Molecular Dynamic Based Study on Heat

Transfer ThroughNanoscale Heat Pipes for

Efficient Heat Removal from Advanced
Electronic Devices
Thesis submitted in partial fulfilment of the requirements for the degree of

Master of Technology
in

Metallurgical and Materials Engineering

by

Rajesh Kumar Goswami

Roll No-17MM4110

Under the supervision of

Dr.Madan Mohan Ghosh

Associate Professor and HoD

Department of Metallurgical and Materials Engineering

National Institute of Technology, Durgapur, WB, India
MAY 2019

i
 Department of Metallurgical and Materials Engineering, National Institute
of Technology, Durgapur-713209,WB, India

CERTIFICATE
This is to certify that the thesis entitled, “Molecular Dynamic Based Study on Heat Transfer
Through Nanoscale Heat Pipes for Efficient Heat Removal from Advanced Electronic
Devices” submitted by RAJESH KUMAR GOSWAMI(17MM4110) in partial fulfilment of
the requirement for the award ofMaster of Technology in Metallurgical and Materials
EngineeringDepartment, National Institute of Technology, Durgapur is a bonafide record
ofresearch work carried out by him under my supervision and guidance. To the best of my
knowledge, the matter embodied in the thesis is based on candidate‟s own work, has not been
submitted to any other university / institute for the award of any degree or diploma.

Date:

Place Dr. MADAN MOHAN GHOSH

Associate professor and Head
Dept. of Metallurgical and Materials
Engg.
National Institute of Technology
Durgapur – 713209,WB, India

ii
 Department of Metallurgical & Materials Engineering
National Institute of Technology, Durgapur
Durgapur-713209, West Bengal, INDIA

THESIS APPROVAL

The forgoing thesis is hereby approved as a creditable study of an Engineering and Technology
subject, carried out and presented in a manner satisfactorily to warrant its acceptance as a pre-
requisite to the degree for which it has been submitted. It is to be understood by this approval
that the undersigned do not necessarily endorse/approve the mode, opinion expressed or
conclusion drawn herein but approve the thesis only for the purpose it has been submitted.

Board of Examiners

...............................................................................

...............................................................................

...............................................................................

...............................................................................

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 ACKNOWLEDGEMENT

This work would not have been possible without the support from NIT, DURGAPUR. I
want to express my utmost gratitude to my supervisor and head of the department Dr.
MADAN MOHAN GHOSH for his support, both intellectual and emotional, throughout the
years of my M.Tech studies and project work. He took me from my infantile knowledge of
Material Science and Engineering and introduced me to a whole new world. Performing
simulation work with him left me in both joy and awe and I hope to retain this excitement in
any future research endeavour. It was through his encouragement and understanding that I
am standing here today, about to embark on a career in academia. I want to thank him for all
the time he spent with me explaining the most obscure concepts, for helping me to view
results with a whole new light and for teaching me how to think by myself. I hope that one
day I may be able to repay him for all the good he have done for me.

I also want to thank ABHIRAM HENS, Assistant Professor ,Department of Chemical

Engineering, who supported in doing my work. I would like to thank my senior AJAY
MISHRA AND KRISHNAN BANDYOPADHYAY for helping me in my project work. I
would like to thank all the staff members of Department of Metallurgical & Materials
Engineering who had been very cooperative with me at all times. Finally, I would like to
express my deepest gratitude to my parents for their unconditional love and encouragement. I
would not be where I am today without the support of them.

Department of Metallurgical & Materials Engineering

NIT, Durgapur, WB, India RAJESH KUMAR GOSWAMI
Date:

iv
 ABSTRACT
Heat generation in the electronic system has become a big concern with the advent of new
technology. Reliability of electronic component depends on operating temperature level and
the dissipated wattage. In addition, the need for cooling compact electronic system has become
a big challenge for traditional cooling systems using air as coolant.Thermal management is an
important issue for electronic cooling application. Choosing an efficient cooling technique
depends on thermal performance, reliability, manufacturing cost, and prospects for
minimization of packaging cost. A detailed overview of heat pipes is presented in this paper,
including a historical perspective, principles of operations, types of heat pipes, heat pipe
performance characteristics, heat pipe limitations, heat pipe frozen start up and shutdown, heat
pipe analysis and simulations, and various applications of heat pipes. Over the last several
decades, several factors have contributed to a major transformation in heat pipe science and
technology. The first major contribution was the development and advances of new heat pipes,
such as loop heat pipes, micro and miniature heat pipes, and pulsating heat pipes. In addition,
there are now many new commercial applications that have helped contribute to the recent
interest in heat pipes, especially related to the fields of electronic cooling and energy. For
example, several million heat pipes are now manufactured each month since all modern laptops
use heat pipes for CPU cooling. Numerical modelling , analysis, and experimental simulation
of heat pipes have also significantly progressed due to a much greater understanding of various
physical phenomena in heat pipes, as well as advances in computational and experimental
methodologies.
A detailed overview of heat pipe is present in this paper. First the model of heat pipe with Ar as
a working fluid is designed and thermal conductivity has been calculated by varying the
parameter. Based on the obtained result a heat pipe with water as a working fluid has been
modelled and the thermal conductivity has been calculated .The obtained thermal
conductivity3.6 W/mK of Cu-water heat pipe is much higher than the Cu-Ar heat pipeamd also
it is higher than the thermal conductivity of water

Keywords: heat pipes, performance characteristics, numerical modelling, heat pipe

applications

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 Table of contents

Certificate...................................……………………………….…………………………........ii
Thesis Approval……………............………..………………………………………..............iii
Acknowledgement......................................................................................................................iv
Abstract…………………………...……………………………………………………...…….v
Table of Contents....................................................................................................................Vi
List Of Figures………………………………………………………………......……….........ix
List of Tables………………………………………………………………………………….X

Chapter 1.0 Introduction………………………………………………………..…………....1

1.1Background of Research………………………………………………………………….…2
1.2 Motivation of Present Study................................................................................................3
1.3 Significance…………………………………………………………………………………4
1.4 Organisation of Thesis………………………………………………………………………4

Chapter 2.0 Literature Survey…………………………………………………………........6

2.1Introduction...........................................................................................................................6
2.2Heat Pipes Operating Principles…..………………………………………………………..7
2.3Historical Development of Heat Pipes..................................................................................8
2.4Application...........................................................................................................................10
2.5Heat Pipe Features and Benefits…………………………………………………………..15
2.6 Heat Pipe Advantages……………………………………………………………………..16
2.7 Some Previous Investigation on Nannoscale Heat Pipe.....................................................16

Chapter 3.0 Molecular Dynamics …………………………………………….....................21

3.1 Molecular Dynamics Simulation…………………………………………………………..22
3.2 Introduction………………………………………………………………………………..22
3.3 Introduction to Classical Molecular Dynamics……………………………………………24
3.3.1. Advantage………………………………………………………………………………24
3.3.2. Limitations……………………………………………………………………………..25
3.3.3. Inter-Atomic Potential………………………………………………………………....25

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3.3.4. Potential in MD Simulation………………………………………………………….26
3.3.5. Simulation Method in Molecular Dynamics……………………..………………......26
3.3.6. General Steps of Molecular Dynamics Simulation......................................................27
3.3.7. Periodic Boundary Condition.....................................................................................28
3.3.8. Ensembles…………………………………………………………………………....29
3.6. Introduction to LAMMPS (Large-Scale Atomic/Molecular
Massively Parallel Simulator)................................................................................................30

Chapter4 Simulation Procedure

4.1Simulation procedure of Cu-Ar heat pipe........................................................................34
4.2 Input of simulation procedure.........................................................................................36
4.3 Output of simulation procedure.......................................................................................37
4.4 Simulation procedure of Cu-water heat pipe...................................................................38
4.5 OVITO............................................................................................................................40
4.6HPC..................................................................................................................................40
4.7 Cu-Ar heat pipe................................................................................................................41
4.8 Cu Ar heat pipe................................................................................................................43
4.9 Calculation of heat flux...................................................................................................44

Chapter 5.0 Result and Discussion……………………………………………………..…..45

5.1 Heat Pipe with Constant Hot End Temperature………………………………………......46
5.1.1 Results ……………………………………………………………………………...…..47
5.2 Heat Pipe with Constant Heat Flux……………………………………………………….49
5.2.1 Results ……………………………………………………………………………….....50
5.3 Comparision of Different Result ………………………………………………………....52
5.3.1. When Different Thickness of Argon Is Used …………………………………..….......52
5.3.2 When Different Temperature Is Applied To Hot End ………………………….……....52
5.3.3 when Different Volume Heat Pipe Used……………………………………….…….....53
5.4 Heat Pipe With Copper At Both End And Working Fluid Is Water……………………...54
5.4.1 Results………………………………………………………………….…………….....56
5.5 Comparision Of Result........................................................................................................57

Chapter 6.0 Conclusion and scope of future work………………………………………...58

5.1 Conclusion………………………………………………………………………………...59

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5.2 Future Scope......................................................................................................................59
References………………………………………………………………………………...…61

viii
 List of Figures

Figure No. Name of Figure Page No.

Fig 1.1 Sketch of a constant conductance heat pipe 2

Fig2.1 Example of heat pipe 6

Fig2.2 Operating principle of heat pipe 7

Fig 2.3 Schematic of a conventional heat pipe showing the 10

principle of operation and circulation of the working fluid

Fig2.4 Heat pipe application in medical 14

Fig2.5 Heat pipe application in cutting tools 15

Fig2.6- Schematic of Ar-filled nano gap. The heat flow, 17

temperature of cold and hot plates, gaseous region,
absorbed layered particles, and periodic boundaries are
shown
Fig. 2.7. Snapshots of argon molecules distribution near above the 18
heating wall with different heating temperatures (1200 Ar
molecules in the system
Fig. 2.8 (a) Rendering of the net gas flow in the void 20
space and net surface-diffusion-driven liquid
return flow on the post surface,
(b) equivalent thermal circuit diagram showing
the heat transfer and thermal resistances, and (c)
geometry and dimensions of the NHP.
(d) Geometry and dimensions of a nano gap
without a post used for model validation.

Fig3.1 Flowchart of MD simulation 23

ix
Fig 3.2. Schematic of a periodic boundary condition. 29

Fig4.1 Snapshot of simple heat pipe 41

Fig4.2 Snapshot of simple heat pipe(Cu-Water) 43

Fig5.1 Snapshot of heat pipe with constant hot end temperature 46

Fig5.2 Graph of heat pipe with constant hot end temperature 47

Fig5.3 Graph of heat flux of cold end 48

Fig 5.4 Heat pipe with constant heat flux at different steps 49

Fig5.5 Graph of heat pipe with constant heat flux 50

Fig 5.6 Graph of heat flux of cold end 51

Fig 5.7 Heat pipe with water as working medium at different steps 55

Fig 5.8 Graph of heat pipe with water as working medium (heat 56
flux)

List of Tables

Table No. Name of Table Page No.

Table5.1 Different thickness of 52
working fluid
Table5.2 When different temperature is 53
applied to hot end

Table 5.3 when different volume of heat 53

pipe is used

x
 CHAPtER1
INTRODUCtIOn

1
1.1BACKGROUND OF RESEARCH

A heat pipe has been known as a thermal superconductor utilizing a liquid-vapor phase change,
and it has drawn significant attentions for advanced thermal management systems.The heat
pipe is a thermal device which allows an efficient transport of thermal energy. It is composed
of a closed structure whose internal surface is lined with a thin layer of porous material, usually
referred to as a wick. The container may have a cylindrical shape, or any other shape that can
be conveniently manufactured. The pores of the wick are filled with a working liquid
appropriate to the application, and the vapour of the liquid occupies the remaining internal
volume. Therefore, since the liquid and its vapour coexist in equilibrium, the pressure inside
the container is equal to the vapour pressure corresponding to the saturation conditions.

This relatively simple configuration allows for a very efficient heat transfer from one end of
the heat pipe to the other, following a quite simple heat transfer mechanism (Figure 1.1). As
heat is applied to one end (the evaporator), the working liquid evaporates from the wick, while
the removal of heat from some other portion of the surface (the condenser) causes the vapour
to condensate on the wick. The pressure gradient resulting from the accumulation of vapour at
one end of the heat pipe and its depletion at the other end causes the vapour to flow though
the core region of the container (the vapour space). But, as the liquid evaporates, it retreats into
the wick pores, then the meniscus there is depressed and the liquid pressure drops below the
pressure of the adjacent vapour. At the other end condensation takes place, so that the working
liquid fills in the wick, tending to maintain a flat surface without any depression of the pressure
in the liquid. Due to capillary forces, the result is a pressure gradient in the liquid that causes
the working liquid to flow through the wick towards the evaporator end, in the opposite
direction to that of the flowing vapour in the core region, completing the flow circuit .

Figure 1.1 Sketch of a constant conductance heat pipe

2
The pressure variations in the vapour core are normally small and, therefore, the heat
pipe temperature is almost uniform and close to the saturated vapour temperature
corresponding to the vapour pressure (heat transfer through a heat pipe is
virtually isothermalbecause the vapour pressure drop is usually of the order of 1% or less).
Therefore, the heat pipe can be considered an extra-high thermal conductivity device, with
reference to Fourier‟s law, as the effective thermal conductivity along the direction of heat
transport is generally at least four to five orders of magnitude greater than the thermal
conductivity of copper.
Yet another interesting heat pipe property is the capability of converting or transforming the
surface heat flux (heat transfer rate per unit surface area) at the heat input zone to a higher or
lower heat flux at the heat output zone. Since the heat flow rate is the same in both zones, the
transformed heat flux varies inversely to the ratio of the surface areas. Thus, to reduce the heat
flux by a factor of ten, the area of the heat output zone should be ten times that of the heat input
zone (Silverstein, 1992).
There is a great variety of heat pipes in terms of their geometry, function, and methods used to
transport the liquid from the condenser to the evaporator. The above-described heat pipe,
consisting of a working fluid, a wick structure, and an envelope, is the most basic type of heat
pipe, and it is known as a constant conductance heat pipe. There are other more
sophisticated heat pipedesigns, namely: variable conductance heat pipes, thermal diodes,
pulsating (oscillating) heat pipes, micro-heat pipes, rotating heat pipes, sorption heat
pipes (SHPs), magnetic fluid heat pipes, loop heat pipes, and capillary pumped loops (LHPs
and CPLs, respectively).

1.2 MOTIVATION OF PRESENT STUDY

Extensive studies using classical molecular dynamics (MD) have been carried out to
understand the phenomena of heat transfer in heat pipe. The variation of thermal conductivity
wrt to pressure ,temperature ,volume thickness of working fluid have been studied at molecular
level by using molecular dynamics . MD simulation is generally believed to be an effective
way in modelling nano scale heat pipe , providing an in situ observation on atomic motions.
Molecular dynamic simulation is useful method to explore the nano scale characteristic of the
heat and mass transfer at solid liquid interface

3
1.3 SIGNIFICANCE
Heat pipes are one of the most effective procedures to transport thermal energy from one point
to another, mostly used for cooling. It is based on a combination of conduction and convective
heat transfer, what makes it to a complex heat transfer problem

Nowadays heat pipes are used in several applications, where one has limited space and the
necessity of a high heat flux. Of course it is still in use in space applications, but it is also used
in heat transfer systems, cooling of computers, cell phones and cooling of solar collectors.
Especially for micro applications there are micro heat pipes developed as for cooling the kernel
of a cell phone down. Due to limited space in personal computers and the growing
computational power it was necessary to find a new way to cool the processors down. By
means of a heat pipe it is possible to connect the processor cooling unit to a bigger cooling unit
fixed at the outside to cart of the energy.
On a first look a heat pipe seems to be a very easy tool to transport energy, but if one looks
closer, it is a very complex heat and mass transfer process which takes place in a heat pipe.
First of all one has convective heat transfer in the adiabatic transport range, and one has
convection through porous materials also. The second major point is mass transfer due to
vaporization and condensation, also through porous media. Furthermore there are capillary
effects, pressure effects and heat conduction effects involved, which creates a complex
structure of heat transfer, where a lot of knowledge is involved. And all of these points can be
treated as a own problem, from this follows that a complete understanding of all involved
processes needs more time and space than it is available for this project report.

1.4 ORGANISATION OF THESIS

The thesis has five chapters. There is brief introduction of heat pipe and MD simulation with
motivation and objectives is mention in Chapter-1. Some relevant literature background
related to nanoscale heat pipe and molecular dynamics simulation has been presented in
Chapter-2.Chapter-3 consists of simulation parameters to perform simulation studies on
nano-scale with copper at both end and working fluid is Ar. Chapter-4consist the results and
discussion related to the above stated objectives. Chapter-5 is an overview of the conclusions
derived from this study which has been analyzed briefly with few directions for future work
related to this section. A comparison has also been made with the results obtained from this
investigation with those of previous investigations. All references cited throughout the work
have been compiled at the end of Chapter 5
4
 CHAPtER2

LITERAtUREREVIew

5
2.1INTODUCTION

The heat pipe (Faghri, 1995) is a highly effective passive device for transmitting heat at high
rates over considerable distances with extremely small temperature drops, exceptional
flexibility, simple construction, and easy control with no external pumping power. Engineers,
scientists and graduate students interested in heat pipe science often times struggle and spend
considerable time poring through archival publications or the contents of heat pipe books in
order to understand and predict a heat pipe system. Being aware of this situation, this review is
a self-contained document of the state-of-the-art heat pipe science and technology.

Fig2.1 Example of heat pipe

The subject of heat pipe science has immense importance in a large variety of traditional
engineering disciplines. The sub-discipline of heat pipe science has its foundation in several
classical fields, such as fluid mechanics, heat transfer, thermodynamics and solid mechanics.
Heat pipe science also provides an opportunity for scientists and engineers to apply a variety of
6
complex physical phenomena and fundamental laws in the thermal-fluids area to a relatively
simple system, such as the heat pipe. This includes the steady and unsteady forced laminar and
turbulent convective heat and mass transfer ,compressible vapour effects, phase-change
phenomena, boiling, condensation/evaporation, two-phase flow, rotating flows, thin film flows,
liquid flow in porous media, rarefied gases, interfacial heat and mass transfer, magneto-
hydrodynamic flows, and conjugate heat transfer effects.

2.2Heat Pipes – Operating Principles

Fig2.2 Operating principle of heat pipe

• Typical use of heat pipe: one end (the evaporator) is attached to the heat source, and the
opposite end (the condenser) to the heat sink. The middle section (the adiabatic section) is
insulated.
• As liquid is vaporized at the evaporator, the vapour pressure builds up, forcing vapour to flow
axially along the centre core to the condenser .
• Vapour condenses at the condenser. Liquid is drawn back to the evaporator by the capillary
force along the grooves.
• The pressure difference between the vapour and liquid phases is sustained by the surface
tension force of the fluid.
• Passive – no external pumping power is required; the waste heat provides the driving force
for the fluid flow.

7
2.3HISTORICAL DEVELOPMENT OF HEAT PIPES

Of the many different types of systems which transport heat, the heat pipe (Faghri,1995) is one
of the most efficient systems known today. The advantage of using a heat pipe over other
conventional methods is that large quantities of heat can be transported through a small cross
sectional area over a considerable distance with no additional power input to the system.
Furthermore, design and manufacturing simplicity, small end-to-end temperature drops, and
the ability to control and transport high heat rates at various temperature levels are all unique
features of heat pipes.
The predecessor of the heat pipe, the Perkins tube, was introduced by the Perkins family from
the mid-nineteenth to the twentieth century through a series of patents in the United Kingdom.
Most of the Perkins tubes were wickless gravity-assisted heat pipes (thermo syphons), in which
heat transfer was achieved by a change of phase (latent heat of evaporation). The Perkins tube
design closest to the present heat pipe was patented by Jacob Perkins (1836). This design was a
closed tube containing a small quantity of water operating as a two-phase cycle. The
introduction of the heat pipe was first conceived by Gaugler (1944) of the General Motors
Corporation in the U.S. Patent No. 2350348.Gaugler, who was working on refrigeration
problems at that time, envisioned a device which would evaporate a liquid at a point above the
place where condensation would occur without requiring any additional work to move the
liquid to the higher elevation. His device consisted of a closed tube in which the liquid would
absorb heat at one location causing the liquid to evaporate. The vapour would then travel down
the length of the tube, where it would recondense and release its latent heat. It would then
travel back up the tube via capillary pressure to start the process over. In order to move the
liquid back up to a higher point, Gaugler suggested the use of a capillary structure consisting of
a sintered iron wick. A refrigeration unit proposed by Gaugler used a heat pipe to transfer the
heat from the interior of a compartment to a pan of crushed ice below. His idea, however, was
not used by General Motors for the refrigeration problem.

In 1962, Trefethen (1962) resurrected the idea of a heat pipe in connection with the space
program. Serious development started in 1964 when the heat pipe was independently
reinvented and a patent application was filed by Grover at Los Alamos National Laboratory in
New Mexico. Grover et al. (1964) and Grover (1966) built several prototype heat pipes, the
first of which used water as a working fluid, and was soon followed by a sodium heat pipe

8
which operated at 1100 K. Grover and his co-workers also demonstrated the effectiveness of
heat pipes as a high performance heat transmission device and proposed several applications
for their use. In a U.S. patent application filed by Grover on behalf of the U.S. Atomic Energy
Commission, Grover (1966) coined the phrase “heat pipe” and described a device almost
exactly the same as Gaugler‟s, stating, “with certain limitations on the manner of use, a heat
pipe may be regarded as a synergistic engineering structure which is equivalent to a material
having a thermal conductivity greatly exceeding that of any known metal.” In the patent
application, Grover (1966) gave a very limited theoretical analysis of heat pipes, but presented
experimental results obtained from stainless steel heat pipes that incorporated a screen wick
with sodium, silver and lithium as working fluids.

The recognition of the heat pipe as a reliable thermal device was initially due to the preliminary
theoretical results and design tools that were reported in the first publication on heat pipe
analysis by Cotter (1965). Following this publication, research began worldwide. The United
Kingdom Atomic Energy Laboratory at Harwell started experimenting with sodium heat pipes
to use as thermionic diode converters. In addition, scientists started conducting similar work at
the Joint Nuclear Research Centre in Ispra, Italy, which soon became the most active research
centre outside the U.S. Shortly thereafter, other countries such as Germany, France, and the
former USSR initiated efforts in this regard.

The early development of terrestrial applications of heat pipes proceeded at a slow pace. Due to
capillary action, heat pipes can operate in micro gravitational fields without any external force
field or pump. Because of this, most early efforts were directed toward space applications.
However, due to the high cost of energy, especially in Japan and Europe, the industrial
community began to appreciate the significance of heat pipes and thermo syphons in energy
savings applications. Today, all developed countries have been actively involved in research,
development, and commercialization of heat pipes. Within the last decade, a major
transformation regarding heat pipe technology and application has occurred due to the critical
need of electronic cooling and energy systems, as well as the invention of new heat pipes.
Several million heat pipes per month are now being manufactured since all modern laptop
computers use heat pipe technology to transfer heat away from the processor. Furthermore,
research and development for new heat pipes such as loop heat pipes, micro and miniature heat
pipes, and pulsating heat pipes, has matured enough for use in various applications.

9
There is a wealth of published literature: several heat pipe books and monographs, as well as
the proceedings of eleven international heat pipe symposiums and seventeen international heat
pipe conferences. In addition, there are a large number of archival and non-archival
publications and reports related to heat pipes, dating back over the last four decades. A
significant amount of basic and applied research & development has been performed since
1985 in the area of heat pipes due to the great potential use of this technology for various
applications.

Fig 2.3 Schematic of a conventional heat pipe showing the principle of operation and
circulation of the working fluid

2.4APPLICATION
A heat pipe is a passive energy recovery heat exchanger that has the appearance of a common
plate-finned water coil except the tubes are not interconnected. Additionally it is divided into
two sections by a sealed partition. Hot air passes through one side (evaporator) and is cooled
while cooler air passes through the other side (condenser). While heat pipes are sensible heat
transfer exchangers, if the air conditions are such that condensation forms on the fins there can
be some latent heat transfer and improved efficiency.

10
Heat pipes are tubes that have a capillary wick inside running the length of the tube, are
evacuated and then filled with a refrigerant as the working fluid, and are permanently sealed.
The working fluid is selected to meet the desired temperature conditions and is usually a Class
I refrigerant. Fins are similar to conventional coils - corrugated plate, plain plate, spiral design.
Tube and fin spacing are selected for appropriate pressure drop at design face velocity. HVAC
systems typically use copper heat pipes with aluminum fins; other materials are available.

2.4.1AEROSPACE
Heat pipes enjoy wide application in the area of spacecraft cooling and temperature
stabilization. They enjoy the distinct advantages of low weight, essentially zero maintenance,
and superior reliability over other devices. Structural isothermal operation is an important goal
in aerospace operations. Thermal stress occurring from heat inequalities is a critical issue in
many orbiting astronomical experiments. While in orbit, for example, an observatory may be
fixed on a single point such as a star. Consequently, one side of the capsule will be subjected to
intense solar radiation while the other is not. Heat pipes in this situation are used to transport
heat from the side facing the sun to the cold side away from it, thus equalizing the temperature
of the structure. Because of the demand for reducing spacecraft costs while maintaining high-
performance characteristics of the spacecraft bus, the mass of satellites has to be minimized.
Thus, the reduction of space cooling by increasing heat density is an important challenge. To
achieve this, heat pipes are commonly used to affect heat transfer and heat redistribution
functions in the microsatellites

2.4.2HEAT EXCHANGERS

Because of flexibility in design, heat pipes can easily be utilized as heat exchangers inside
sorption and vapour-compression heat pumps, refrigerators, and other types of heat transfer
11
devices. For example, heat pipe heat exchangers (HPHE) used for controlling humidity in air
conditioning systems have been exhaustively researched. The purpose of the HPHE is to
recover heat from warm outdoor air to reheat the dew point airstream, thereby minimizing
heating costs. Also, the evaporator of the HPHE acts as a pre cooler to the warm outdoor air
before it reaches the air conditioner, thus enhancing the effectiveness of the cooling coil. When
the condenser of the HPHE is used as a reheater to heat the airstream coming from the cooling
coil, the relative humidity can more easily be reduced to the comfort zone, below 70

2.4.3 ELECTRONIC COMPONENTS

As of the present, one of the largest applications of heat pipe technology is the cooling of
electronic components such as central processing units (CPUs), circuit boards, and transistors.
For example, the CPU, one of the most important parts of any PC, is becoming increasingly
more compact, faster, and more efficient. This leads to higher heat density, resulting in
increasing CPU temperature, threatening a shortened life of the chip, or resulting in
malfunction or failure. A conventional method used to keep a CPU from overheating is to use
an extruded aluminum heat sink. This is an efficient method in terms of unit price, weight, and
performance. However, as computers become smaller, the ability of the heat sink to effect
cooling becomes insufficient to meet demands, chiefly because of insufficient space. The use
of heat pipes in such situations has marked advantages

2.4.4OVENS AND FURNACES

One of the earliest applications of heat pipe technology was in conventional baking
ovens. Previously, flames were applied to the firebrick lining the oven which in turn
transmitted the heat to the items baked in the oven. Unfortunately, the baked items were
contaminated by smoke and soot and other combustion products produced by the flames.
In improved models using heat pipes, the transfer of heat to the oven was effectuated by the
evaporation and condensation of the working fluid in the closed heat pipe system, which
transferred the heat, but not the combustion products. The use of heat pipes conferred two other
advantages: a more uniform oven temperature, and a savings of up to 25% of the fuel normally
consumed.

12
2.4.5SOLAR THERMAL APPLICATIONS

Due to a shortage in the supply of fossil fuel, renewable energy sources have become one of
many alternative solutions. Solar energy is a renewable energy resource, and it is abundant. It
has been used in a variety of applications in generating electricity, in cooling, and even in
heating.

2.4.6SOLAR COOKING

Preparation of foods requires some amount of energy. Wood fuel and agricultural residues
are the main energy sources for cooking in developing countries, normally accounting for 50%-
90% of all energy consumed in those countries. However, the rate of wood fuel consumption
exceeds its replacement, and this results in deforestation, pollution, soil erosion, global
warming, and a worsening of the welfare of millions of people all over the world. Although
electric cooking is comparatively convenient, its production from fossil fuel has cumulative
consequences resulting in the emission of high quantities of carbon dioxide and sulfur dioxide
into the atmosphere. The use of solar cooker technology is an alternative solution to the fuel
problem. Heat pipes are utilized for solar cookers in transporting heat from the heat source to
its destination

2.4.7AGRICULTURE

In the process of agricultural production, a soil-free planting system is widely accepted as

an efficient means of improving production. There are two types of soil-free planting systems:
hydroponic and aeroponic systems. The aeroponic system is a soil-free system in which the
roots of the plants are completely or partially exposed to air in a plant chamber. The plants are
anchored in holes atop a panel of polystyrene foam. Inside the chamber, a fine mist of nutrient
solution is sprayed onto the roots.

2.4.8TRANSPORTATION SYSTEMS

Several heat pipe applications are used to improve the safety and reliability of air, surface, and
rail transportation systems. In Siberia, during the long winter, snow may fall at the rate of
1000-1500 mm per day with the ambient air at - 5 to - 7°C. Heat pipe technology is used to

13
heat the rails to prevent ice formation. The condenser end of the heat pipe is located at the point
of contact between the heat pipe and the rail.

2.4.9MEDICAL APPLICATIONS

One of the more practical heat pipe applications in medicine is in the heat pipe cooler (see
Fig. 2.4). This cooler has a copper-methanol heat pipe with a copper sintered powder wick and
four Peltier elements, cooled by a water heat exchanger. It is used for non invasive treatment of
an inflamed vagina, rectum, or pelvis and for some common gynaecological and rectal
conditions. The main component of the cooler used in this application is the heat pipe
(1). The condenser of the heat pipe is thermally contacted with the cold surfaces of Peltier
elements
(2). The evaporator of the heat pipe is cooled by the water in the heat exchanger
(3). Peltier elements and this heat exchanger are located inside the handle of the cooler
(4). During the medical treatment, the heat pipe cooler is introduced into the rectum or vagina,
cooling the mucous membrane.
The cooling effect is not only positive for the above-mentioned organs, but also effective in the
indirect cooling of reflex ganglions in conditions such as chronic gastritis, ulcerative colitis,
acute gastritis, and gastric and duodenal ulcers.

Fig2.4 Heat pipe application in medical

2.4.10 ENGINES AND THE AUTOMOTIVE INDUSTRY

Many sources of heat are available for low-temperature applications, including solar
ponds, industrial waste, and geothermal energy. These sources of heat could be utilized for
power generation. Many attempts to use this low-grade heat to produce electricity have been

14
proposed. One of the attempts to integrate a turbine with a heat pipe was introduced in the
Thermo syphon Rankine (TSR) engine for generating electricity. The heat pipe used in this
application transfers heat from the evaporator through the turbine to the condenser.. The
working fluid located in the lower evaporator end of the pipe is evaporated and rises to the
upper region with the application of the heat source. It is fed through the turbine, which in turn
generates electricity.

2.4.11CUTTING TOOLS

Cutting processes are being used in many factories. In the process, the energy supplied is
converted to heat energy at the cutting zone. The heat generated in the tool and work piece is
carried away by the working fluid. Three types of fluid sare commonly used: oil (with additives
such as sulfur, chlorine, and phosphorus), emulsions, and synthetics. Although this cooling
method shows some promise in increasing tool life, the exposure of the fluids to the working
environment may cause significant contamination to the environment and increased health
hazards to the workers. Currently, there is a strong worldwide trend toward minimizing the use
of cutting fluids, as they have been shown to be a primary source of industrial pollution. For a
cutting process to run without the use of fluids, alternative methods to remove the heat
accumulated in the tool and the work piece had to be developed. Heat pipes provide an
effective alternative solution to the problem, as shown in Fig 2.5.

Fig2.5 Heat pipe application in cutting tools

2.5HEAT PIPE FEATURES AND BENEFITS:

 Tube material: Copper/ Aluminum

 Wick structures:

 Grooved– Low Cost, does not work well against gravity

15
  Wire Mesh – Most common method
 Sintered – Highest performance and cost
 High thermal conductivity

 Light weight

 Fast thermal respons

2.6 HEAT PIPE ADVANTAGES:

 Passive Operation

 Long Life

 Zero cross contamination since streams of source and sink are physically separated

 Minimum Maintenance

 Compact Size

 Practically zero back pressure

2.7SOME PREVIOUS INVESTIGATION ON NANNOSCALE HEAT PIPE

Mdmoulodetal had designed the nano scale heat pipe employing the gas-filled nanostructure,
while transferring heat via ballistic fluid-particle motions with a possible returning working
fluid via surface diffusions along the nanostructure. The enhanced heat flux for the nano heat
pipe is demonstrated using the non equilibrium molecular dynamics simulations (NEMDS) for
the argon gas confined by the 20 nmlong Pt nanogap with a post wall with the temperature
difference between the hot and cold surfaces of 20 K. The predicted results show that the
maximum heat flux through the gas-filled nanostructure (heat pipe) nearly doubles that of the
nanogap without the post wall at 100 < T < 140 K. The optimal operating conditions/material
selections are discussed. The results for the nano gap agree with those obtained from the
kinetic theory, and provide insights into the design of advanced thermal management systems.

16
Fig2.6- Schematic of Ar-filled nanogap. The heat flow, temperature of cold and hot plates,
gaseous region, absorbed layered particles, and periodic boundaries are shown.

The predicted heat fluxes show the significant heat flux enhancement by nearly an order of
magnitude compared to that of the Ar-gas-filled nanogap (no post wall). It is found that the
enhancement becomes pronounced at a low temperature (nearly triple phase temperature of
Ar). The enhancement may be caused by the adsorption-based surface diffusion through the
post wall from the cold to hot surfaces. The enhancement can be further improved by the
optimal material selection and geometries for the desired ballistic and adsorption-based surface
diffusion motions of the fluid particles in the gas region and adsorbed layer. The gas-filled
nanostructures can serve a nanoscale, high heat flux thermal management system such as nano
heat pipe for small scale efficient cooling systems [1]

C Y Ji et alstudiedthe liquid-vapour-solid system near triple-phase contact line in a

microchannel heat sink is studied numerically. Molecular dynamics (MD) method is employed
aiming to get a microscopic insight into the complex liquid-vapour-solid system. In the present
model, the Lennard-Jones potential is applied to mono-atomic molecules of argon as liquid and
vapour, and platinum as solid substrates, to perform a simulation of non-equilibrium molecular
dynamics. The results of numerical simulation suggest that for a complete wetting system, such
as argon on a platinum substrate, there is a non-evaporating liquid film with thickness in
nanometres existing on the heating solid surface. The minimum film thickness near the triple
phase contact line under different conditions of the substrate temperature is predicted. The
thickness of such an ultra-thin liquid film varies only slightly with the number of argon
molecules but decreases with the increase of heating substrate temperature. The decrease in
17
potential energy toward the region near the heating wall is considerably large indicating that
the interactions of solid and liquid molecules are very strong

Fig. 2.7. Snapshots of argon molecules distribution near above the heating wall with different heating
temperatures (1200 Ar molecules in the system)

Numerical simulations based on the nonequilibrium molecular dynamics (NEMD) are

performed to investigate liquid-vapour-solid system near triple-phase contact line of flow
boiling in a microchannel. The main findings can be summarised as follows:
1) For a completely wetting system of mono-atomic fluid and substrates, an ultra-thin liquid
film in nanometres is adhered on heating surface even when the surface temperature reaches
above the critical temperature.
2) The minimum film thickness near triple-phase contact line under different conditions of the
substrate temperature is predicted to be within 2 nm.
3) For the systems with different number of argon molecules, the film thickness remains
almost the same if the heater temperature is constant.
4) The liquid film thickness decreases with the increase of wall heating temperature. However,
a complete evaporation does not take place when the solid wall superheat is extremely high.
5) The decrease in potential energy toward the region near the heating wall is considerably
large indicating that the interactions of solid and liquid molecules are very strong.[2]
IlnazNorouzi et al performed Non Equilibrium Molecular Dynamics (NEMD) simulations
combined with Grand Canonical Monte Carlo (GCMC) simulations to investigate the
nanoscale heat and mass transfer in ananoscale heat pipe (NHP) enabled by the surface-
18
diffusion-driven return flow of the adsorbed gas under various operating conditions
(temperature and pressure and temperature gradient), material selections (fluid-solid
interaction), and geometries (axial length) using an Ar-filled Pt-based nanogap with a post
connecting two parallel surfaces of heat source and heat sink. The condensate return from
the condensing (cold) to evaporating (hot) surfaces by pressure-driven surface diffusion
over the post enabled the heat pipe operation using phase-change heat transfer. The hot
and cold surface temperatures, fluid-solid surface interaction on the post, number density
of Ar atoms, and post height were found to greatly affect the atomic heat and mass transfer
in the NHP. It was also found that for a given average surface temperature, regardless of
the surface temperature difference between the hot and cold surfaces, the ratio between the
fluid (of gaseous and adsorbed Ar atoms) and solid (of Pt atoms in the post) heat transfer
remains relatively constant. The heat transfer through the adsorbed Ar atoms reaches to a
maximum value around e =1.5 kcal/mol due to theformation of a dense layer of the adsorbed
Ar atoms with less mobility on the post. For the post height larger than 1000 Å, the heat
transfer of the gaseous and adsorbed Ar atoms outpaces the solid conduction heat transfer
of the Pt post. It is concluded that the effective thermal conductivity of the NHP is
increased by using higher average surface temperature, larger surface temperature
difference, more Ar atoms, taller post, and smaller interatomic potential (weaker coupling)
between Ar and Ptatoms.[3]

19
Fig. 2.8 (a) Rendering of the net gas flow in the void space and net surface -diffusion-driven
liquid return flow on the post surface, (b) equivalent thermal circuit diagram showing the heat
transfer and thermal resistances, and (c) geometry and dimensions of the NHP. ( d) Geometry
and dimensions of a nanogap without a post used for model validation .

20
 CHAPtER3
MoLECULAR DynAMICS

21
3.1 MOLECULAR DYNAMICS SIMULATION

In this chapter, a brief introduction of the molecular dynamics (MD) simulation will be

provided, followed by details regarding the computational steps behind the molecular

simulations performed, different inter-atomic potential functions used, force-field parameters

used for the simulations, different MD simulation modules‟ implementation in the in-house

software, and the thermodynamic properties evaluation. These methodologies were used while

creating and using our own MD simulation software written in C++ language and are explained

in the subsequent sections of this chapter.

3.2 INTRODUCTION

Molecular dynamics is a computer simulation method for studying the transient physical

movements of atoms and molecules, and is thus a type of N-body simulation [4]. Atoms and

molecules are allowed to interact each other using a potential for a desired period of time,

giving a view of the dynamical evolution of the system. In the most common version, the

trajectories of atoms and molecules are determined by numerically solving Newton's equations

of motion for a system of interacting particles, where forces between the particles and their

potential energies are calculated using interatomic potentials or molecular mechanics force

fields.

A graphical representation of main steps involved is shown in Figure 2-1. These steps will be

explained in detail in the following sections.

22
 MD IMPIMENTATION

Assign particle positions

Assign particle velocities
Initialize
Specify type of ensembles
Specify potential

Force Integration and

calculation by updation of
using current position and Run
position velocities after t

Use 6N variables to evaluate properties andvisualize

Average properties
Analyse
Transportproperties

States ofMatter

Fig3.1- flowchart of MD simulation

23
3.3 INTRODUCTION TO CLASSICAL MOLECULAR DYNAMICS
Classical molecular dynamics (MD) is a simulation tool used to understand the property of

assemblies of molecules in terms of their structure and the microscopic interactions between

them. It allows one to gain insight into situations that are impossible to study experimentally

such as extreme temperature and pressure conditions. In MD simulations atoms and molecules

are supposed to follow the Newtonian dynamics and have “force field” present between them for

interaction to occur. MD simulation is often used in the study of biomolecules and proteins and

also in material science. MD was introduced for the first timein 1957 [5] and 500 hard spheres

were simulated and studied. Further, some 864 atoms were studied with motion of individual

atoms in liquid Argon [6]. But after the invention of Teraflop parallel simulating system using

massively parallel computers about 109 atoms were simulated together [7]. The workload is

distributed among various processors of parallel computers which increases the calculation. Most

time consuming task during simulation is the calculation of potential (force field) as a function of

coordinates of atoms. Another factor which affect the time taken by CPU evaluation is the size of

integration time-step i.e., time length between evaluation of potential. Time-step chosen in MD

calculation should be small so as to avoid discretization errors (much smaller than the fastest

vibrational frequency in the system). Typically it is of the order of 1 femtosecond (10-15).

Simulation and calculation between atoms is done only if potential between atoms are known or

given as input to the computer.

3.3.1. ADVANTAGES:

a) It is based on the solution of the equations of motion for all particles in the system.

b) Complete information on atomic trajectories can be obtained, but time of the

simulations is limited (up to nanoseconds).

c) The main strengths of the MD method is the ability to study fast non-equilibrium

processes with atomic-level resolution (e.g. microscopic mechanisms of

24
 damage/plastic deformation due to a shock wave propagation, dynamic fracture and

crack growth, ion bombardment, cluster impact, etc.).

d) The only input in the model – description of interatomic/intermolecular interaction

3.3.2. LIMITATIONS:

a) With MD we can only reproduce the dynamics of the system for ≤ 100 ns. Slow

thermally activated processes, such as diffusion, cannot be modelled.

b) Potentials are available for only few metallic systems.

c) Electrons are not present explicitly; they are introduced through the potential energy

surface that is a function of atomic positions only (Born-Oppenheimer

approximation).

3.3.3. INTER-ATOMIC POTENTIAL

In MD, atoms interact with each other and forces act among them which changes along with the

change of position of atoms. These forces (Fi) are calculated as gradient of potential energy

function which is dependent on atom/particle coordinate as

…………………3.1
…..

where, ri is the position vector of an atom i. Potential energy, U is a function of atomic position

and never changes with translation or rotation of atomic position. Equation (3.1) represents the

law of conservation of mechanical energy E=K+U, where E is total energy, K is kinetic energy

and U is potential energy.

25
3.3.4. POTENTIAL IN MD SIMULATION

Embedded atom method potential describes the energy between the two atoms present. The

energy is sum of functions of separation between atoms and its neighbours. It was developed

by(Daw and Baskes 1984)[7] to study defects in metals. The total energy (Etot) of an N-

atomsystem is given by

……………………3.2…

r
where, ∅ij( ij)is a short range pair potential between atoms with separation ri,j Fi ρi is the

embedding energy of atom i with electron density ρdue to all its neighbours is expressed below:

………………..3.3
…

The other type of potentials are L-J potential [8], Empirical potential [9].

3.3.5. SIMULATION METHOD IN MOLECULAR DYNAMICS

In MD atomic/molecular motion obeys the law of classical mechanics. Set of initial position and

velocities of various atoms are given and subsequent time evolution is determined. The result

shows how position and velocities of atoms are changing with time. The differential equation

embodied in Newton‟s second law (Force = mass × acceleration) is solved for obtaining the

trajectory of atoms.

………………………3.4
…

26
The above equation describes the motion of particle of mass mialong one coordinate (xi) with Fxi

being the net force on particle in the same direction.

3.3.6. GENERAL STEPS OF MOLECULAR DYNAMICS SIMULATION

a) Initial position and velocity is assigned to every atom.

b) Force on all the atoms are computed with inter-atomic potential known.

c) Newton‟s equation of motion is integrated to obtain trajectory of atoms. They are repeated

again and again until desired property of all the atoms of system is obtained.

3.3.6.1. INITIALIZING POSITIONS AND VELOCITY OF ATOMS

Initial position of all atoms is determined either by lattice structure and composition or by

random method. This depends on whether the system to be simulated is crystalline or

amorphous. These positions can also be assigned from earlier simulation results. Initial velocity

is found from the temperature of the system and calculated from random distribution given by

statistical mechanics. Systems containing small number of atoms, their linear momentum are

scaled to zero because the random assignment of velocity may not sum to zero exactly.

Velocities can also be assigned from previous simulation results

3.3.6.2. FORCE CALCULATION

Force calculation on each atom is the most time consuming part in MD simulation. The force on

atom „i’ due to the other atoms „j’ surrounding it is calculated from the inter-atomic potential

which exist between each pair of atom and controls interaction among them. If U(dij) is the

interaction potential between any pair of atom ‘i’ and ‘j’,the force on atom ‘i’ due to atom ‘j’ is

given by

…………………..3.5

27
where, riand rj are position vectors of atoms „i’ and ‘j’ and dij is distance between them andis

given by

................3.6

In the present simulation studies EAM-FS potential is used for binary Cu-Ar system developed

by Mendeleev [10]. In Finnis /Sinclair model [11] total energy of an atom is represented by

………………3.7
….…

where, F is the embedding energy which is a function of ρ is a pair potential interaction, ρ is the

electron density which is a functional specific to the atomic types of both atoms i and j so that

different elements can contribute differently to the total electron density at an atomic site

depending on the identity of the lement at that atomic site and alpha and beta are the element

types of atom i and j.

3.3.7. PERIODIC BOUNDARY CONDITION

Periodic boundary condition is employed to simulate an infinite amount of matter with a finite

simulation box size. Atoms coming out from one boundary of simulation cell emerge back from

the opposite boundary. Fig. 3.2 represents the schematic of a periodic boundary condition.

28
Figure 3.2.Schematic of a periodic boundary condition.

3.3.8. ENSEMBLES
(a) NVE

In the microcanonical NVE ensemble the system is isolated from changes in atoms (N), volume

(V) and energy (E). NVE integrator updates position and velocity for atoms in the group each

time-step. There is no heat exchange with the surrounding. A trajectory of atoms is generated in

the system and exchange of potential and kinetic energy occurs and the total energy remains

conserved

(b) NVT

In NVT ensemble the number of atoms (N), volume of the system (V) and the system

temperature (T) remain independent variable and are constant during any process. Temperature

is controlled by Noose-Hover thermostat

(c) NPT

NPT is the isothermal-isobaric ensemble in which number of atoms (N), pressure (P) and

temperature (T) are conserved. The volume of the system is allowed to change over time.

Temperature and pressure are controlled by Nose-Hoover thermostat and Nose-Hoover barostat
29
3.6. INTRODUCTION TO LAMMPS
LARGE SCALE ATOMIC/MOLECULAR MASSIVELY PARALLEL
SIMULATOR

3.6.1. BACKGROUND

LAMMPS is a classical molecular dynamics simulation code run on parallel computers. It was

developed at Sandia National Laboratories, US. It is a free source code which is distributed free

of cost under the tem of GNU public license. The primary developers of this code were Steve

Plimpton, Aidan Thompson and Paul Crozier [14].

3.6.2. GENERAL FEATURES

a) It runs on single or parallel processors

b) Optional libraries used: MPI and single-processor FFT

c) Distributed-memory message-passing parallelism (MPI)

d) Open source distribution

e) Easy to extend with new features and functionality

f) Syntax for defining and using variables and formulas

g) Run one or multiple simulations simultaneously (in parallel) from one script

3.6.3. FORCE FIELDS

Some of the force fields that are employed in LAMMPS are:

a) pairwise potentials: Lennard-Jones, Buckhingam, Morse, Born-Mayer-Huggins,

Yukawa,

b) manybody potentials: EAM, Finnis/Sinclair EAM, modified EAM (MEAM),

embedded
30
3.6.4. ENSEMBLES, CONSTRAINTS, AND BOUNDARY CONDITIONS

In LAMMPS „fix‟ is any operation that is applied to the system during time-stepping or

minimization. For example, the updating of atom positions and velocities due to time integration,

controlling temperature, applying constraint forces to atoms, enforcing boundary conditions, and

computing diagnostics etc. Fixes perform their operations at different stages of the time-step. If

two or more fixes operate at the same stage of the time-step, they are invoked in the order they

were specified in the input script.

a) 2D or 3D systems

b) Constant NVE, NVT, NPT, NPH, Parinello/Rahman integrators

c) Thermostatting options for groups and geometric regions of atoms

d) Pressure control via Nose/Hoover or Berendsenbarostatting in 1 to 3 dimensions

e) Simulation box deformation (tensile and shear)

3.6.4.2. BOUNDARY CONDITIONS

The boundary conditions that are employed in LAMMPS are:

i. p pp

ii. p p s

iii p f p

where „p‟ stands for periodic along the three directions, „f‟ and „s‟ stand for fixed and shrink

wrapped, which are non-periodic.

3.6.5. INTEGRATORS

The integrators that are available in LAMMPS are:

31
i. velocity-Verlet integrator

ii. Brownian dynamics

iii. rigid body integration

iv. energy minimization via conjugate or steepest descent relaxation

3.6.6. ENERGY MINIMIZATION

Atom coordinates are adjusted in LAMMPS so as to perform energy minimization. When one of

the conditions of minimization criteria is satisfied, iterations are terminated. At that position

system remain in local minimum potential energy state. The minimization algorithm is set by

„minstyle‟ command.

3.6.7. OUTPUT

The output of LAMMPS simulation i.e., position and velocity of each atom is written on the

dump file. It writes position and velocity of each and every atom dumped at an interval of time-

steps. The values like temperature, pressure, potential energy of system at some particular

number of iterations is written on the log file.

3.6.8. LAMMPS INPUT SCRIPT

LAMMPS simulation runs by reading the text file (in file). It reads one line at a time and as the

whole program is read, it exits. Each command used causes LAMMPS to take action

accordingly. LAMMPS input script consist of four parts:

(a) initialization

(b) atom definition

(c) interatomic potential

(d) run a simulation

32
CHAPtER4

SIMULATION

PROCEDURE

33
4.1 SIMULATION PROCEDURE OF Cu –Ar HEAT PIPE

Flow chart of simulation procedure is given below

Dimension
Unit
Initialization Atom style

Boundary condition, lattice,

Structure generation creation of atom and simulation
box

EAM (Embeded Atom Method)

Definition of
interatomic potential

Velocity, Ensembles, Time steps,

Thermal equilibration Thermo, Dump output

Calculation of heat flux of cold

,thermal conductivity variation
Thermal conductivity wrt to temperature pressure and
calculation volume

34
4.1.1 PROCEDURE OF SIMULATION

STEP-1 Initialization

In this step we will define the dimension, unit atom style

STEP-2 Structure generation

In this step boundary condition, lattice parameter creation of atom has been define

STEP-3 Definition of interatomic potential

In this step interatomic potential will be define. Here we have use LJ potential

STEP-4 Thermal equilibration

In this step velocity ensembles ,time steps thermo dump output has been define .Here time
step has been taken as 1 fm

STEP-5 Thermal conductivity calculation

Based on obtained heat flux the effective thermal conductivity is calculated by using fourier
law

35
4.2 Input of simulation procedure:

Installation of LAMMPS Software

Creating programme files containing Exe file ,

Potential file

Open the command prompt

Give the path address of directory & programme file

For ex: C:\users\hp>E:enter
C:\users\hp>E:\>cd

Give the exe. File address and press enter to run the
programme For ex:
C:\users\hp\>E:\>cd>Lmp_serial<in.file enter

36
4.3 Output of simulation procedure:

Containing the atomic coordinates

Dump file of the final structure after
simulation and also for thermal
conductivity calculation it contain
flux values temperature, pressure,
total energy

Configuration
Contains coordination value of atom and
file radial distribution function value

Contains thermodynamics data e.g

Log file temperature, pressure ,volume ,heat flux
,kinetic energy ,and total energy

Help to see the final structure (Hot

OVITO end ,cold end and working fluid )

37
4.4 SIMULATION PROCEDURE OF Copper-Water HEAT PIPE

Flow chart of simulation procedure is given below

Dimension
Unit
Initialization Atom style
Atom style

Boundary condition, lattice,

Structure generation creation of atom and simulation
box

COMB
Definition of inter
atomic potential

Velocity, Ensembles, Time steps,

Thermal equilibration Thermo, Dump output

Thermal conductivity Calculation of heat flux of cold

,thermal conductivity variation
calculation

38
4.4.1 PROCEDURE OF SIMULATION

STEP-1 Initialization

In this step we will define the dimension, unit atom style

STEP-2 Structure generation

In this step boundary condition, lattice parameter creation of atom has been define

STEP-3 Definition of interatomic potential

In this step interatomic potential will be define. Here we have use LJ potential

STEP-4 Thermal equilibration

In this step velocity ensembles ,time steps thermo dump output has been define .Here time
step has been taken as 0.1 fm

STEP-5 Thermal conductivity calculation

Based on obtained heat flux the effective thermal conductivity is calculated by using fourier
law

39
4.5 OVITO (Open Visualization Tool)

OVITO is visualization and analysis software used to understand atomistic simulation

models. It is open source software freely available on internet. It is used to do cento-

symmetry parameter analysis, common neighbour analysis coordination number analysis and

radial distribution function.

4.6 HPC (High Performance Computing)

HPC is used to describe computing environment which utilize processing power of cluster of

computers to address complex computational requirements, support application that require

significant processing time or handle significant amount of data. All LAMMPS simulation

codes were run on HPC with model no-HP Compaq LE1902x. It is placed in UG Lab,

computer centre, NIT Durgapur, WB

40
4.7Cu-Ar HEAT PIPE

Molecular dynamics simulations are performed for a liquid Ar attached to solid Copper
surface Fig.1 shows the initial configuration of simulation system, Periodic boundary
conditions are applied in the horizontal y- and z-directions whereas a simple non periodic
fixed boundary condition is assumed in the upper x-direction.

Fig4.1 snapshot of simple heat pipe

The size of simulation box before equilibration 110*50*50 before equilibration and after
equilibration the size is 319*50*50. Solid Ar is attached to hot end. Full system has been
equilibration at 85K
At the left end(x= 0) a solid wall of 40 thickness is placed which consists of FCC unit cell
and on the solid surface aliquid block of atoms is placed which is of 20 thickness and at

41
some distance solid wall of 40 is placed With appropriate initial conditions and at
moderate temperature, surface evaporation takes place when the middle region is filled with
vapour phase.
We assume the Lennard–Jones (LJ) 12–6 model potential as a force field for all the cases of
MD simulations which is of the following form:

where is the particle–particle distance, e is the potential depth andr corresponds to the particle
diameter.

Parameters used for atomic interactions are listed in Table 1 .The parameters of 𝜀𝐶𝑢− 𝑟 and
𝜎𝐶𝑢− 𝑟 were calculated according to the Lorentz-Berthelot mixing rule , namely,

𝜀𝐶𝑢− 𝑟 = √𝜀 𝜀𝑟
𝐶𝑢 *

𝜎𝐶𝑢− 𝑟= (𝜎𝐶𝑢 + 𝜎 𝑟)/2

Argon-Argon Copper-Copper Argon-Copper

ε (eV) 0.52031 0.0103 0.0732

σ (Å) 3.41 2.297 2.8535

During equilibration stage, canonical ensemble (NVT) is employed to both the upper layers
of the Copper atoms and Ar atoms. After equilibration, when dynamics is started the argon
atoms in the liquid layer is subjected to micro canonical (NVE) ensemble where no effect of
external thermostat is involved. Temperature of the surface is being maintained by using
Nose–Hoover [20,21] thermostat which is a simplified formulation of Nose dynamics [22].
This eliminates time scaling and yields trajectories in real time and with evenly spaced time
points.
Once the temperature of the left side Copper surface is increased, the average KE of the
atoms reaches high and as a result collision between the Cu atoms and Ar atoms increases

42
and KE transfer takes place during these collisions which explains the heat transfer
mechanism from Cu surface to liquid Ar.
For all the cases, the first 30,00,00 steps are considered for equilibration of the initial
configuration at a temperature of 85 K which is near the boiling point of Ar at normal
pressure. The equilibration state is ensured from the steady temperature and pressure profile
of the dynamics. The temperature of the Cu molecules (except the bottom layer) is increased
during the next step to the desired higher temperatures using the same thermostat and
simulations are run for longer times to get the temporal evolution of the equilibrated system.
All the simulations are performed using Large-scale Atomic/Molecular Massively Parallel
Simulator (LAMMPS) [15,16]which is an open source code for classical MD simulation
developed by Sandia National Laboratory, USA.

4.8 Cu-Water HEAT PIPE

Molecular dynamics simulations are performed for Cu-water heat pipe surface.Fig.1 shows
the initial configuration of simulation system, Periodic boundary conditions are applied in the
x, y and z-directions

Fig4.2 snapshot of simple heat pipe (Cu-Water)

At the left end (z=0 ) a solid wall of 25.92 thickness is placed which consists of FCC unit
cell and on the solid surface a liquid block of water is placed which is of 21.31 thickness
and at distance 53.92 solid wall of 10.82 is placed With appropriate initial conditions and
at moderate temperature, surface evaporation takes place when the middle region is filled
with vapour phase .The temperature of hot end is maintained at 400K and cold end is
maintained at 298 K

43
We assume the Lennard–Jones (LJ) 12–6 model potential as a force field for all the cases of
MD simulations which is of the following form:

where is the particle–particle distance, is the potential depth and corresponds to the particle
diameter.
During equilibration stage, canonical ensemble (NVT) is employed to both the upper layers
of the Copper atoms and Water atoms. After equilibration, when dynamics is started the
argon atoms in the liquid layer is subjected to micro canonical (NVE) ensemble where no
effect of external thermostat is involved. Temperature of the surface is being maintained by
using Nose–Hoover [20,21] thermostat which is a simplified formulation of Nose dynamics
[22]. This eliminates time scaling and yields trajectories in real time and with evenly spaced
time points.
Once the temperature of the left side Copper surface is increased, the average KE of the
atoms reaches high and as a result collision between the Cu atoms and Ar atoms increases
and KE transfer takes place during these collisions which explains the heat transfer
mechanism from Cu surface to liquid Ar.

For all the cases, the first 10,00,00 steps are considered for equilibration of the initial
configuration at a temperature of 298 K.. The equilibration state is ensured from the steady
temperature and pressure profile of the dynamics. The temperature of the Cu molecules is
increased during the next step to the desired higher temperatures using the same thermostat
and simulations are run for longer times to get the temporal evolution of the equilibrated
system. All the simulations are performed using Large-scale Atomic/Molecular Massively
Parallel Simulator (LAMMPS) [15,16]which is an open source code for classical MD
simulation developed by Sandia National Laboratory, USA.

4.9CALCULATION OF HEAT FLUX

The hot end temperature is. Solid Ar starts melting and it will reach to cold end due to
difference in pressure between hot end cold end . Thermal conductivity will be calculated

44
based on the heat flux obtained at cold end .Based on heat flux the effective thermal
conductivity is calculated based Fourier law given below

̇ = Keff
Where ̇ =heat flux at cold end
Keff=effective thermal conductivity
dT= temperature difference b/w hot and cold end
dx= distance b/w hot and cold end.

CHAPtER5
RESUlts ANdDISCUSSIONs

45
5.1 HEAT PIPE WITH CONSTANT HOT END TEMPERATURE

FRONT VIEW PERSPECTIVE VIEW

(After equilibration)

(After 2000000 steps)

(After 4100000 steps)

Fig5.1 Snapshot of heat pipe with constant hot end temperature at different steps

46
Fig shows the heat pipe with hot end temperature is fixed at 135.From figure it can be seen
that with increase in timestep Ar attached to hot end will start vapourising and it will move
towards cold end and cold end temperature is rising When all the Ar reached to cold end .The
effective thermal conductivity is calculated by using Fourier law
5.1.1 RESULTS

Fig5.2graph of heat pipe with constant hot end temperature

47
The graph shows the variation of hot end and cold end temperature due condensation of Ar at
the cold end the the temperature of cold end is increasing. When all the Ar reached to the
cold end the temperature difference b/w hot and cold become stable .Thermal conductivity is
calculated by using heat flux of cold

Fig5.3 Graph of heat flux of cold end

From above graph it can be seen that with increase in temperature of hot end, The Ar layer
attached to that end starts melting and also the temperature difference b/w hot end and cold
end is reducing.The effective thermal conductivity is calculated by taking takingthe average
obtained eat flux. With decrease in difference b/w hot end and cold ,from Fourier law the
effective thermal conductivity is increasing .

AVERAGE HEAT FLUX EFFECTIVE THERMAL CONDUCTIVITY

(J/ sec) (W/mK)
7.5× 0.03585

48
5.2 HEAT PIPE WITH CONSTANT HEAT FLUX

Fig shows the heat pipe when constant heat flux is supplied to hot end

FRONT VIEW PERSPECTIVE VIEW

(After equilibration 400000 steps)

(After 800000 steps)

(After 1200000 steps)

Fig 5.4 Heat pipe with constant heat flux at different steps

Fig shows the heat pipe when constant heat flux is supplied to hot end. With the application
of heat flux to hot end the temperature of hot end is raising as a result the Ar attached to hot
ends starts vapourising and it will move towards cold which will increases the cold end
temperature

49
5.2.1RESULTS

760ps

71020ps

Fig5.5 Graph of heat pipe with constant heat flux

50
Fig5.6 Graph of heat flux of cold end

The above graph shows the heat pipe when constant heat flux is applied to hot end .From
graph we can see that with the application of constant heat flux the temperature of hot end
increasing continuously and the temperature difference b/w hot end and cold end is also
increasing .Upto 760ps the increase in temperature difference b/w hot and cold end is gradual
,but when all the Ar reached to cold end the increase in difference of temperature is high .The
effective thermal conductivity is calculated by taking taking the average obtained eat flux.
Also from table we can see that with increase in temperature difference b/w hot and cold end
the effective thermal conductivity is reducing.

AVERAGE HEAT FLUX EFFECTIVE THERMAL CONDUCTIVITY

(J/ sec) (W/mK)
4.4× 0.04

51
5.3 COMPARISION OF DIFFERENT RESULT

5.3.1WHEN DIFFERENT THICKNESS OF ARGON IS USED

THICKNESS TEMPERATURE VAPOUR Keff

( ) (HOT END IN K) PRESSURE(Bar)
(W/mK)
10 135 1794 9.98×

20 135 1828.46 0.0064

40 135 2061 0.0489

60 135 2444 0.0580

Table5.1 Different thickness of working fluid

The above table shows the different layers of Ar which is attached to hot end .We can see
from table with increase in thickness of Ar vapour pressure which ultimately increases the
effective thermal conductivity.

5.3.2WHEN DIFFENT TEMPERATURE IS APPLIED TO HOT END

THICKNESS TEMPERATURE VAPOUR Keff

( ) (HOT END IN K) PRESSURE(Bar) (W/mK)
20 115 1837.5 0.05810

52
 20 170 1878.19 0.00134

20 210 1943 0.00838

20 250 2028 0.0183

20 298 2079 0.0106

20 310 2103 0.00604

Table 5.2When different temperature is applied to hot end

From table it can be seen that with increase in temperature of hot end there is a fluctuation of
thermal conductivity.

5.3.3 WHEN DIFFERENT VOLUME HEAT PIPE USED

THICKNESS TEMPERATURE VOLUME VAPOUR Keff

( ) (HOT END IN K) PRESSURE(Bar) (W/mK)
20 135 339*50*50 1375.66 0.0606

20 135 389*50*50 1216.77 0.0595

20 135 439*50*50 1091.61 0.0571

20 135 539*50*50 913 0.0548

Table 5.3 When Different Volume of Heat Pipe is used

From above table it can be concluded that with increase in volume of heat pipe vapour

pressure of the system decreasing and the effective thermal conductivity is also decreasing

gradually.

53
Also if we will not use any working fluid then the thermal conductivity in that case is zero.

Thus we can conclude that with the use of working fluid there will be a great enhancement in

thermal conductivity

5.4 HEAT PIPE WITH COPPER AT BOTH END AND WORKING

FLUID IS WATER

FRONT VIEW PERSPECTIVE VIEW

(Before Equilibration100000Steps )

(After 43000 Steps)

54
 (After 144000 Steps)

(After 206500 Steps)

(After 741000 Steps)

Fig 5.7 heat pipe with water as working medium at different steps

The above fig shows the model of heat pipe with water as a working fluid. The temperature

of hot is Cu is fixed at 400K and cold end is at room temperature .The water attached to hot

55
end start vapourising and it will move towards cold end. By using Fourier law of ,the

effective thermal conductivity is calculated by using the heat flux value obtained

5.4.1 RESULTS

Fig 5.8 Graph of heat pipe with water as working medium (heat flux)

THICKNESS TEMPERATURE VAPOUR Keff

OF WATER (HOT END IN K) PRESSURE(Bar) (W/mK)
( )
21.31 400 29414 3.6

Above results shows the heat pipe with copper at the both end and working fluid is water
.The effective thermal conductivity in this case is 3.6 W/mK which is much higher than the

56
previous case and also this thermal conductivity is higher than the thermal conductivity of
water.It shows that with the use of water as a working fluid there will be greater enhancement
in the thermal conductivity of heat pipe

5.5 COMPARISION OF RESULTS

VARIABLE CONST HOT CONST HEAT WATER AS

END TEMP FLUX WORKING
FLUID

Keff 0.035 .04 3.6

(W/mK)
vapour
pressure(Bar) 1837.5 2061 29414

From above table it can be seen that the thermal conductivity of copper-water heat pipe is
much greater than the Copper-Ar heat pipe. It shows that if we use water as a working
fluid there will be a great enhancement in thermal conductivity.

57
 CHAPtER6
ConcLUSIONs AN ScoPE
FOR

FUTURe woRK

58
6.1 CONCLUSIONS

1. The effective thermal conductivity of heat pipe is depends upon vapour pressure,

temperature, working fluid.

2. With increase in volume of heat pipe thermal conductivity is decreasing and pressure is

also decreasing

3. With increase in thickness of working fluid thermal conductivity is increasing

4. There is no thermal conductivity without any working fluid

5. With the use of water as the working fluid there is great increase in the thermal

conductivity .The obtained thermal conductivity is higher than the thermal conductivity of

water

6.2 FUTURE SCOPE

In recent paper single fluid used as working media in different type of heat pipes. In future
aspect two or more fluids will be using as working media in different heat pipes and
determine the effect of thermal performance of two or more nanofluds i.e.hybrid nanofluds
used on different concentration and different inclination angle of heat pipes. The direction of
the future research on the application of working fluids in heat pipes is mainly. Also, it is also
a hot spot for future research To and the impacts of various operating parameters, such as the
operating temperature, the heat flux and the ambient temperature on the heat transfer
enhancement of nanofluids in heat pipes. To find the effect on overall heat transfer
coefficient and Heat transfer rate with variation in base Fluid of Hybrid Nanofluid in
connection with Heat Pipe. To Find the thermal Performance of heat pipe for different angle
of Inclination. To Find the thermal Resistance of heat pipe for different angle of Inclination,
particle size, various concentration of fluid.
From the exhaustive literature review, it is observed that heat pipe is most developing and
widely used heat transfer device for various applications such as electronics cooling, space
application, medical applications etc. With the advancement in electronics devices, it is very
essential to cool the component effectively and efficiently using less space. Therefore there
seems to be essential to increase the performance of heat pipes using different alternatives.

59
Application of various working fluids in enhancement of performance of heat pipe is the
relative recent and one of the alternative available for this. Yet it requires extensive
experimentations on various types of heat pipes along with various types of working fluids.

60
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