain the exact result by analytical method. For instance, if the performance of

TEG device is simulated in a large temperature range, the material properties should

be treated as temperature-dependent parameters15, 16. Under such nonlinear


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conditions, the numerical method is a better approach to solve these problems than

the analytical method. In addition, even if a group of equations can be solved,

analytical method is time consuming and not so accurate as we expect, especially,

when problems involve in multi-dimensional and multi-physical fields2, 17.

However, the drawbacks of analytical solution can be dealt with FEM18, 19. FEM is

a time-saving method to solve complex issues. But FEM is not a panacea, because

it sacrifices the accuracy to some extent. It can only provide approximate solutions

to mathematical models, which may just approach to the analytical solutions

infinitely. Therefore, the reliability and accuracy should be focused on, when FEM

is used to solve problems. The accuracy of FEM solution is verified through

comparing to the exact solution. If the errors are acceptable and less than the pre-

set tolerance, the FEM solution will be regarded as correct. To solve some

complicated problems, researchers have tried to combine the advantages of

analytical solution with FEM. For example, some researchers investigated the

influence of the geometry of heat sink and the dimensions of TEG on the

performance of devices20. They solved the mathematical model of heat sink with

analytical method. Then, this analytical solution was used as boundary condition in

the study of TEG models with FEM.

FEM is used to solve mathematical models in the discretization process. The

fundamental idea of this process is that the smooth functions in differential form or


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variation integral can be simplified into the approximation of small regions21, 22.

These small regions are known as elements whose values at the nodes are in the

place of the governing equations. As the elements are generated as the result of

mesh, the quality of mesh directly affects the accuracy of FEM solution. Mesh

quality must simultaneously satisfy the demands of model geometry, boundary

conditions and physics. Poor mesh quality increases the discretization error. It can

be improved by two approaches: one is to change element size, which controls the

space between nodes; another is to select appropriate element shape21. Besides, the

number of elements is a crucial factor to influence the calculation time. While, too

dense mesh has the possibility to inevitably increase the calculation error and

unnecessarily extend the calculation time. Thus, in order to save time and remain

accuracy, the common operation is to verify the result being grid-independent

through solving the same model with different mesh density20, 23-27.

2.3.2. Brief Introduction to the COMSOL Multiphysics® Software

COMSOL Multiphysics® is a commercial software solving mathematical models

with FEM28. It is used in this research, for taking its most important advantage that

is its powerful function to deal with the coupled physical fields problems. As

mentioned in Section 2.2, the study of FTEGs involves the calculation of thermal

and electrical fields at the same time. In the interactive environment of COMSOL,

the main steps to build and solve models are as follows:


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(1) To select the space dimension from three-dimension (3D), two-dimensional

(2D) axisymmetric, 2D, 1D axisymmetric, or zero-dimension (0D). In this

research, 2D axisymmetric and 3D are used.

(2) To add one or more physics interfaces. Thermoelectric Effect and Electric

Circuit, two physics branches in the software, are applied in this research.

(3) To select the Study type. In this research, Stationary, one of the Study types, is

applied.

(4) To design the geometric model in the operation interface.

(5) To selected appropriate materials for different geometric domains.

(6) To set boundary conditions in former selected physical branches.

(7) To build the suitable mesh for the models.

(8) To accomplish the calculation in the Study nodes of the software.

(9) To collect the results.


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2.3.3. Application of FEM to TEGs

Theoretical analysis and structure optimization of traditional TEGs with FEM have

been reported. The conductive heat transfer attracts much attentions, because it is

the main reason for the thermoelectric effect of TEG devices. Some researchers

have calculated the mathematical models under the ideal condition that thermal

energy is only transmitted by conductive heat transfer16, 20, 29-34. The work in one of

the published papers solved conventional TEG models with FEM30. The models

considered about the specified electrical contact resistance at the interface between

the TE legs and electrodes. If thermal energy was only transmitted through

conductive heat transfer, the solution of the figure-of-merit of device was higher

than the experimental result. The authors explained that this phenomenon was

caused by the absence of radiative and convective heat transfer in the simulation.

Although the solution was adjusted with considering these factors, the important

parameters like emissivity and convection coefficient were not mentioned in the

article. This led the explanation to be questionable. Except for specified temperature

at the hot side and heat flux, models of solar-driven TEGs have also been

investigated with FEM33, 35. The authors considered that only the conductive heat

transfer transmitted thermal energy in these models. And the radiative heat transfer

of solar energy was commonly treated as boundary condition to confine these

models.


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Based on the conductive heat transfer, thermal transmission by the radiative or/and

convective heat transfer has been considered in some mathematical models. FEM

was applied to solve the problem that the conductive, radiative and convective heat

bypass happened in the gap region among TE legs36. Its results showed that the

transmission of thermal energy caused the change of heat flow, when the gap region

was filled with different materials. The variety of heat flow had an effect on the

efficiency of the TEG device. In another article, a 3D TEG model was investigated

by a FEM software: COMSOL Multiphysics®37. The assumption was that the device

was in a closed and sealed module. The influence of conductive, convective and

radiative heat transfer was analyzed. When the radiative heat transfer was simulated,

the property of side walls of the module was specified as diffuse mirror. Although

this setting allowed the side walls be insulated the radiation transmitting to the

outside of the geometry, it also assumed that the walls did not absorb radiation.

Additionally, considering the convective heat transfer, a model of TEG-driven

thermoelectric cooler (TEC) was investigated with FEM38.

Except for studying and optimizing the transmission of thermal energy, FEM has

also been applied to the analysis of classical problems like the deformation of TEGs

caused by the thermal stress3, 27, 39-42. The thermal stress, as the result of the

temperature gradient, affects the device function. Especially, if TEGs suffer high

temperature at the hot side and large temperature difference between two sides, the

2.4 Structure of FTEG devices

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thermal stress can lead to the material failure and the shorten life cycle of device.

In some models whose TE legs were composed with two or more kinds of materials,

one neglected issue was the radiative heat transfer. However, as depicted in Eqn.

(2-4), the radiation can significantly influence heat transfer, because the

temperature as a boundary condition for these models were usually high. Thus, it is

necessary to consider the radiative heat transfer in the calculation. In addition, FEM

is also applied to study the influence of carrier density on the performance of TEG

device43.

Structure of FTEG devices

Similar to the research stage of FTEGs with FEM, the development of FTEG

devices is still in an infant stage now. In the published work, structure of these

devices can be divided into 2D and 1D form. For taking advantages of fabric and

improving the drawbacks of traditional TEGs, one popular approach to fabricate

devices in 2D structure is to insert the rigid TEGs into the flexible fiber-based

substrates. Although these devices exhibit perfect thermoelectric properties as well

as excellent deformability, they can bring uncomfortable touch feeling when they

contact with human skin directly. Meanwhile, FTEGs in 1D structure have already

caught much eyeballs from researchers, for having great potential to be fabricated

into multi-dimensional devices. The development of 1D and 2D FTEGs is reviewed

briefly in this section. More thorough information can be found in the published


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article1.

2.4.1. One-dimensional (1D) structures

1D FTEGs are devices owning large aspect ratio, which are usually fabricated with

fibers/filaments or yarns as substrate materials. This exerts the considerable

influence of the aspect ratio on the mechanical properties of device, because these

substrates have strong deformability and flexibility. Besides, these 1D FTEGs are

probably being fabricated in textiles. For example, as shown in Figure 2.2, the work

in early stage was depositing two metal materials, nickel and silver, at regular

intervals on a silicon fiber44. But, the problem was these metal materials owning

lower Seebeck coefficient than semiconductors. Recently, it has been reported that

FTEG devices were fabricated with depositing thermoelectric semiconductors,

Bi2Te3 (n-type) and Sb2Te3 (p-type), on polyacrylonitrile (PAN) nanofibers45. In this

work, the 1D FTEGs exhibited good TE properties with great flexibility, which can

be easily bent and twisted. However, the electrospinning technology was applied in

the fabrication process, which was just suitable for laboratory research.


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Figure 2.2 Schematic of nickel and silver at regular intervals on silicon fiber44.

Although the problems and difficulties exist in fabrication, the significant of the

research of 1D FTEGs should be emphasized. The outstanding characteristics of 1D

FTEGs makes them to be great potential candidates for forming 2D or 3D FTEG

devices. However, the veil of the theoretic limitation of 1D FTEGs is waiting to be

uncovered. For example, the geometric parameters of 1D FTEGs, such as the

fiber/filament radius and the thickness of TE material, have effects on the

temperature distribution in the device, which further affect TE performance.

Moreover, if the substrate material is yarn, the device performance may be

influenced by the interaction between fibers.

2.4.2. Two-dimensional (2D) structures

The flexibility of devices can be achieved if the substrate is thin film or ultra-thin

film46. But, the disadvantages are poor air-permeability and damage tolerance, if

the thin film is fabricated with polyimide or ultra-thin glass, etc. For overcoming

these drawbacks of thin film, 2D FTEG devices have been designed. For instance,


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the rigid TEGs have been embedded into fabrics in some research47, 48. Obviously,

the existence of rigid TEGs may cause uncomfortable feeling when the device

contacts with human body. The possible solution to this problem is to directly

fabricate the 2D devices with 1D FTEGs in knitted or woven textiles45, 49, 50.

The benefits of 2D FTEGs are outstanding, especially, when the devices are in

textile structure. For example, they can cover objects in arbitrary configuration. But

the research on 2D FTEGs just springs up. At this beginning stage, the theoretical

study and the fabrication method need to be explored and attempted. For example,

the textile structure may influence the performance of 2D FTEGs. The factors can

be the porosity, the thickness of fabrics, the threads per unit length, etc. And what

is the appropriate fabrication process that can keep the 1D FTEGs function

normally?

2.4.3. Influence of structure parameters on FTEGs performance

For the same physical process, the performance of FTEGs is dramatically

influenced by the structure parameters. The reason is that the structure can directly

affect the temperature distribution and the electrical performance. For example, the

cross-sectional area and length of thermoelectric junctions have effects on the

internal resistance of FTEGs, which can further influence the maximum of the

output power of devices. Meanwhile, the arrangement parameters of these junctions

2.5 Materials and Fabrication Methods of FTEGs

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like the distance between them can change the amount of thermal energy

transmitted through heat transfer15, 18, 37, 51. Thus, the efficiency of the devices is

influenced by these factors. Additionally, FTEGs are composed of porous materials

and structures whose influence on heat transfer have been noticed for nearly thirty

years52. However, few work has been done for analyzing their effects on the

performance of FTEGs. Besides, textile material parameters also affect the process

of heat transfer. Although many studies about the fiber diameter, pore size,

thickness of fabrics influencing on heat transfer has been reported53-61, to my

knowledge, no research about these factors affecting the performance of FTEGs has

been done.

Materials and Fabrication Methods of FTEGs

To a considerable extent, material properties decide the fabrication and application

of FTEGs. Among the components of FTEGs, TE materials is a crucial factor in the

device performance. They are expected to convert thermal energy into electrical

energy with high efficiency. As the energy conversion is accomplished by the

movement of carriers in TE materials, the carrier mobility should be high and the

carrier concentration should be appropriate. Meanwhile, compared with rigid and

bulk TE materials, the additional requirement for FTEGs is that the materials are

friendly to environment, easy to be fabricated at room temperature, and so on. Thus,

this section begins with the introduction to TE materials, following by the summary


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of fabrication method.

2.5.1. Thermoelectric materials

Generally, TE materials can be divided into four categories: inorganic, organic and

polymer materials, graphene, and composites, in which the TE effect happens under

appropriate condition. The identified inorganic TE materials are some conductors

and semiconductors. Conductors include pure metals like copper and gold, and

some metallic alloys62, metal oxides63, 64 and metal chalcogenides65, 66.

Semiconductors can be Bi–Te alloys67-71, skutterudite compounds72-74, half-Heusler

compounds75-79, metal silicide80, Ag–Pb–Sb–Te quaternary systems and some high-

ZT oxides. Many reviews have rendered comprehensive and thorough summary and

discussion about these materials1, 81-85. The primary advantage of inorganic TE

materials is their high figure-of-merit value, 𝑍𝑇, which is given by:

𝑍𝑇 =𝛼2𝜎𝑇

𝑘

𝑍𝑇 depicts the energy conversion efficiency of TE materials. However, although

its highest value has been above 2.5 for the measurement at over 900 K86, many

inorganic TE materials can hardly exhibit their best performance at around 310 K

which is around the temperature of human body. Thus, except for Bi–Te alloys,

many inorganic TE materials may not be the proper candidates for FTEGs.

Additionally, compared with other types of TE materials, the inorganic ones are


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costly and toxic, whose fabrication is usually under high temperature condition.

These drawbacks impede inorganic TE materials to be a good choice for FTEGs.

Unlike inorganic TE materials, organic ones are commonly flexible, light weight

and non-toxic, which can be fabricated at low or room temperature. And they are

less expensive than inorganic TE materials, because of their abundance. The low

thermal conductivity is also an expected property of organic TE materials. The

applied organic materials in the research of thermoelectric conversion are

polyacetylene (PA)87, polyaniline (PANI)88, poly(3,4-ethylenedioxythiophene)

(PEDOT)46, 89-97, poly(3-hexylthiophene) (P3HT)98, polypyrrole99, and others.

Among them, the poly(styrenesulfonic) acid (PSS)-doped PEDOT, known as

PEDOT: PSS, has exhibited the best thermoelectric properties100. However,

although organic TE materials have many advantages, their essential disadvantages

are low electrical conductivity and low Seebeck coefficient, leading to low 𝑍𝑇

value101. Therefore, many efforts have been made to improve the properties of these

materials82, 100, 102-105.

Except for inorganic and organic TE materials, graphene and graphene-like

materials have been applied by many researchers to fabricate large-scale devices106-

108. The reason why these materials have attracted much attention is that they shows

many desirable characteristics like strong mechanical and electrical properties109.


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But the thermal conductivity of these materials is so large that limiting their

development and application1. One method to improve the thermal conductivity is

to fabricate the graphene composite like reduced graphene oxide (rGO)/PANI110, 111,

rGO/PEDOT: PSS97, 112.

In addition, a significant method to develop TE materials is the incorporation of

inorganic ones into organic ones. These composite materials can effectively

enhance the TE properties of organic materials. For example, nanoparticles or

nanotubes of carbon can be added into conducting polymers.94, 113-119. These

composites own the expected properties of each material: the outstanding electrical

conductivity of nano-sized carbon and the low thermal conductivity of the polymer.

Meanwhile, the Seebeck coefficient of conducting polymers is improved. More

comprehensive review of polymer TE composite materials can be found in the

literature120, 121.

2.5.2. Fabrication methods

Fabrication methods of FTEGs can be divided into two categories: surface

modification and embedding. Surface modification can be accomplished by drop-

casting46, 89, 94, 101, 103, 105, 115, 122-126, dip coating49, 102, 127, 128, spin coating129-132, radio-

frequency (RF) magnetron sputtering45, 133, 134, thermal vapour deposition44, 135-137,

screen printing138, 139 and dispenser printing47. Moreover, embedding method is to

2.6 Summary

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combine the p-/n-type junctions with the textile materials directly. As the junctions

are usually rigid TEGs, the devices fabricated through embedding method damage

the flexibility and comfort of the textile materials. The detailed review about

fabrication of FTEGs has been reported in the article1.

Summary

This chapter rendered a review of FTEGs with respect to the operational principles,

FEM and its application, structure, materials, and fabrication methods. The

operational principles of FTEGs mainly involved TE effects and heat transfer. FEM

was a powerful method to help scientists and engineers to discover the essential

problem behind phenomenon and to explore the theoretical limitation. The

structures of FTEGs were summarized and compared. Materials were classified into

four categories: inorganic, organic and polymer TE materials, graphene, and

composites. The state-of-art application of these materials to FTEGs were presented.

Fabrication methods, including surface modification and embedding, were briefly

introduced.

Although FTEGs exhibit many advantages, very few works have been reported.

Thus, research about FTEGs is still in an infant stage. Many issues of FTEGs

impedes their development and application. For example, the appropriate materials,

which have not been found, should simultaneously fulfil demands of different

2.7 References

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aspects, such as the device performance, the mechanical properties, the fabrication

process, the comfortable feeling, the cost-effectiveness, and so on. These materials

may be found in the future. But to deeply understand the mechanism of FTEGs can

be conducted immediately through taking advantages from the analytical and

numerical solutions. However, few research has been published to reveal the

relationship between the structure and performance of FTEGs. To fill this research

gap, this research will design 1D FTEGs in different geometric parameters. Their

performance will be studied under different conditions. Besides, a feasible method

will be applied to fabricate the 1D FTEGs.

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Copyright Undertaking · Kevin Hui, and Mr. Kwan-on Choi. Thanks for the help from Ms. Sicily Ho, Ms. Lemona Kong, and Ms. Wu Chunyan Tracy. They helped me to deal with many miscellaneous