EXPERIMENTAL INVESTIGATION OF 
BENDABLE HEAT PIPES 
 
 
Dhananjay Dilip Odhekar 
 
 
 
A Thesis 
Submitted to 
the Graduate Faculty of 
Auburn University 
in Partial Fulfillment of the 
Requirements for the 
Degree of 
Master of Science 
 
 
 
 
Auburn, Alabama 
August 8, 2005 
EXPERIMENTAL INVESTIGATION OF 
BENDABLE HEAT PIPES 
 
Except where reference is made to the work of others, the work described in this 
thesis is my own or was done in collaboration of my advisory committee. 
This thesis does not include proprietary or classified information. 
 
 
_________________________________________________ 
Dhananjay Dilip Odhekar 
 
 
Certificate of Approval: 
 
 
 
 
_____________________________   _____________________________ 
Daniel W. Mackowski    Daniel K. Harris, Chair 
Associate Professor     Associate Professor 
Mechanical Engineering    Mechanical Engineering 
 
 
 
 
_____________________________   _____________________________ 
Jay Khodadadi      Stephen L. McFarland 
Professor      Acting Dean 
Mechanical Engineering    Graduate School 
 
 iii 
EXPERIMENTAL INVESTIGATION OF 
BENDABLE HEAT PIPES 
 
Dhananjay Dilip Odhekar  
 
 
Permission is granted to Auburn University to make copies of this thesis at its discretion, 
upon request of individuals or institutions and at their expense. 
The author reserves all publication rights. 
 
 
       _____________________________ 
       Signature of Author 
 
 
       _____________________________ 
       Date 
 
 
 
Copy sent to: 
 
Name       Date
 
 iv 
VITA 
Dhananjay Dilip Odhekar, son of Dilip K. Odhekar and Suniti D. Odhekar, was 
born on November 9, 1977 in Dhule, Maharashtra, India. In August 1995, he entered the 
K. K. Wagh College of Engineering at University of Pune, Maharashtra, India and earned 
the degree of Bachelor of Mechanical Engineering in June 1999 with first class. He 
worked for Mahindra Tractors Limited, India as Trainee Engineer in manufacturing for a 
period of one year. Dhananjay worked for Syndicate Services, Nasik, India as an 
Assistant Engineer in 2001. He then entered the Graduate School at Auburn University in 
August 2002. 
 
 v 
THESIS ABSTRACT 
EXPERIMENTAL INVESTIGATION OF 
BENDABLE HEAT PIPES 
Dhananjay Dilip Odhekar 
Master of Science, August 8, 2005 
(B.E. Mech, K.K.W.C.O.E., University of Pune, 1999) 
126 Typed Pages 
Directed by Dr. Daniel K. Harris 
Heat pipes are highly conductive heat transfer devices. They use the latent heat of 
the working fluid for efficient heat transfer over a very small temperature drop. They 
have been a subject of numerous studies since the early 1950s and are commercially 
available in a variety of forms. This thesis is an investigation of the effect bending has on 
the performance of heat pipes. Flexible and pre-bent heat pipes have been studied and 
successfully demonstrated in the past. Bendable heat pipes, which can be bended after 
fabrication as needed are a novel device developed during this study. The effect of 
bending on temperature drop, performance and performance limits was investigated. The 
heat pipes used for testing were made using oxygen free copper for the container and 
water as the working fluid. The wick was made from sintered copper felt and provided 
the post fabrication bendability feature of these heat pipes. The concept of copper 
equivalence to compare disparate data is also developed and explained. It is used to 
benchmark the test data against copper conductivity. 
 vi 
ACKNOWLEDGEMENTS 
I would like to acknowledge the Dana Corporation contract at Auburn University 
through Auburn Thermal Management Laboratory for providing the funding. 
I would like to thank my advisor, Dr. Daniel K. Harris for his guidance and 
suggestions throughout this research. I would also like to thank Bhavin Vadgama for his 
assistance in designing and fabricating heat pipes. 
Most importantly, I am sincerely grateful to my parents. The unselfish support 
they provided so that I could go back to school will always encourage me to walk in their 
footsteps. 
 vii 
Style manual or journal used:   IEEE
Computer software used:   Microsoft Office System 2003
 viii 
TABLE OF CONTENTS 
LIST OF FIGURES ........................................................................................................... xi 
LIST OF TABLES........................................................................................................... xiv 
1 HEAT PIPES ................................................................................................................ 1 
1.1 Introduction............................................................................................................ 1 
1.2 Heat Pipe................................................................................................................ 2 
1.3 Construction........................................................................................................... 2 
1.4 Operation ............................................................................................................... 3 
1.5 Operating Limits.................................................................................................... 7 
1.5.1 Capillary Limit............................................................................................ 7 
1.5.2 Sonic Limit.................................................................................................. 8 
1.5.3 Boiling Limit............................................................................................... 9 
1.5.4 Entrainment Limit....................................................................................... 9 
1.5.5 Viscous Limit.............................................................................................. 9 
1.5.6 Condenser Limit........................................................................................ 10 
2 BACKGROUND ........................................................................................................ 12 
2.1 Scope of Bendable Heat Pipe .............................................................................. 12 
2.2 Review ................................................................................................................. 13 
3 FACTORS AFFECTING DESIGN AND PERFORMANCE.................................... 32 
3.1 Introduction.......................................................................................................... 32 
3.2 Working Fluid...................................................................................................... 32 
3.2.1 Compatibility with Wick and Container................................................... 34 
3.2.2 Thermal Stability ...................................................................................... 34 
3.2.3 Wetting of Wick and Container ................................................................ 34 
3.2.4 High Latent Heat and Thermal Conductivity............................................ 35 
3.3 Container.............................................................................................................. 35 
 ix 
3.4 Capillary Structure............................................................................................... 36 
3.4.1 Homogeneous Wicks ................................................................................ 36 
3.4.2 Composite Wicks...................................................................................... 37 
4 TESTING AND PERFORMANCE EVALUATION................................................. 39 
4.1 Performance Evaluation....................................................................................... 39 
4.1.1 Testing Procedure ..................................................................................... 40 
4.1.2 Conductance.............................................................................................. 42 
4.2 Copper Equivalence............................................................................................. 42 
4.2.1 Measurement Errors and Losses ............................................................... 44 
4.2.2 Parasitic Losses......................................................................................... 45 
4.2.3 Benchmarks............................................................................................... 46 
4.2.4 Concept of Copper Equivalence ............................................................... 48 
4.2.5 Why Copper Equivalence Works?............................................................ 49 
4.2.6 Application................................................................................................ 50 
5 BENDABLE HEAT PIPES ........................................................................................ 53 
5.1 Introduction.......................................................................................................... 53 
5.2 Bendable Wicks................................................................................................... 53 
5.3 Performance Limit............................................................................................... 57 
5.3.1 Vapor Pressure Drop................................................................................. 57 
5.3.2 Other Pressure Drops ................................................................................ 62 
5.3.3 Capillary Limit.......................................................................................... 63 
5.3.4 Other Limits.............................................................................................. 66 
5.3.5 Bend Loss.................................................................................................. 66 
5.3.5.1 Bend Loss Coefficient for Vapor Flow ....................................... 68 
5.3.6 Capillary Limit for Bended Heat Pipe ...................................................... 69 
5.4 Testing and Evaluation ........................................................................................ 71 
5.4.1 Specifications of HP01 ............................................................................. 73 
 x 
5.4.2 HP01 Bending Test Results ...................................................................... 73 
5.4.3 Capillary Limits for HP01 ........................................................................ 79 
5.4.4 Specifications of HP02 ............................................................................. 84 
5.4.5 HP02 Bending Test Results ...................................................................... 84 
5.4.6 Capillary Limits for HP02 ........................................................................ 94 
5.5 Results................................................................................................................ 103 
5.5.1 Possible Capillary Limit ......................................................................... 104 
5.5.2 Boiling Limit Encountered ..................................................................... 104 
5.5.3 Condenser Limit...................................................................................... 105 
5.5.4 Bending Issues ........................................................................................ 105 
6 DISCUSSION........................................................................................................... 106 
6.1 Conclusion ......................................................................................................... 106 
6.2 Future Work....................................................................................................... 107 
BIBLIOGRAPHY........................................................................................................... 109 
 
 xi 
LIST OF FIGURES 
Figure 1.1: Schematic of construction and operation of a typical heat pipe....................... 5 
Figure 1.2: Pressure variation along a heat pipe................................................................. 6 
Figure 1.3: Operating limits for a heat pipe...................................................................... 11 
Figure 2.1: Flexible cryogenic heat pipe [10]................................................................... 16 
Figure 2.2: Heat pipe bends [16]....................................................................................... 20 
Figure 2.3: ?T between evaporator exit and end of condenser versus bend angle of 
heat pipe [26] .................................................................................................................... 23 
Figure 3.1: Homogeneous wicks....................................................................................... 38 
Figure 3.2: Composite wicks ............................................................................................ 38 
Figure 4.1: Heat pipe test setup for conductance measurement........................................ 41 
Figure 4.2: Steady state temperature curves during testing .............................................. 43 
Figure 4.3: Heat pipe conductance against input power applied ...................................... 43 
Figure 4.4: Estimation of parasitic losses ......................................................................... 47 
Figure 4.5: Conductance corrected to account for parasitic losses................................... 47 
Figure 4.6: Schematic of heater blocks used .................................................................... 51 
Figure 4.7: Comparison of copper rod data on heater blocks........................................... 52 
Figure 5.1: Wick separation near heat pipe wall due to bending...................................... 55 
Figure 5.2: Bending effects on heat pipe wall and wick................................................... 56 
Figure 5.3: Heat Pipe Nomenclature................................................................................. 60 
Figure 5.4: The correction function a(z) [38] ................................................................... 61 
Figure 5.5: Hydrostatic pressure drops in a bended heat pipe .......................................... 65 
Figure 5.6: Resistance to flow with Dean number............................................................ 70 
Figure 5.7: Schematic of bending configurations for HP01 ............................................. 72 
Figure 5.8: Test results for HP01 in straight horizontal position...................................... 75 
Figure 5.9: Test results for HP01 in straight vertical gravity assist position.................... 75 
Figure 5.10: Test results for HP01 in 15? bended vertical gravity assist position............ 76 
 xii 
Figure 5.11: HP01 Test results for HP01 in 30? bended vertical gravity assist 
position.............................................................................................................................. 76 
Figure 5.12: Test results for HP01 in 45? bended vertical gravity assist position............ 77 
Figure 5.13: Test results for HP01 in 60? bended vertical gravity assist position............ 77 
Figure 5.14: Test results for HP01 in 90? bended vertical gravity assist position............ 78 
Figure 5.15: ?T across HP01 for various bend angles ..................................................... 78 
Figure 5.16: Capillary limit for HP01 in straight horizontal orientation .......................... 80 
Figure 5.17: Capillary limit for HP01 in straight vertical orientation .............................. 80 
Figure 5.18: Capillary limit for HP01 in 15? bended vertical orientation ........................ 81 
Figure 5.19: Capillary limit for HP01 in 30? bended vertical orientation ........................ 81 
Figure 5.20: Capillary limit for HP01 in 45? bended vertical orientation ........................ 82 
Figure 5.21: Capillary limit for HP01 in 60? bended vertical orientation ........................ 82 
Figure 5.22: Capillary limit for HP01 in 90? bended vertical orientation ........................ 83 
Figure 5.23: Effect of bending angle on capillary limit for HP01.................................... 83 
Figure 5.24: Test results for HP02 in straight horizontal orientation ............................... 86 
Figure 5.25: Test results for HP02 in straight vertical orientation ................................... 86 
Figure 5.26: Test results for HP02 in 15? bended horizontal orientation ......................... 87 
Figure 5.27: Test results for HP02 in 15? bended vertical orientation ............................. 87 
Figure 5.28: Test results for HP02 in 30? bended horizontal orientation ......................... 88 
Figure 5.29: Test results for HP02 in 30? bended vertical orientation ............................. 88 
Figure 5.30: Test results for HP02 in 45? bended horizontal orientation ......................... 89 
Figure 5.31: Test results for HP02 in 45? bended vertical orientation ............................. 89 
Figure 5.32: Test results for HP02 in 60? bended horizontal orientation ......................... 90 
Figure 5.33: Test results for HP02 in 60? bended vertical orientation ............................. 90 
Figure 5.34: Test results for HP02 in 90? bended horizontal orientation ......................... 91 
Figure 5.35: Test results for HP02 in 90? bended vertical orientation ............................. 91 
Figure 5.36: ?T across HP02 for various bend angles in horizontal orientation.............. 92 
Figure 5.37: ?T across HP02 for various bend angles in vertical orientation.................. 92 
 xiii 
Figure 5.38: Evaporator of HP02 could not attain steady state at 40W power input in 
90? bended vertical orientation ......................................................................................... 93 
Figure 5.39: Heater of HP02 could not attain steady state at 40W power input in 90? 
bended vertical orientation................................................................................................ 93 
Figure 5.40: Capillary limit for HP02 in straight horizontal orientation .......................... 95 
Figure 5.41: Capillary limit for HP02 in straight vertical orientation .............................. 95 
Figure 5.42: Capillary limit for HP02 in 15? bended horizontal orientation.................... 96 
Figure 5.43: Capillary limit for HP02 in 15? bended vertical orientation ........................ 96 
Figure 5.44: Capillary limit for HP02 in 30? bended horizontal orientation.................... 97 
Figure 5.45: Capillary limit for HP02 in 30? bended vertical orientation ........................ 97 
Figure 5.46: Capillary limit for HP02 in 45? bended horizontal orientation.................... 98 
Figure 5.47: Capillary limit for HP02 in 45? bended vertical orientation ........................ 98 
Figure 5.48: Capillary limit for HP02 in 60? bended horizontal orientation.................... 99 
Figure 5.49: Capillary limit for HP02 in 60? bended vertical orientation ........................ 99 
Figure 5.50: Capillary limit for HP02 in 90? bended horizontal orientation.................. 100 
Figure 5.51: Capillary limit for HP02 in 90? bended vertical orientation ...................... 100 
Figure 5.52: Effect of bending angle on capillary limit for HP02 in vertical 
orientation ....................................................................................................................... 101 
 
 
 xiv 
LIST OF TABLES 
Table 2.1: Summary of published work on flexible heat pipes ........................................ 30 
Table 2.2: Summary of published work on flexible heat pipes ........................................ 31 
Table 3.1: Thermo physical properties of working fluids used at AuTherMML [3]........ 33 
Table 4.1: Conductance values of copper 101 rod............................................................ 52 
Table 5.1: Effect of bending angle on capillary limit for HP02 in horizontal 
orientation ....................................................................................................................... 102 
 
 
1 
CHAPTER 1 
HEAT PIPES 
1.1 Introduction 
Heat transport has been one of the most difficult and inefficient tasks in thermal 
management. It often results in costly heat transfer losses and reduced overall 
efficiencies. Performance of mechanical and electronic components inside automobiles is 
now governed by the efficiency of cooling system [1]. Heat transfer by heat pipes is one 
of the fastest and most efficient methods for thermal management. In automobiles, the 
stress of modern design is on reducing bulk weight and volume of all components. This 
results in densely packaged components including drive trains and electronic 
components. The heat pipe is a promising technology that has received significant 
research interest since early 1950s. The early studies mostly concentrated on heat pipes 
used in straight configurations. But many practical designs demand heat pipes in 
contorted shapes [2]. This thesis investigates the feasibility of bendable heat pipes. These 
heat pipes can be bent after fabrication without affecting their performance. 
 
2 
1.2 Heat Pipe 
The heat pipe concept was initially investigated by R.S. Gaugler in 1942 [3]. The 
remarkable properties of the heat pipe became appreciated and serious development work 
took place after its independent invention by G. M. Grover in the early 1960?s [3]. 
A heat pipe typically has high conductance, usually an order of magnitude higher 
than a metal conductor of similar specifications. It transfers heat from a source to a sink 
by means of cyclic evaporation and condensation of a working fluid. It uses the latent 
heat of vaporization of the working fluid to transfer heat. The heat pipe does not require 
any external energy to function and it has no moving parts. For the same heat load, a heat 
pipe has a very low temperature drop due to its high efficiency. However, unlike a metal 
conductor a heat pipe has a limit on the amount of heat it can transfer. 
1.3 Construction 
The basic heat pipe concept can be demonstrated by a simple tubular metal casing 
with a wick covering the inner surface (Figure 1.1). The wick is made of different 
materials and has been one of the most investigated aspects of heat pipes. It is usually 
made of a porous material. A grooved structure can also be used. A working fluid is 
vacuum-sealed in a pre-determined quantity [4]. The working fluid inside can be any 
compound that has good wetting characteristics on the wick and is selected on the basis 
of working temperatures of the heat pipe. If kinetic pressure losses of the vapor and 
gravitation head losses are neglected the properties of the working fluid can be combined 
to form a figure of merit M. The merit number determines the maximum possible heat 
transport using the heat pipe. 
 
l
ll
L
M
?
??
=  
1.1
where 
l
?  = density of working fluid in liquid phase 
l
?  = surface tension of the working fluid 
l
?  = dynamic viscosity of working fluid in liquid phase 
L  = length of the heat pipe 
1.4 Operation 
A heat pipe is broadly divided in three sections namely, evaporator, adiabatic and 
condenser. A typical heat pipe as shown in Figure 1.1 has one evaporator section that 
takes heat from a source. The heat absorbed in the evaporator causes change of phase of 
the working fluid from liquid to vapor. The increased vapor pressure in the evaporator 
causes the vapor to exit from the evaporator section and travel through the adiabatic 
section. Traveling through the adiabatic section the vapor reaches the condenser region 
where condensation rejects the latent heat of the fluid to the sink. The condensed liquid is 
pumped back against an adverse pressure gradient to the evaporator by a combination of 
the capillary pumping action and/or bulk forces. This fluid circuit is repeated during the 
normal operation of the heat pipe and can continue as long as there is sufficient vapor 
pressure and capillary pressure to support its operation.  
3 
4 
At the evaporator end the liquid recedes into the wick pores and hence the menisci 
in the pores at the vapor interface are highly curved. Whereas the liquid menisci at vapor 
interface in the condenser end are almost flat. This difference in the interface curvature of 
the menisci at the vapor interface coupled with the surface tension of the working fluid 
causes a capillary pressure gradient at the liquid-vapor interface along the length of the 
pipe. This capillary pressure gradient pumps the working fluid against various pressure 
losses such as friction, inertia and against bulk body forces [3]. This axial variation of 
pressure is illustrated in Figure 1.2. 
Container 
Source 
Liquid 
5 
 
Figure 1.1: Schematic of construction and operation of a typical heat pipe 
Evaporator 
Section 
Condenser 
Section
Adiabatic 
Section
Vapor 
Sink
Wick 
Vapor 
Vapor Pressure 
Drop 
Pressure 
Capillary 
Pressure 
Difference 
Liquid Pressure 
Drop 
Liquid 
Evaporator 
Adiabatic  Condenser  
 
Figure 1.2: Pressure variation along a heat pipe 
6 
7 
1.5 Operating Limits 
As with any other system, the performance and operation of a heat pipe is limited 
by various parameters. Physical phenomena that might limit heat transport in heat pipes 
include capillary forces, choked flow, interfacial shear and incipient boiling. The heat 
transfer limitations depend on the size and shape of the pipe, working fluid, wick 
parameters, and operating temperature. The lowest limit among these constraints defines 
the maximum heat transport limitation of a heat pipe at a given temperature [5]. 
1.5.1 Capillary Limit 
The difference in the capillary pressure across the liquid-vapor interfaces governs 
the operation of the heat pipes. This is one of the most important parameters that affect 
the performance and operation of a heat pipe. It is usually a major limiting factor in the 
working of low-temperature heat pipes. The capillary limit is encountered when the 
capillary pressure is not sufficient to pump the liquid back to evaporator causing the dry 
out of the wick of the evaporator end. The physical structure of the wick is one of the 
most important reasons for this limit and the type of working fluid also affects it. Once 
limit is encountered, any further increase in heat input may cause serious damage to the 
heat pipe [5]. 
When a heat pipe is operating in steady state, there is a continuous flow of vapor 
from the evaporator section to the condenser section and liquid from the condenser 
section to the evaporator section through the wick. These flows are possible because of 
the vapor pressure gradient (?p
v
) and the liquid pressure gradient (?p
l
)  along the length 
of the heat pipe (Figure 1.2). There exists a capillary pressure due to the menisci formed 
at the liquid-vapor interface; this capillary pressure (?p
cap,max
) is necessary for the flow of 
liquid back to the evaporator. In addition, there are pressure gradients due to phase 
change taking place at the evaporator (?p
e,phase
) and the condenser (?p
c,phase
) ends and due 
to gravity (?p
g
). The capillary limit is expressed as, 
 
gphasecphaseevlmaxcap
pppppp ?+?+?+?+???
,,,
 
1.2
For the heat pipe to work normally, the capillary pressure should be greater than 
all the pressure gradients across the liquid-vapor path. 
1.5.2 Sonic Limit 
The evaporator and condenser sections of the heat pipe undergo addition and 
removal of mass due to the circulation of the working fluid. They act like a nozzle where 
vapor flows from the adiabatic section into or out of the end sections. The converging-
diverging nozzle like nature of the vapor flow path imposes a choking flow condition on 
the vapor velocity. The velocity at a choke point cannot be greater than the local speed of 
sound. This is called the sonic limit and the heat transfer can now only increase by 
increasing the operating temperature of the heat pipe. Although, the operation of a heat 
pipe under such condition causes a substantial temperature drop across the heat pipe, it is 
not considered a serious risk [5]. 
8 
9 
1.5.3 Boiling Limit 
A typical cylindrical heat pipe receives heat at the evaporator end where it is 
transferred to the working fluid radially. When the input flux is sufficient, nucleation 
sites are formed inside the wick and bubbles are trapped in the wick, blocking liquid 
return that results in evaporator dry out [6].  As compared to other heat pipe limits, 
boiling limit is a radial flux constraint and not an axial flux constraint. For liquid-metal 
heat pipes, the boiling limit is not very common [5]. 
1.5.4 Entrainment Limit 
As liquid and vapor move in opposite directions, the vapor exerts a shearing force 
on the liquid at the liquid-vapor interface. If this shear force exceeds the surface tension 
of the liquid, liquid droplets are entrained into the vapor flow and are carried towards the 
condenser section. The magnitude of this shear force depends on the thermo-physical 
properties of the vapor and its velocity and if it becomes large enough, it causes dry out 
of the evaporator [3,5]. 
1.5.5 Viscous Limit 
At low temperatures or low vapor densities, the viscosity of the vapor flow may 
be dominant as the flow progresses towards the condenser end. If the vapor pressure in 
the condenser is very low then the heat transfer under such a condition is limited. This 
usually occurs during the startup phase of a heat pipe [5,7]. 
10 
1.5.6 Condenser Limit 
For proper working of a heat pipe it is necessary that the heat is removed from the 
condenser end at the same rate as it is being added at the evaporator end. If non-
condensable gases are accumulated at the condenser end, they reduce the working length 
of the condenser end, limiting the heat removing capacity of the condenser. This limit 
increases the possibility of capillary limit [5]. 
Condenser Limit 
11 
 
Figure 1.3: Operating limits for a heat pipe 
 
Heat Flux 
Temperature 
Boiling Limit 
Entrainment Limit 
Capillary Limit 
Sonic Limit 
12 
CHAPTER 2 
BACKGROUND 
2.1 Scope of Bendable Heat Pipe 
A capillary pumped heat pipe is one of the most efficient and yet very simple 
methods of heat transfer. A typical heat pipe is a cylindrical straight pipe which is easy to 
fabricate and has a low cost of production. But in practice there is seldom any space 
available that can accommodate a straight heat pipe. The size of a heat pipe usually 
depends on the heat load it is subjected to. The lack of enough space demands a heat pipe 
that can be flexed to fit in available pockets of space in a system. Also it allows for 
compact and flexible overall system design. 
Typical applications of heat pipes include desktop and laptop computers, 
transmission and engine cooling systems in automobiles. Other electronic components 
like circuit boards, transformers and power supplies are also common applications [7]. 
The ever-reducing size of computers, electronic instruments and automobiles puts severe 
restrictions on the physical dimensions of heat pipes. Even when a heat pipe is not 
required in contorted configurations, the flexibility allows for misalignment between 
source and sink due to operational vibrations or oscillations.  
13 
As with the rest of the heat pipes, flexible heat pipes have received regular 
attention over the years and not surprisingly many of the problems were put forth by the 
aerospace industry. A thorough literature review is presented to summarize the previous 
work done in this area. Also, since the focus of this study is bent heat pipes, only portions 
pertaining to these types of heat pipes are covered. 
2.2 Review 
A flexible heat pipe was developed and built by F. E. Bliss, E. G. Clark and B. 
Stein to analyze its operating characteristics for varying degrees of bend and under 
vibration in an unbent mode [8]. The purpose of this study was to design a flexible heat 
pipe capable of being bent or flexed during its operation allowing efficient heat transfer 
between an oscillating heat source and a stationary sink. The heat pipe was built using a 
rigid evaporator and condenser sections made from thick drawn copper tubing. A flexible 
adiabatic section fabricated from a seamless brass bellows connected them. A wick made 
of four layers of 150 mesh type 304 stainless steel screen, was held against the inside 
wall using a stainless steel coil spring. It was tested for bends of 0?, 45? and 90? during 
horizontal operation and also at inclined orientations. The authors noted that the tests for 
various bends demonstrated an increase in the maximum heat flux associated with wick 
dry out after each flexing. It was speculated that this was due to the changes in the 
capillary passage between the layers of screen and wall as the heat pipe was flexed. 
One interesting aspect of this study was the internal fins present in the condenser 
section. It was noted that since the fins significantly reduced the difference between the 
vapor temperature and the outside temperature of the condenser wall, it had greatly 
14 
improved the operating efficiency of the heat pipe. The study concluded that the degree 
of bending had a minimal effect on the working of the heat pipe and a flexible heat pipe 
is a feasible idea. 
Basiulis and Hummel investigated heat pipe techniques and their applications for 
electronic component cooling. The various techniques considered were heat pipes, cold 
plates, gas buffered heat pipes and unidirectional heat pipes. The flexible heat pipes 
provided relative motion between the heat source and heat sink [7]. This publication steps 
through the design process starting with the selection of a working fluid. The authors 
listed various applications for each type of heat pipes studied. 
F. Edelstein designed and fabricated a variable conductance heat pipe radiator 
capable of passively controlling Freon-21 fluid loop temperatures under varying loads 
[9]. It was made from six grooved heat pipes attached to an aluminum panel. The heat 
pipes had a flexible section that could bend up to 90?. Tests were carried out with radiator 
loads up to 800 W. 
Saaski and Wright described a proof of concept for a flexible cryogenic heat pipe 
designed for space operations [10]. This heat pipe was meant for transmitting parasitic 
heat and generated heat from an infrared sensor on a satellite. In many satellite systems, a 
U shaped configuration of heat pipes is needed. A 20 W flexible heat pipe designed for 
operations at 100 K was described.  The axial wick structure needed to be considerably 
flexible to allow bending. A multiple artery structure developed by McDonnell Douglas 
Astronautics Corporation (MDAC) was chosen due to its considerable capacity for 
bending. The artery was composed of a tightly wrapped bundle of many fine tubes, each 
15 
of which functions independently as an artery to assure redundancy of fluid transport. 
The composite tube structure allowed for flexibility because each small tube could move 
independently to some degree. The evaporator and condenser were rigid sections 
connected by an adiabatic section made from bellows as shown in Figure 2.1.Thermal 
performance tests were carried out with R-21 at 293 K and methane at 100 K with the 
heat pipe in horizontal orientation and U shape configuration. The test results for both 
straight and bent mode were compared and it was concluded that there was no significant 
effect due to bending. 
A comprehensive test program was executed to determine the physical and 
thermal performance of two flexible cryogenic heat pipes to provide an efficient and 
flexible thermal link between a detector and a space radiator by Wright et al. at Rockwell 
International Corp., Space Division [11]. To determine the optimum geometry and 
materials for the container and the wick, parametric studies were performed and the 100 ? 
200 K pipe was designed with methane and ethane as the working fluid, with nitrogen 
and oxygen for the 15 ? 100 K pipe. The wick selected was a multi wrap composite, 
which consisted of a spirally wrapped coarse mesh screen surrounded by a fine mesh 
outer wrap. V-groove screw threads were machined into the evaporator and condenser 
whereas a braided flexible bellows made from stainless steel was used for the adiabatic 
section. This flexible section together with the spiral multi wrap wick demonstrated good 
flexibility and compatibility with methane as the working fluid. The authors concluded 
that overall this configuration worked well as a highly flexible link between the source 
and the sink and had good potential for high power transport scenarios. 
 
Evaporator Flexible section Condenser 
 Figure 2.1: Flexible cryogenic heat pipe [10] 
16 
17 
H. Koch, H. Kreeb and M. Perdu developed a modular axial grooved heat pipe 
system for an operating temperature range of 100 ? 400 K intended for typical space 
applications [12]. Various tests were performed to evaluate the performance as a function 
of temperature or inclination angle, start up, operating life, working fluid and of bended 
heat pipes. 
Munzel et al. conducted an experiment for the European Space Research and 
Technology that consisted of two bendable artery heat pipes which were flown aboard a 
rocket Centre as a part of the International Heat Pipe Experiment [13]. It consisted of two 
aluminum heat pipes having a length of about 90 cm with an outer diameter of 0.7cm. 
The wick and artery systems were made from 160 mesh stainless steel screen and 
ammonia was the intended working fluid. The two arteries were positioned to lie in the 
same diametric plane so that the pipes could be bent with no reduction in the heat 
transport capability. The experiment was supposed to test two heat pipes; one straight and 
one bent into a z-shape. The bent heat pipe was later replaced with a straight one due to 
priming problems. 
There is growing interest in heat pipe thermal diodes and thermal switches for 
space applications. A thermal diode can protect electronic components from overheating 
during mission critical periods like pre launch operations, vehicle maneuvers and reentry 
into the earth?s atmosphere [15]. Similarly, a thermal switch can be used for transport of 
heat from a source to one of several heat sinks depending on the operating conditions. 
Development work was undertaken for near room temperature applications of a thermal 
diode for spacelab by M. Groll et al. The focus of this study was to predict the transient 
shutdown of the thermal diode using a mathematical model and experimental results, 
18 
both of which were in good agreement. It was noted that bendability is no serious 
constraint for all three designs, though in the case of complex artery structures, e.g. 
modular artery with 4 or 5 webs, the bend radius has to be relatively large to avoid 
performance degradations. 
Three variable conductance heat pipes were fabricated by M. E. Peeples and L. D. 
Calhoun in order to investigate the effect of tight radius bends in the adiabatic section on 
the heat pipe performance [16]. Analytical studies were conducted to evaluate the 
geometry and performance requirements of candidate heat pipe designs. The heat pipes 
were bent in the adiabatic section to make a J or L shape with a very small bend radius. 
There was a probability that capillary pumping could be reduced due to deformation of 
internal structure in the bent area, resulting in performance degradation. Two pipes were 
fabricated from a thin wall stainless steel with a multi-tube central artery and a wall 
screen wick. Freon 21 was the working fluid. The third pipe was made of aluminum with 
an axially grooved wick and ammonia was used as the working fluid. All the pipes were 
bent using a conventional pipe bender and it was found using a radiograph image (Figure 
2.2-a), that in the bent area the deformation of the artery lowered the permeability of 
artery, effectively reducing the heat transfer capacity of the pipe due to inadequate flow 
of condensate from condenser to evaporator. The corrugations in the inner bend surfaces 
of the heat pipe tube, and local separation of the wall wick, caused unpredictable voids 
and it also made it difficult to determine the exact charge of the working fluid required. 
In order to circumvent these problems, the heat pipes were fabricated in such a way that 
the heat pipe tube was bent before inserting the wick structure and also wick in the bent 
19 
area was removed to minimize cavities caused. The radiograph in Figure 2.2-b clearly 
shows the improvement in the fabrication quality of the heat pipes. 
A bendable gas controlled variable conductance heat pipe was developed and 
made entirely from stainless steel with ammonia as working fluid and a homogeneous 
wick as capillary system [17]. Designed by Mathieu et al., it presented an excellent 
potential for high performance because of its heat transport capability of 100 W through a 
1 cm diameter tube. There were performance requirements to transport a minimum of 100 
Wm, in zero gravity and in the presence of control gas (variable conductance) and, the 
heat pipe should not lose any performance when curved in U-shape with a radius of 
curvature of 10 cm. 
Meier et al. designed a heat pipe for use in a space reactor where it was required 
to bend around the reactor core in two approximately 90? bends on a 180 mm radius and 
have design lifetime of 7 years [18]. Because of this lifetime requirement and working 
temperature of 1400 K, molybdenum was the material chosen for the container with 
sodium as the compatible working fluid. It employed a non-concentric screen annular 
sintered wick. Before fabrication of the heat pipe, a series of bending experiments were 
carried out to finalize proper bending procedure and temperature so that no cracks or 
breaks were generated. A bending test when conducted on an unsupported wick at 353 K 
that showed the compression side of the bent wick was severely buckled. The buckles 
caused a reduction of 17% in the vapor flow area and an increase in pore size was also 
observed at the sharp corners, which would lead to significant reduction in performance. 
The conclusion was that bending on an unsupported wick would not produce satisfactory 
 
(a) Conventional wick structure 
 
(b) Modified wick structure 
Figure 2.2: Heat pipe bends [16] 
20 
21 
results. Another bending test with a steel tube mandrel to prevent buckling of the wick 
was performed, but large tears were generated on the tension side. Finally, a stainless 
steel heat pipe was completely filled with sodium at 1070 K. When the pipe was bent at 
365 K (highest attainable temperature to provide required ductility for molybdenum but 
still low enough to keep the sodium mandrel in solid state), the results were successful 
with no tears  in the tension side and very little buckling on the compression side with a 
very minute change in porosity. 
D. M. Ernst in a report to NASA JPL for a heat pipe heat rejection system and 
demonstration model for the nuclear electric propulsion (NEP) spacecraft evaluated and 
redesigned prototype heat pipe components, and then further fabricated and tested them 
[19]. The evaluation demonstrated the validity of several complicated geometries and 
wick structures including bends in the heat pipe. Two types of heat pipes with 30? bends 
at each end of the adiabatic section were tested for several wick designs. A heat pipe with 
four wraps of 325 mesh wick was found as a good design with respect to performance 
and mass. It transferred 3800 W over a temperature drop of 117.9?C. 
Merrigan et al. demonstrated in a 1984 publication that flexible sodium/stainless 
steel heat pipes can be fabricated and operated at temperatures up to 1100 K with an axial 
heat flux of 1950 W/cm
2
 [20]. The relevance of this publication to the work in this thesis 
is the study of the effect of bend angle on the heat pipe temperature distribution. There 
was a requirement for high power, flexible heat pipe capable of bending through angles 
of up to 180? and working temperatures of both cold and high temperatures. Therefore, as 
a demonstration flexible heat pipe employing sodium as working fluid and using stainless 
steel wick and tube was fabricated and tested. ?This device has been flexed repeatedly 
22 
through angles of 180?, both at room temperature with the sodium working fluid frozen 
and at temperatures to 1000 K while radiating heat to a room temperature environment?. 
A 100 mesh stainless steel screen wrapped in 3 layers in alternating directions was used 
to make the wick. The adiabatic section was made from a standard high vacuum flexible 
line section. The heat pipe was tested at a temperature of 1000 K in the horizontal 
orientation. Then the condenser end was elevated upward through an arc up to a bend of 
180? in the vertical plane. The heat pipe operation was visually verified during this 
bending experiment.  
Later to determine the effect of bending on the performance, the heat pipe was 
operated in the horizontal position and tested in three positions of 0?, 90? and 180?. 
During testing axial temperatures were recorded against input power to the heat pipe. 
Figure 2.3 shows the results of these experiments. While the data indicates a significant 
increase in axial temperature drop, there was no loss of heat pipe function due to bending 
even under test loads up to 1950 W/cm
2
. Repeated startup tests were conducted from 
below the freezing point of sodium (working fluid) with no apparent effect due to 
bending. The authors concluded that this heat pipe could be bent up to 180? even when 
under load. 
R. M. Shaubach and N. J. Gernert worked on a project to develop and 
demonstrate flexible heat pipes for transport of heat from stationary to translating 
sections of spacecraft [21]. Previous flexible heat pipes concepts employed flexible 
bellows with a screen wick that allowed bending. Such heat pipes are typically low power 
devices due to the high flow resistance of the screen wick structure. 
1550 W 
 
 
 
2000 W 
0              30              60              90             120            150            180          210 
                                          Bend Angle (Deg) 
  Delta 
Temp
eratu
r
e 
(K) 
0
10
20
30
40
50
60
 
Figure 2.3: ?T between evaporator exit and end of condenser versus bend angle of heat 
pipe [26] 
 
23 
24 
Flexible heat pipes with high power capacity are made possible by using flexible 
screen arteries, which can be made from several different alloys and mesh sizes. These 
flexible screen arteries are integrated with high performance circumferential distribution 
wicks in an envelope that is flexible in the adiabatic section. Three heat pipes identical in 
all respects except that the wicks were built using screens, powder metal and spiral ?V? 
grooves were tested. A computer program developed at Thermacore Inc. was used to 
estimate the performance of each heat pipe; these calculations showed that for the same 
power the lowest ?T was predicted for the heat pipe with the microgrooves followed by 
the sintered powder metal and the wrap screen, whereas the sintered powder metal wick 
had the highest predicted heat transport capability followed by the wrapped screen wick 
and then the microgrooves. The microgrooves design was dropped due to difficulties 
faced in fabrication. The better performance obtained with sintered powder wicks as 
compared to the screen wicks was attributed to the bonding of wick structure to the heat 
pipe wall. A screen wick has empty clearances between the layers and gap between the 
screen and the heat pipe wall. These clearances are filled with a comparatively low 
thermal conductivity working fluid that increases the thermal resistance of the heat pipe 
and consequently causes increase in the temperature drop. This difference causes an 
increase in performance by a factor of 3 in sintered powder wicks.  
Hwangbo and Joost developed a variable conductance heat pipe with a flexible 
joint for temperature control of high power electronics using a space radiator [23]. The 
design requirements for this pipe mandated that a 0.5? O.D. heat pipe should be able to 
sustain loads up to 3500 W-inch at a vapor temperature of 80 ?F. The design consisted of 
a sintered screen axial slab made by a 20 mesh screen sandwiched between two 100 
25 
meshscreens. This benefited from the increased permeability due to the 20 mesh screen as 
well as better capillary pumping by the 100 mesh screens. An analytical model was 
developed and several operating conditions were simulated to demonstrate the feasibility 
of this design with ammonia as working fluid. 
G. P. Peterson [24] developed a bellows heat pipe using analytical and computer 
modeling for cooling of electronic components. This study first developed an analytical 
model that was used to build a computer model. Since the design of the heat pipe was 
governed by the evaporator temperature i.e. temperature of electronic component, the 
source heat flux was not specified in the model. The results from the computer model 
were benchmarked against previous work in this field and were found to agree with the 
results obtained by others. This computer model was then used for designing and 
optimizing a bellows heat pipe, which was designed to maintain the heat source at a 
constant temperature of 40?C. It is noted that this heat pipe was capable of transporting 
45 W with a thermal resistance of 0.47?C/W. 
A flexible loop heat pipe cold plate was developed by N. J. Gernert and J. Brown 
[28], which was very similar to the work done earlier by Gernert et al. [26]. The major 
difference is that this prototype operates in any orientation. It sustained a heat load of 45 
W over a temperature drop of 20 ?C. 
The Advanced Camera for Surveys (ACS) is an instrument containing two CCD 
cameras. It operates at temperatures below -80 ?C. The camera was cooled by using two 
thermo-electric coolers, which transported the heat from the cameras to heat pipes, which 
in turn transported it to the sink. The heat pipes were chosen since they are frequently 
26 
used in space applications for passive heat transport to remotely and awkwardly located 
radiator panels. Since the location and alignment of the CCDs were important, the heat 
pipes were designed with a flexible section to minimize the thermal induced structural 
loads. This work by R. B. Schweickart and M. M. Buchko [32] discussed the design and 
testing of these heat pipes. The flexible heat pipes used ammonia as working fluid and a 
rolled screen mesh wick supported by screen mesh web. Both the evaporator and 
condenser were 316L stainless steel and the flexible section was made from Swagelok
?
 
flexible stainless steel hose. As the flexible sections of the heat pipes were pre-formed 
after the wicks were inserted, additional bending of the flexible section posed little risk of 
wick damage. Thermal performance testing showed that both pipes exceeded their 
minimum required heat transport capacity by a wide margin. 
In an effort to build a flexible heat pipe that can provide for bending, twisting, 
oscillating and deforming that is typically required in compact electronics, Lu Shaoning 
and Li His-Shang designed and built prototypes of a mini flexible heat pipe with a 
vacuum grade transparent plastic tube [2]. The heat pipes were small in diameter, 
typically few millimeters, so as to accommodate mobile computers. New wick structures 
were designed to make internal two-phase flow visible while providing the required 
capillary pumping action. The evaporator and condenser of the heat pipes were made of 
brass tubes and a transparent polyurethane tube was used for the flexible adiabatic 
transport section. Transparent wick structures were built from copper wire spring with a 
spring-braid wick and helical mesh stripe. This work however only discussed results from 
spring wick heat pipe that made good contact with the heat pipe container and flexibility 
27 
was maintained in any bent position. The spring was made from copper wire and water 
was used as working fluid. 
Ultra-high-molecular-weight (UHMW) film wicks and formed UHMW wicks 
with Kapton and aluminized Mylar containers were used to design, fabricate and test 
flexible heat pipes by Glass et al. [33]. The heat pipes used methanol as the working fluid 
and tests were carried out at steady state. The authors note ?The successful fabrication 
and operation of the heat pipe demonstrated that flexible polymeric heat pipes are 
feasible. From preliminary design studies, it appears that the design of a wick such that 
capillary and boiling limits are satisfied is the primary challenge?. 
The following references are given for the reader interested in further studies. 
Test results for lifetests of heat pipes used in a telecommunications satellite are 
discussed with the test setup by W. D. Muenzel in a report for ESA [14]. Four bendable 
artery heat pipes 7 mm in diameter were subjected to lifetests under a variety of operating 
conditions, both stationary and accelerated as well as under thermal shocks. 
Ernst and Eastman studied designs for liquid metal heat pipes for space and 
terrestrial applications for high temperature heat recovery [22]. The design criterion and 
several wick designs like sintered powder wick/arteries, sintered axial grooves and 
flexible screen arteries were discussed. 
R. S. Bhatti and S. Vanoost [25] considered A95 stainless steel heat pipes with 
ammonia as working fluid for all possible cases of space applications. Different bend 
configurations and lengths were also included in the study. 
28 
A flexible heat pipe cold plate technology was developed by Gernert et al. for 
aircraft thermal control [26]. Four such heat pipes were built for a variety of difficult 
aircraft cooling situations. In each case, a cold plate transferred the source heat to the 
most convenient heat sink by an integrally connected flexible heat pipe. This permitted 
relative motion between the electronics package to be cooled and the heat sink and it also 
allowed cooling system access in awkward places. 
A method was suggested by Gus?kov et al. for calculating the thermal resistance 
and constraints on the load for an arterial flexible heat pipe working in cryogenic and low 
temperature modes [27]. It permitted prediction of the heat pipe operation with various 
working fluids and different design variations; one such result for propylene heat pipe 
was presented. 
A report of joint activities of various Russian organizations aimed at the 
development of a flexible heat pipe and its modified version intended for thermal 
management of spacecraft instrumentation was presented by Zelenov at al [29]. A 
flexible heat pipe increased reliability of units moving, folding and opening in space in 
addition to a reduction in power consumption of the thermal control system. Different 
heat pipes were developed as an outcome of experimental and theoretical studies of 
various configurations of the evaporator, condenser and adiabatic zones. It was shown 
that the principal performance characteristics of these pipes were comparable to other 
flexible heat pipes? performance. 
29 
Quasi steady state operating characteristics of a flexible copper-water heat pipe 
were obtained experimentally by investigating its thermal performance under varying 
acceleration loading by S. K. Thomas and K. L. Yerkes [30,31]. 
Ozaki et al. designed a bent aluminum looped heat pipe as a part of a graphite 
faceskin panel on a deployable radiator panel [34].  
A summary of the literature reviewed is presented in Table 2.1 and Table 2.2. 
 
Table 2.1: Summary of published work on flexible heat pipes 
Reference     Wick Type Working
Fluid 
 Flexible/Bends Load Operating
Temperature 
F. Edelstein [9] Grooved 
? 
Up to 90 800 W
?
Methane 
? 
20 W 100 KE. W. Saaski and J. P. Wright 
[10] 
Tightly wrapped fine 
screen 
R-21 
? 
20 W 293 K
J. P. Wright, P. J. Brennan and 
C. R. McCreight [11] 
Spiral coarse mesh 
screen encapsulated by 
fine mesh outer wrap 
Methane, 
ethane 
? 
110 W 100-200 K
W. D. Muenzel, C. J. Savage, A. 
Accensi and B. G. M. Aalders 
[13] 
160 mesh stainless steel 
screen 
Ammonia Z shaped 30 W 303 K
Multi-tube central
artery, wall screen wick 
 Freon-21 U Bend 20 W 293 KM. E. Peeples, L. D. Calhoun 
[16] 
Axial grooves Ammonia U Bend 20 W 293 K
J. P. Mathieu, B. Moschetti and 
C. J. Savage [17] 
Homogeneous wick Ammonia U Bend 100 W.m 293 K
K. L. Meier, H. E. Martinez and 
J. E. Runyan [18] 
Non-concentric screen 
annular sintered wick 
Sodium Two 90? bends 15000 W 1400 K
D. M. Ernst [19] 325 mesh stainless steel Sodium Two 30? bends 3800 W 923 K
M. A. Merrigan, E. S. Keddy, J. 
T. Sena and M. G. Elder [20] 
Stainless steel wick Sodium 90?, 180? 1950 W/cm
2
 
axial flux
1000 K
30 
31 
     
Table 2.2: Summary of published work on flexible heat pipes 
Reference Wick Type Working
Fluid 
 Flexible/Bends Load Operating
Temperature 
Spiral grooves Acetone Flexible 135 W 333 K
Screen    Acetone Flexible 690 W 333 K
R. M. Shaubach and N. J. 
Gernert [21] 
Powder metal Acetone Flexible 2350 W 333 K
H. A. N. Hwangbo and T. E. 
Joost [23] 
Sintered screen axial 
slab 
Ammonia
? 
3500 W-in 300 K
G. P. Peterson [24] 5 layer 100 mesh 
stainless steel screen 
Ammonia Flexible   45 W 313 K
N. J. Gernert and J. Brown [28] Porous polymer Methanol Flexible loop heat 
pipe 
45 W ?T of 20 K
30 W 249 ? 273 K
20 W 249 K
R. B. Schweickart and M. M. 
Buchko [32] 
Rolled screen mesh Ammonia Flexibility required 
for misalignment 
30 W 273 K
Shaoning Lu and His-Shang Li 
[2] 
Copper spring Water Flexible 
? ? 
 
32 
CHAPTER 3 
FACTORS AFFECTING DESIGN AND PERFORMANCE 
3.1 Introduction 
As described before, the basic components of a heat pipe are the working fluid, 
the container and the capillary structure. During the construction of a heat pipe a number 
of factors control the type of materials that can be used. Also, it is obvious that there will 
be some conflicting combinations that will not work when used in a heat pipe [3]. 
3.2 Working Fluid 
Every heat pipe is designed for a particular operating temperature range. The 
selection of the working fluid mainly depends on this range of temperatures. Some of the 
commonly used working fluids in AuTherMML are listed in Table 3.1 along with their 
related thermo physical properties and useful ranges. The useful range of a working fluid 
extends from the point where the saturation pressure is greater than 0.1 atm and less than 
20 atm [5]. 
Within the operating temperature range, a variety of possible fluids can be used. 
In order to determine the best working fluid, a number of characteristics must be 
examined. The main characteristics are discussed in following pages [3]. 
 
33 
Table 3.1: Thermo physical properties of working fluids used at AuTherMML [3] 
Working Fluid 
Melting Point, K at 1 
atm 
Boiling Point, K at 
1 atm 
Useful 
Range, K 
Water 273.1 373.1 303 ? 473 
Methanol 175.1 337.8 283 ? 403 
R134a 172.0 246.4 208 ? 343 
34 
3.2.1 Compatibility with Wick and Container 
Chemical compatibility of the heat pipe container metal and the working fluid is 
important. The working fluid and the container might work as a galvanic cell in tandem 
with other parts of the heat pipe. Any such reaction may generate non-condensable gases 
degrading the overall performance of the heat pipe [3,5]. 
3.2.2 Thermal Stability 
At working temperatures that are typically higher than room temperatures, the 
container metal may act as a catalyst in decomposition of the working fluid. Some 
organic fluids break down into different compounds necessitating the need to keep the 
film temperature below certain temperatures [3,5]. This is not a problem for inorganic 
fluids. 
3.2.3 Wetting of Wick and Container 
Any fluid can be used in a conventional heat pipe provided it has good wetting 
characteristics with the wick and container wall material. The capillary pressure 
generated in the wick is subject to wettability of the fluid with the wick structure. Also, 
the superheat required to initiate boiling can be increased by good wetting. When a fluid 
does not have good wetting characteristic, it can be improved by surface treatments. To 
improve wetting characteristics, the copper containers were oxidized during fabrication 
of the heat pipes used in this research [36]. 
35 
3.2.4 High Latent Heat and Thermal Conductivity 
The heat transport through the heat pipe is a direct function of the latent heat of 
the working fluid. The performance of the heat pipe is directly proportional to the latent 
heat. Also, a higher latent heat allows for good heat transfer at lower temperatures. 
Thermal conductivity of the working fluid is of major concern at the condenser end. The 
condensed liquid has a comparatively lower conductivity and increased thermal 
resistance. 
3.3 Container 
The function of the container is to provide a hermetically sealed enclosure for the 
working fluid. It is necessary to avoid any diffusion of air into the heat pipe. The type of 
the heat pipe and its application decides the shape of the container. The desired 
characteristics are, wick type & material and working fluid compatibility, strength to 
weight ratio, thermal conductivity, ease of machining and wettability. 
Degradation of the container material leads to chemical reaction with the working 
fluid. In addition to generating non-condensables, these reactions tend to corrode the 
internal surfaces of the container, increasing the thermal resistance and also reducing the 
surface tension and wetting angle. Such chemical reactions also cause pitting of the inside 
wall that promotes formation of enhanced nucleation sites which leads to premature 
boiling of the working fluid [6]. 
Apart from the chemical compatibility, a heat pipe container is necessarily a 
pressure vessel and hence careful attention is required for selection of material grade. 
36 
Also, it is required to make a leak proof seal and structural integrity must be ensured for 
the entire working pressure range of the heat pipe [6]. 
3.4 Capillary Structure 
The capillary wick structure in a heat pipe provides a mechanism by which the 
working fluid returns to the evaporator and evenly distributes the liquid film over the 
evaporator surface on the inside. Since the capillary force is of premier importance to 
sustain the working of heat pipes, the wick pores must be small. Smaller pores provide 
for greater capillary pumping pressure but also increase resistance to liquid flow through 
the wick, thereby increasing the overall liquid pressure drop across the wick. The wick 
covers the entire inner surface of the heat pipe and hence, the heat must travel through 
heat pipe container walls and wick to evaporate the liquid. The radial temperature drop 
due to this is dependent on the thickness of the wick and its thermal conductivity. For a 
higher thermal conductivity the wick must have lower porosity but this conflicts with the 
need for lower liquid pressure gradient [3,5,6]. 
The wick structures are broadly classified into two categories as discussed in 
following sections. 
3.4.1 Homogeneous Wicks 
Homogeneous wicks are constructed from a single material that has a uniform 
cross section. The common materials used include metal screens, sintered metal felts, 
sintered metal powders and axially grooved wicks (Figure 3.1). Each type of wick made 
37 
from these materials has its own advantages and limitations, and a detailed discussion on 
this topic is beyond the scope of this work. 
3.4.2 Composite Wicks 
A composite wicking structure is built using two or more materials described in 
section 3.4.1 thus taking advantage of their respective strengths. A composite wick 
typically handles the two main functions of capillary pumping and liquid transport in 
different sections of the wick. A typical example is a screen wick covering the axially 
grooved wick structure as shown in Figure 3.2. 
 
 
 
(a) Wrapped screen (b) Sintered metal (c) Axially grooved 
 
Figure 3.1: Homogeneous wicks 
 
(d) Composite screen (e) Slab (f) Screen covered grooves 
 
Figure 3.2: Composite wicks 
 
38 
CHAPTER 4 
TESTING AND PERFORMANCE EVALUATION 
4.1 Performance Evaluation 
The performance evaluation of a heat pipe is a necessary step that has to be often 
repeated in order to characterize many factors such as working temperature and 
maximum heat transfer capacity (as described in Section 1.5). The heat pipe performance 
is usually defined in terms of the temperature drop across the working length of heat pipe 
at a given power level. Lowering the temperature drop between the evaporator and 
condenser is the goal of a heat pipe. The electrical circuit analogy can be easily used to 
explain this. 
The heat pipe is like an electrical conductor. The heat flowing (current) across is 
reduced by losses (resistance - mainly frictional pressure drop) causing a temperature 
drop (voltage drop) across evaporator-condenser circuit. In this way the heat pipe 
performance is quantified for a lower resistance or a higher conductance value. If Q is the 
heat load on the system and ?T is the temperature drop across the heat pipe then the 
thermal resistance R is given by, 
 
Q
T
R
?
=  
4.1
39 
The relation shown in the above equation is a derivative of the classic conduction 
equation, 
 
L
TAK
Q
???
=  
4.2
It is clear that resistance R is defined as, 
 
AK
L
R
?
=  
4.3
During this work the heat pipe performance was measured in terms of 
Conductance, which is a reciprocal quantity of Resistance as defined above. In a way this 
measured quantity is similar to material thermal conductivity. 
4.1.1 Testing Procedure 
The testing procedure devised was based on the same principle. The heat pipe was 
subjected to a heat load across its working length. The evaporator is connected to a heat 
source, typically a heater block. This heater block was powered by cartridge heaters 
whose power input was controlled by a regulated power supply. Heat was extracted from 
the condenser end by a water circulator that has a supply of constant temperature water 
from a chiller. The setup is shown in Figure 4.1. A record of temperatures at different 
power levels was kept using two thermocouples mounted on the evaporator and 
condenser end as indicated. 
The chiller was started first and allowed to attain a steady 20?C bath temperature. 
The heat pipe was also allowed to attain a steady state temperature of 20?C to assure a 
common starting point for all the tests performed. The power was then supplied to the 
heater in uniform increments and the heat pipe temperatures were observed until steady  
40 
Water OUT 
Water IN 
L
c 
41 
  
Figure 4.1: Heat pipe test setup for conductance measurement 
 
DC Power Supply 
Thermocouples 
T
c
L
a 
L
e 
Heater block
T
e
Agilent Data Logger 
state was reached and maintained for at least fifteen minutes. The ambient temperature 
was maintained between 20-23?C to keep the parasitic losses at approximately the same 
levels for all tests. A sample graph is shown in Figure 4.2. At this point, a note of all the 
readings was taken and used for further analysis. 
4.1.2 Conductance 
The temperatures of the evaporator and condenser at steady state were recorded 
and a temperature gradient was calculated. With the known power input, the heat pipe's 
performance at that load was measured in terms of conductance G as defined below, 
 
L
AK
T
Q
G
?
=
?
=  
4.4
 The unit of conductance is W/?C or W/K. Thus for a heat pipe with a steady state  
heat load of 12W and ?T of 0.72?C (Figure 4.2) the conductance was 16.8 W/K. The heat 
pipe performance was then plotted as a graph of conductance against input power. A 
sample graph is shown in Figure 4.3. 
4.2 Copper Equivalence 
As mentioned above, this measurement technique converts the heat pipe into a 
quasi solid material. As shown in Equation 4.4, the thermal conductivity is expressed in 
the form of thermal conductance. However, unlike a solid, the heat pipe's conductivity 
depends on many factors due to the complexity of two phase heat transfer and flow that 
occurs inside the heat pipe as described in Section 1.4. The location of temperature 
measurement chosen during testing is a major factor influencing the thermal conductivity 
reported. 
42 
35
37
39
41
43
45
47
0 100 200 300 400 500 600 700 800 900
Time (sec)
T
e
m
p
er
at
u
r
e
 (
C
)
Heater
Evaporator
Condenser
 
Figure 4.2: Steady state temperature curves during testing 
0
5
10
15
20
25
30
35
40
0 102030405060708
Power (W)
C
onduct
a
nce (W
/K)
0
 
Figure 4.3: Heat pipe conductance against input power applied 
43 
4.2.1 Measurement Errors and Losses 
The measurement of thermal conductance is complicated by a number of other 
parameters not related to the physical state of the material. The nature of the test setup 
affects the data reduction due to various losses and leakages of the applied heat load. 
Thermal contact resistance is one of the major causes of heat loss in a test setup. It 
depends on factors such pressure, surface roughness and hardness etc [35]. Contact 
resistance comes into importance at two points in the setup, the contact between electrical 
heaters and heater block and the contact resistance between heater block and the test 
subject.  
The heat is transmitted across the interfacial contacts by conduction, through the 
air trapped in the gaps and via radiation [35]. Thermal resistance is caused by oxidation 
of contacting surfaces, gaps between interfacial surfaces, and radiation heat transfer 
between microscopic voids due to surface roughness. Additionally, heat loss through the 
insulation also adds to the parasitic losses in the system. The heat supplied by the heaters, 
Q, is split into, 
? Q
Heater block
 = heat dissipated by the heater block  
? Q
Insulation
 = heat loss through the insulation 
? Q
Adiabatic
 = heat loss through the adiabatic section of the heat pipe 
? Q
Condenser
 = heat rejected to circulating water 
 
CondenserAdiabaticInsulationblockHeater
QQQQQ +++=  
4.5
 
44 
45 
Assuming that the condenser rejects all the heat to circulating water, Q
Condenser
 is 
the actual heat transferred through the heat pipe and all others are lost through the system. 
As shown in Equation 4.5, since all of these are included in the evaluation of heat pipe 
conductance (Equation 4.4), it introduces a corresponding error in recording of data. 
The other factors that indirectly contribute to heat loss include errors in the 
measurement of input power and recorded temperatures. Also the variation in the 
temperature of cooling water is unpredictable. The changes in surrounding conditions 
increase or decrease the heat loss to the environment.  
It is obvious that a number of such systematic errors are present in testing and that 
any reporting of thermal conductance of the heat pipe is subjective to the viewpoint of the 
person conducting test. Under such conditions, there is a possibility of disagreement in 
the results and trends for tests conducted at different periods of time on the same test 
subject using the same test setup. All such factors can be termed as a ?system bias? 
towards the reliability of the test results. The literature is full of measurements and 
performance estimates reported by different sources, and they are affected by the same 
problem i.e. it is difficult to gauge the system bias and compare the results of tests 
conducted by separate entities. The absence of any standards based testing method makes 
it impossible to evaluate all literature on a common basis. 
4.2.2 Parasitic Losses 
The data obtained during testing includes heat loss as described in the previous 
section. To estimate parasitic losses during each test, a separate test was carried out on 
each heat pipe where the water circulator was removed and the condenser end of heat 
46 
pipe was insulated. Then, the heat input was arranged similar to normal testing 
conditions. Since there is no cooling, once the heat pipe comes to steady state the power 
input corresponding to the evaporator temperature is the parasitic loss at that particular 
temperature. In the absence of cooling, to protect the heat pipe from damage, the applied 
heat loads during such tests were typically very low. The power losses for higher range of 
evaporator temperature were then extrapolated from this data. It was observed that this 
method resulted in a linear relation between the parasitic heat loss and the evaporator 
temperature. A typical plot is shown in Figure 4.5. 
After each test, the power applied for heat load was corrected using this relation 
for parasitic loss. A graph of power vs. conductance (Figure 4.6) showing the original 
and corrected conductance values is included to demonstrate the concept. All similar 
plots always show only corrected conductance values thereby excluding parasitic losses 
unless otherwise specified. 
4.2.3 Benchmarks 
As mentioned in section 1.1, efficient heat removal is critical to many devices and 
the steady increase in energy density means that solid metal conductors can no longer be 
used to transfer the high amount of heat flux produced. However heat pipes can be 
compared with the high thermal conductivity metals like Copper (401 W/m.K),
y = 0.04599x - 1.12622
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0 1020304050607
Evaporator Temperature (C)
Power (W)
0
 
Figure 4.4: Estimation of parasitic losses 
0
5
10
15
20
25
30
35
40
0 1020304050607080
Power (W)
Conductanc
e (W/
K
)
Conductance
Corrected Conductance
 
Figure 4.5: Conductance corrected to account for parasitic losses
47 
48 
Silver (429 W/m.K) and Aluminum (237 W/m.K). These well-established values provide 
an easy way of benchmarking any test setup that measures thermal conductivity by 
verifying these material conductivities. Since all the heat pipes used for this project were 
made of copper, use of copper as a benchmark was a natural choice. Oxygen free copper 
was used in all the tests and the dimensions were chosen to match that of the heat pipe. 
4.2.4 Concept of Copper Equivalence 
There is a need for a quick and easy method to record performance characteristics 
of heat pipes using parameters that are reproducible. As shown in Section 4.2.1 the 
measurement of thermal conductivity is a fairly complicated process which involves 
many parameters that can influence the data and ultimately cause deviation in the final 
result. 
A simple approach is adopted to tackle this problem. Once a heat pipe is ready for 
testing and a corresponding test setup is designed, a solid copper rod of known thermal 
conductivity of the same dimensions as the heat pipe is prepared. This copper rod is now 
the benchmark for all tests done on that heat pipe. The copper rod is then tested in the 
same setup and a dataset of its conductance is recorded. Since the copper rod is of the 
same physical shape and size, once it is replaced with the heat pipe, everything remains 
the same in the test setup including the insulating material. This means that both the test 
subjects undergo performance testing under exactly similar conditions. 
The data with such test for two completely different test objects now includes a 
common system bias, which covers all parasitic losses and contact resistances. The 
conductance of the heat pipe is usually very high as compared to that of the copper rod, 
therefore the copper equivalence CE is defined as, 
 
rodcopper
pipeheat
G
G
CE =  
4.6
 Once a CE value is recorded for a heat pipe, it effectively neutralizes the 
discrepancies due to system bias and since a standard copper alloy is used for evaluation, 
it is used to compare performance of heat pipes from different sources. The standard 
benchmark also enables a comparison between different types of heat pipes which 
otherwise cannot be directly matched due to the differences in physical and operational 
characteristics. 
4.2.5 Why Copper Equivalence Works? 
The vast amount of past work on heat pipes shows that there is a tendency to 
study performance of heat pipes in terms of its heat transfer limits and the temperature 
and pressure profiles along its length. Although this data is important, for most 
applications it is imperative to explore all available heat pipe variations. A data pertaining 
to heat transfer limits, pressure and temperature profiles can do little in providing a 
common ground for comparison. Theoretical models, both analytical and numerical are 
complicated and time consuming to develop. These models typically require a lot of 
assumptions to allow a solution and hence may not be directly comparable. This is where 
copper equivalence greatly helps because of its straightforward application and 
procedure. By comparing results with a standard copper rod on the same test setup this 
49 
50 
method effectively eliminates a large number of unknowns (Equation 4.5), which are 
difficult to evaluate due to the complexity of the various modes of heat transfer involved. 
4.2.6 Application 
The application of copper equivalence was advantageous during the testing phase 
of this thesis. The first test setup, shown in Figure 4.1, was later modified and a new 
heater block was designed that used two heaters on either side of the heat pipe. It used a 
split design and allowed minor variation in pipe diameter, which also helped reduce the 
contact resistances (Section 4.2.1) as there was a tighter integration between heaters, 
heater block and the heat pipe. Both heater blocks are shown in Figure 4.6. But it was 
clear that this changed the parasitic losses associated with the setup and hence it was not 
possible to directly compare the results obtained with different heat pipes. Thus the 
copper equivalence was really useful for studying the results described in this thesis. 
A comparative study of copper 101 rod on both heater blocks showed that the 
conductance values for heater block 02, although followed the same trend, were on an 
average 9% lower that those for heater block 01. Since all the other parameters were 
constant, this indicated that the test setup using heater block 02 had lower parasitic losses. 
The relevant data is included in Table 4.1. 
 
? 0.25, 2 Holes 
51 
 
(a) Heater block 01 used with HP01 
 
(b) Split heater block 02 used with HP02 
 
Figure 4.6: Schematic of heater blocks used 
0.5
1 
1.5 
?
 0.25, 3 Holes 
Not to scale 
All dimensions in inches 
10.375
1.5 
0.375 
Table 4.1: Conductance values of copper 101 rod 
Heater Block 01 Heater Block 02 
Power 
(W) 
Conductance 
(W/K) 
Power 
(W) 
Conductance 
(W/K) 
0.50 0.0698 0.51 0.0578 
1.00 0.0761 1.01 0.0671
1.49 0.0790 1.50 0.0699 
2.01 0.0820 2.04 0.0761
3.08 0.0850 3.04 0.0789 
3.99 0.0845 4.03 0.0806
5.14 0.0884 5.02 0.0814 
6.01 0.0865 5.99 0.0824
 
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
01234567
Power (W)
Conduct
a
nce (W/
K
)
Heater Block 01
Heater Block 02
 
Figure 4.7: Comparison of copper rod data on heater blocks 
52 
53 
CHAPTER 5 
BENDABLE HEAT PIPES 
5.1 Introduction 
As discussed in Chapter 2, flexible heat pipes have garnered significant research 
interest in the past due to their obvious advantages. Flexible heat pipe designs include 
flexible sections made from bellows or bendable tubing. These types of heat pipes are 
usually designed to be fabricated in a particular shape. Fabrication techniques were 
developed to make bended heat pipes in required shapes and in some cases wicks were 
totally removed from the flexible sections to avoid potential problems with deformed 
wicks.  
It is observed that there are no references in the literature for heat pipes that can 
be bent into a contorted shape after fabrication. This thesis documents the evaluation and 
testing of bendable copper-water heat pipes made using sintered copper felt wicks. Once 
fabricated, this heat pipe can be twisted to fit into the available space or reach narrow 
spaces. 
5.2 Bendable Wicks 
Only certain types of wicks can be used in bendable heat pipes. And wick will 
have a tendency to separate from the container walls under bending. This separation has 
54 
two adverse effects, a reduction in the vapor core area that reduces heat transfer capacity 
and a disruption in the path of liquid flowing back to the evaporator. If the bending angle 
is severe, the wick can crumple [16] and even tear off in extreme cases. The sintered 
copper felt wick provides a very flexible wick material that does not crack after bending 
as well. However, a wick made from sintered metal powder will crack under bending. 
Although other wicks made from metal screens may also work with supporting springs, 
this work is a continuation of ongoing work on metal felt heat pipes at AuTherMML [37]. 
The heat pipe was bent in only one location to reduce the complexities in testing. After 
successful tests on such heat pipes further studies on multiple bends could be carried out. 
Several bending angles (15?, 30?, 45?, 60? and 90?) with a constant bending radius of 
18.18mm (pipe axis) were tested. 
A series of photographs of the heat pipe cross section after bending were taken for 
various bent configurations and expectedly separation of wick was observed. However, it 
was noted (Figure 5.1) that the separation from the wall slowed down after 45?.  Also a 
90? bend was cut and, it was observed that the wick was not damaged due to stretching 
and crumpling at outer and inner walls as shown in Figure 5.2 (a) & (b). It can be seen in 
Figure 5.2 (c)-(e) that the inner and outer walls of the curved part of the heat pipe had 
deformed due to crumpling and stretching respectively. The working fluid gets trapped in 
the gaps created by the separation of the wick from the container walls. This film of 
working fluid has a lower conductivity as compared to that of the wick and it reduces the 
heat transfer to the heat pipe. Therefore, deformation is acceptable only in the adiabatic 
section and not in the condenser section and the evaporator section. 
 
 
 
(a) Straight Heat Pipe 
(10x  magnification) 
(b) 15? Bend 
(10x  magnification) 
  
(c) 30? Bend 
(10x  magnification) 
(d) 45? Bend 
(10x  magnification) 
  
(e) 60? Bend 
(10x  magnification) 
(f) 90? Bend 
(10x  magnification) 
Figure 5.1: Wick separation near heat pipe wall due to bending 
55 
 
  
(a) No damage to wick due to bending 
(90?) 
(10x  magnification) 
(b) No damage to wick due to bending 
(90?) 
(10x  magnification) 
  
(c) Straight heat pipe wall texture 
(5x  magnification) 
(d) Bended heat pipe inner wall 
(5x  magnification) 
 
(e) Bended heat pipe outer wall 
(5x  magnification) 
Figure 5.2: Bending effects on heat pipe wall and wick 
56 
5.3 Performance Limit 
As discussed in Section 1.5, a heat pipe has various performance limits. However, 
when the heat pipe has a single bend at the center, the only limit affected is the capillary 
limit. As shown in Equation 1.2, the vapor pressure drop and liquid pressure drop will be 
affected due to bending as the flow paths are altered. Low fluid velocities typically 
characterize the liquid flow and bending effects can be neglected [5]. Therefore, at steady 
mass flow, the vapor velocities are very high and the flow is laminar or turbulent 
depending on working temperature and heat load. 
5.3.1 Vapor Pressure Drop 
A detailed analysis of vapor flow by C. A. Busse [5,38] was used to study 
bending effects on the capillary limit. 
The capillary limit is given by, 
 
gphasecphaseevlmaxcap
pppppp ?+?+?+?+???
,,,
 
1.2
 
The maximum capillary head is given by, 
 
eff
cap
r
p
?2
max,
=?  
5.1
where r
eff
 is the effective capillary radius and ? is the surface tension. Busse assumed that 
the vapor flow was laminar and the heat pipe was isothermal, so density was constant. 
Also the axial pressure gradient was assumed constant over the heat pipe cross section. 
57 
The two dimensional steady flow of the incompressible vapor is represented by 
the conservation equations for mass and momentum (Figure 5.3), 
r momentum equation: 
 
?
?
?
?
?
?
?
?
+
?
?
?
?
?
?
?
?
?
?
+
?
?
?=
?
?
+
?
?
2
2
)(
11
z
v
rv
rrrr
p
z
v
w
r
v
v ?
?
 
5.2
z momentum equation: 
 
?
?
?
?
?
?
?
?
+
?
?
?
?
?
?
?
?
?
?
+
?
?
?=
?
?
+
?
?
2
2
11
z
v
r
w
r
rrz
p
z
w
w
r
w
v ?
?
 
5.3
Continuity equation: 
 
() 0
1
=
?
?
+
?
?
z
w
rv
rr
 
5.4
Boundary conditions: 
At r = 0 0,0 ==
?
?
v
r
w
 
5.5
At r = R
v
?
?
?
?
?
<<+?
+<<
<<
==
tae
aee
e
LzLLv
LLzL
Lzv
vw
,
,0
0,
,0
?
?
5.6
A radial Reynolds number Re
r
 is defined as vapor velocity distributions are related to 
interfacial velocity v
?
, 
 
v
vv
r
Rv
Re
?
?
?
=  
5.7
This is related to the rate of mass flow per unit length by, 
 
dz
md
Re
v
v
r
&
??2
1
=  
5.8
 
58 
To solve these equations, Busse proposed an approximate expression for the axial 
velocity profile, 
 
()
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?+
?
?
?
?
?
?
?
?
?=
3
1
)(11)(2,
2
2
2
2
vv
R
r
za
R
r
zwzrw  
5.9
 
where a(z) is an arbitrary function for the correction to the parabolic Poiseuille velocity 
profile that was found by assuming that the average pressure gradient over the cross 
section equals the axial pressure gradient at the center [5]. The values of a(z) for various 
values of radial Reynolds numbers are shown in Figure 5.4. This gives results for the 
pressure drops in all three sections [5]. 
Evaporator: 
 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+?+?=?
405
23
27
8
9
7
1
2
8
2
4
AA
Re
L
hR
Q
p
r
e
fgvv
ev
e
??
?
 
5.10
Adiabatic: 
 
?
?
?
?
?
?
?
?
?
?
?
?
?
? ?
+
?
+?=?
405
)(23
27
)(8
8
1
8
22
4
aAaA
L
RRe
L
hR
Q
p
a
vz
a
fgvv
ev
a
??
?
 
5.11
Condenser: 
 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+?+?=?
405
23
27
8
9
7
1
2
8
2
4
aa
Re
L
hR
Q
p
r
c
fgvv
ev
e
??
?
 
5.12
59 
60 
 
Figure 5.3: Heat Pipe Nomenclature 
Evaporator 
Section 
L
e
Condenser 
Section 
L
c
Adiabatic 
Section 
L
a
z, w 
 
r, v 
R
o
R
i
R
v
Re =
r 
 ?
61 
 
Figure 5.4: The correction function a(z) [38] 
 
a       0 
z 
0.50 
10 
3 
0.25 
1.67 
0 
-0.25 
-1.67 
-0.50 
Evaporation zone Adiabatic zone Condensation 
Where Re
z
 is the axial Reynolds number, 
 
v
vav
z
wR
Re
?
?2
=  
5.13
and A is 
 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+?+=
5
44
Re
18
5
Re
18
5
22
15
2
rr
A
5.14
For the case, when the wet point is near the condenser end cap (Figure 1.2) the 
pressure drop in the entire heat pipe is found by adding Equation 5.10, Equation 5.11 and 
Equation 5.12, 
 ( )
effe
fgvvv
vz
v
LQ
hAR
fRe
p
?
?
2
2
?=?
5.15
where L
eff
 is the effective length of heat pipe, 
 
22
c
a
e
eff
L
L
L
L ++=  
5.16
5.3.2 Other Pressure Drops 
The liquid pressure drop is given by 
 
effe
fglw
l
l
LQ
hKA
p
?
?
=?  
5.17
where K is the wick permeability and is given by an empirical relation [5], 
62 
 
strandfelt copper  ofdiameter 
103.3
106
)1(
1
1
)1(
27
210
2
32
2
2
=
?=
?=
?
+=
+
?
=
?
?
d
mB
mA
Bd
X
X
XA
K
?
?
5.18
The pressure drops due to phase change at the evaporator, ?p
e,?
, and the 
condenser, ?p
c,?
, are very small and can be neglected [6]. The hydrostatic pressure drop 
has two components, normal hydrostatic pressure drop ?p
?
 and axial hydrostatic pressure 
drop ?p
||
. 
 
?? sin
vl
gDp =?
?
 
5.19
 
?? cos
|| tl
gLp =?  
5.20
Depending on the inclination ? of heat pipe the axial pressure drop either assists 
or works against the capillary pumping pressure [6].  
5.3.3 Capillary Limit 
Combining Equation 5.15, Equation 5.17, Equation 5.19 and Equation 5.20 the 
expression for capillary limit 1.2 is given by [5], 
 
( )
????
?
?
?
??
sincos
2
2
2 vltleffe
fgvvv
vz
fglw
l
eff
gDgLLQ
hAR
fRe
hKAr
+?
?
?
?
?
?
?
?
?
+=  
5.21
Let the liquid and vapor frictional coefficients be respectively defined as, 
 
fglw
l
l
hKA
F
?
?
=  
5.22
63 
 ( )
fgvvv
vz
v
hAR
fRe
F
?
?
2
2
=  
5.23
therefore the capillary heat input limit is given by, 
 
()
vleff
vltl
eff
cap
FFL
gDgL
r
Q
+
??
=
????
?
sincos
2
5.24
This is the base relation for a straight cylindrical heat pipe that has inclination ? 
with respect to the vertical. It should be noted that since this heat pipe uses a wick, which 
allows circumferential communication of liquid, the normal hydrostatic pressure drop 
term has to be accounted for in the capillary limit [6]. 
When the heat pipe is in the horizontal position, ? is 90? and the axial pressure 
drop is eliminated, therefore the capillary limit is given by,  
 
()
vleff
vl
eff
horizontalcap
FFL
gD
r
Q
+
?
=
?
?2
,
5.25
Similarly in the vertical orientation, the inclination is zero and there is no normal 
pressure drop term, 
 
()
vleff
tl
eff
verticalcap
FFL
gL
r
Q
+
?
=
?
?2
,
 
5.26
When the heat pipe is in gravity assisted mode of operation, the axial pressure 
drop term is positive in Equation 5.26 otherwise when the evaporator is on the top and 
the heat pipe is working against the gravity, it has a negative sign. 
64 
65 
 
?
90-?
g
?? cos
2
t
L
g
?? sin
v
gD
2
t
L
g?
r
Figure 5.5: Hydrostatic pressure drops in a bended heat pipe 
5.3.4 Other Limits 
In addition to the capillary limit, other performance limits were also calculated to 
check if they could be responsible for heat pipe failure. The relations required for these 
limits were used from available literature [5,6] and are listed below, 
? Sonic Limit 
()
2
1
0
12
474.0
?
?
?
?
?
?
+
=
v
vv
fgvvsonic
TR
hAQ
?
?
?  
5.27
? Entrainment Limit 
2
1
,
2
?
?
?
?
?
?
?
?
=
sh
v
fgvtentrainmen
R
hAQ
??
 
5.28
? Boiling Limit 
()
?
?
?
?
?
?
?
?
??=
max,
2
ln
2
cap
nvivfg
veffe
boiling
p
rrrh
TkL
Q
?
?
?
 
5.29
 
5.3.5 Bend Loss 
When a pipe is bended, there is an additional pressure drop caused primarily due 
to result of secondary flow and is usually represented by an equivalent length of a straight 
pipe [39]. The secondary flows are rotating motion, normal to the pipe axis and are 
superimposed on the main flow in the direction of the axis. The friction at the pipe walls 
and the centrifugal force combine to produce these rotations [40]. The bend loss can be 
accounted for as a function of dynamic pressure of the vapor, 
 
22
2
2
2
2
fgv
e
b
bbend
hA
Q
K
w
Kp
?
?
=
=?
 
5.30
66 
Most of the available data in the literature relate this loss to the relative radius of 
the curvature, 
r
R
v
or the Dean number, De and account for the bend angle in terms of the 
length of the curvature.  The technical paper No. 410 by the Crane company [40] 
provides a relation for calculating bend loss coefficients, K
b
. The relation provided by the 
Crane company [40] is for turbulent flows in bends of 90?. Also the published work on 
evaluating bend losses is for losses in pipelines and their joints and fittings for turbulent 
flows. The work available on laminar flow is very limited and the only reported study 
included experimental results for a loss factor K
b
 as a function of the Reynolds number 
[41]. The data is available for some limited radii ratios of 4.52, 6.08, 13.06 and 23.42. 
The data indicates that as the Reynolds number increases the friction factor for the bend 
decreases. 
H. Ito [42] and Misra et al. [43] have published results of their work on the 
laminar flows in curved pipes. Both of them have produced similar relations for the 
relative friction factor of a curved pipe in terms of the Dean number. 
Where the Dean number is defined as 
 
r
R
ReDe
v
=  
5.31
The relation by Ito [42] is 
 
3
2
1
2
1
315.1729.1
11033.0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+=
DeDe
De
f
f
s
b
 
5.32
Misra et al. [43] have presented following relation 
67 
 
3
2
1
2
1
4729355.21154102.6
16341628.0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+=
De
De
De
f
f
s
b
 
5.33
For laminar flow through a bend of angle? , the bend loss is a sum of the pressure 
drops due to bend and frictional pressure drops in a straight pipe of an equivalent length. 
This results in a relation between friction factor f
b
 for bends and friction factor f
s
 for the 
straight sections. 
 
sbb
p
w
Kp ?+=?
2
2
 
5.34
or 
v
bs
b
v
bb
R
wLfw
K
R
wLf
424
222
+=
5.35
where, K  
b
is bend loss coefficient and L
b
 is length of bend. 
For a bended pipe with a curvature radius r and angle ?  the length L
b
 is given by 
?r . Therefore Equation 5.35 becomes, 
 
v
s
b
v
b
R
rf
K
R
rf
22
??
+=  
5.36
 
s
bv
b
f
r
KR
f +=
?
2
 
5.37
 
?
?
?
?
?
?
?
?
?= 1
2
s
b
v
s
b
f
f
R
fr
K
?
 
5.38
 
5.3.5.1 Bend Loss Coefficient for Vapor Flow 
Ito?s relation from Equation 5.32 was selected for calculating the bend pressure 
loss in this study. From Equations 5.32and 5.38, 
68 
 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+=
?
1
315.1729.1
11033.0
2
3
2
1
2
1
De
De
De
R
fr
K
v
s
b
?
 
5.39
A plot of K
b
 vs De is shown in Figure 5.6. The above relation was directly used in 
the calculations for the capillary limits reported in the following section. 
5.3.6 Capillary Limit for Bended Heat Pipe 
It was proposed in the last two sections that the effect of the bending angle can be 
accounted for by representing the bending losses as a function of the axial velocity. Due 
to various possible orientations of a bended heat pipe, expressions for the capillary limit 
in various orientations are given below [5]. 
? Heat pipe oriented horizontally 
 
()
vleff
fgv
e
bvl
eff
horizontalcap
FFL
hA
Q
KgD
r
Q
+
?
?
?
?
?
?
?
?
??
=
22
2
,
2
2
?
?
?
 
5.40
? Heat pipe in a vertical gravity assisted orientation 
 
()
()
vleff
fgv
e
bvl
t
l
eff
gravityverticalcap
FFL
hA
Q
KgD
L
g
r
Q
+
?
?
?
?
?
?
?
?
??++
=
22
2
,,
2
sincos1
2
2
?
????
?
5.41
? Heat pipe in a vertical adverse gravity orientation 
 
()
()
vleff
fgv
e
bvl
t
l
eff
adverseverticalcap
FFL
hA
Q
KgD
L
g
r
Q
+
?
?
?
?
?
?
?
?
??+?
=
22
2
,,
2
sincos1
2
2
?
????
?
5.42
69 
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 50 100 150 200 250 300 350 400
Dean Number
Bend Loss
 Coef
f
i
ci
ent
 Kb
15 Deg
30 Deg
45 Deg
60 Deg
90 Deg
 
Figure 5.6: Resistance to flow with Dean number 
 
70 
71 
In Equations 5.41 and 5.42, the axial hydrostatic pressure loss is divided into two 
parts. The cosine component accounts for reduction in the axial drop due to bending. 
These relations were used along with the temperature and power data taken from the 
operation of the bent heat pipes to study the change in the capillary limit due to bending. 
5.4 Testing and Evaluation 
Two heat pipes were tested for studying the concept of bendable heat pipes. The 
heat pipes tested consisted of a wick made from the sintered copper felt with water as the 
working fluid. The two heat pipes were designated as HP01 and HP02. The first set of 
tests were carried out on HP01 and included testing in horizontal, vertical gravity assisted 
and bended in the vertical gravity assist orientation for the angles of 15?, 30?, 45?, 60? 
and 90? with a constant bending radius of 18.18mm. 
For HP02, additional tests were carried out for bended heat pipes in both the 
horizontal and the adverse gravity orientation for the same series of angles. This allowed 
for the elimination of the effects caused by the axial hydrostatic pressure drop. The axial 
hydrostatic pressure drop is a significant component in the total capillary pumping 
pressure in the vertical gravity assisted position. Testing in the horizontal and vertical 
adverse gravity orientation meant that the heat pipe was working solely on the capillary 
pumping pressure. A schematic of bended configurations is shown in Figure 5.7 
 
15? 
30? 
45? 
60? 
90? 
 
Figure 5.7: Schematic of bending configurations for HP01 
72 
73 
5.4.1 Specifications of HP01 
? Container outer diameter (D)  ? 6.35 mm 
? Working length (L)   ? 276.2 mm  
? Evaporator length (L
e
)   ? 38.1 mm 
? Condenser length (L
c
)   ? 38.1 mm 
? Adiabatic section length (L
a
)  ? 200 mm 
? Sintered metal felt wick thickness  ? 0.3175 mm 
? Porosity (?)    ? 87% 
? Length of metal felt strands  ? 10 mm 
? Diameter of metal felt strands  ? 3.5 x 10
-2
 mm 
? Charge     ? 1.3g 
? Permeability    ? 442.76 ?m
2
 
5.4.2 HP01 Bending Test Results 
The results are presented in the graphical format due to the large number of 
readings for each test. The charts are included for input power against copper equivalence 
for following cases: 
? Straight horizontal and vertical 
? 15? bended vertical 
74 
? 30? bended vertical 
? 45? bended vertical 
? 60? bended vertical 
? 90? bended vertical 
Vertical refers to gravity assisted operation. 
Finally a graph showing measured increase in ?T with the bending angle is 
included. It was noticed that in all tests the copper equivalence vs power plots showed a 
similar trend. A peculiar bell shaped curve was observed for all tests for HP01. As the 
power was increased, the copper equivalence went up till it reached a maximum value 
and then it came down. The test was stopped when the heat pipe either stopped working 
or the temperatures did not attain a steady state. 
It was noticed that the tests for 45? and 90? bends produced abnormally high 
conductance values and it is not possible to relate this behavior to any particular cause. 
These tests were repeated two and four times respectively with similar outcomes. 
0
20
40
60
80
100
120
140
160
180
102030405
Power (W)
C
opper Equiva
lence
0
 
Figure 5.8: Test results for HP01 in straight horizontal position 
0
50
100
150
200
250
20406080
Power (W)
C
opper Equiva
lence
10
 
Figure 5.9: Test results for HP01 in straight vertical gravity assist position 
75 
0
50
100
150
200
250
300
0 1020304050607080
Power (W)
C
opper Equiva
lence
 
Figure 5.10: Test results for HP01 in 15? bended vertical gravity assist position 
0
20
40
60
80
100
120
140
160
180
0 1020304050607080
Power (W)
C
opper Equiva
lence
 
Figure 5.11: HP01 Test results for HP01 in 30? bended vertical gravity assist position 
76 
0
50
100
150
200
250
300
350
400
20406080
Power (W)
C
opper E
qui
val
e
nce
10
 
Figure 5.12: Test results for HP01 in 45? bended vertical gravity assist position 
0
20
40
60
80
100
120
20406080
Power (W)
C
opper Equiva
lence
10
 
Figure 5.13: Test results for HP01 in 60? bended vertical gravity assist position 
77 
0
100
200
300
400
500
600
0 1020304050607080
Power (W)
C
opper Equiva
lence
 
Figure 5.14: Test results for HP01 in 90? bended vertical gravity assist position 
0
1
2
3
4
5
6
7
0 15304560759010
Bend Angle (Deg)
Delta Temper
ature (C)
5
64 W
32 W
16 W
8 W
 
78 
Figure 5.15: ?T across HP01 for various bend angles 
79 
5.4.3 Capillary Limits for HP01 
The capillary limit was calculated using the equations presented in Section 5.3.3. 
Since a heat pipe typically has a very low temperature gradient over its length, the 
temperature measured at the evaporator end was used as the operating temperature for the 
heat pipe. This temperature was used for the thermo physical properties of the water 
vapor. Also, whenever any of the other performance limits was lower than the capillary 
limit, it was included on the chart. 
The capillary limit charts are presented for following cases, 
? Straight horizontal and vertical 
? 15? bended vertical 
? 30? bended vertical 
? 45? bended vertical 
? 60? bended vertical 
? 90? bended vertical 
Vertical refers to gravity assisted operation. 
Each chart also shows steady state heat input from the tests described in previous 
section. 
 
1
10
100
30 40 50 60 70 80 90
Evaporator Temperature (C)
Power (W)
Capillary Limit
Heat Input
 
Figure 5.16: Capillary limit for HP01 in straight horizontal orientation 
1
10
100
1000
30 40 50 60 70 80 90
Evaporator Temperature (C)
Power (W)
Capillary Limit
Heat Input
 
Figure 5.17: Capillary limit for HP01 in straight vertical orientation 
80 
1
10
100
1000
30 40 50 60 70 80 90
Evaporator Temperature (C)
Po
w
e
r (
W
)
Capillary Limit
Heat Input
 
Figure 5.18: Capillary limit for HP01 in 15? bended vertical orientation 
1
10
100
1000
30 40 50 60 70 80 90
Evaporator Temperature (C)
Power (W)
Capillary Limit
Heat Input
 
Figure 5.19: Capillary limit for HP01 in 30? bended vertical orientation 
81 
1
10
100
1000
10000
30 40 50 60 70 80 90 100 110
Evaporator Temperature (C)
Po
w
e
r (
W
)
Boiling Limit
Capillary Limit
Heat Input
 
Figure 5.20: Capillary limit for HP01 in 45? bended vertical orientation 
1
10
100
1000
30 40 50 60 70 80 90 100
Evaporator Temperature (C)
Power (W)
Capillary Limit
Heat Input
 
Figure 5.21: Capillary limit for HP01 in 60? bended vertical orientation 
82 
1
10
100
1000
10000
30 50 70 90 110 130 150
Evaporator Temperature (C)
Pow
e
r (W)
Boiling Limit
Capillary Limit
Heat Input
 
Figure 5.22: Capillary limit for HP01 in 90? bended vertical orientation 
0
50
100
150
200
250
30 50 70 90 110 130 150
Evaporator Temperature (C)
Power (W)
Vertical
Deg 15
Deg 30
Deg 45
Deg 60
Deg 90
Horizontal
 
Figure 5.23: Effect of bending angle on capillary limit for HP01 
83 
84 
From these charts it is evident that as the bending angle increases, the capillary 
limit decreases, mainly due to the decrease in the axial hydrostatic pressure drop. The 
loss due to the bending itself was not significant and is almost negligible compared to the 
loss in the axial hydrostatic pressure drop. Also for vertical, 45? and 90? configurations, 
the boiling limit was approached (Figure 5.20 and Figure 5.22) due to the high 
temperature and input heat flux during the later part of the operating range. Therefore, 
even though the conductance values for 45? and 90? were doubtful, it can be seen that the 
imminent dry out due to boiling limit coincided with the lack of steady state. This gives 
confidence in the results obtained. 
5.4.4 Specifications of HP02  
HP02 was identical to HP01 in all aspects; the only differences were in the 
geometric dimensions and the quantity of working fluid used. 
? Working length (L)  ? 274.1 mm  
? Evaporator length (L
e
)  ? 25.4 mm 
? Condenser length (L
c
)  ? 48.65 mm 
? Adiabatic section length (L
a
) ? 200 mm 
? Charge    ? 1.26g 
5.4.5 HP02 Bending Test Results 
During the testing of HP01, it was noticed that the hydrostatic pressure drop in the 
axial direction made all other pressure drops insignificant. Hence, testing was extended to 
85 
include bending in the horizontal orientation as well. In this orientation, only the normal 
hydrostatic pressure drop is effective and it is very small in comparison to the axial 
hydrostatic pressure drop. 
Results are included for following cases, 
? Straight horizontal and vertical 
? 15? bended horizontal and vertical 
? 30? bended horizontal and vertical 
? 45? bended horizontal and vertical 
? 60? bended horizontal and vertical 
? 90? bended horizontal and vertical 
Vertical refers to gravity assisted operation. 
 
0
20
40
60
80
100
120
140
160
102030405
Power (W)
C
opper Equiva
lence
0
 
Figure 5.24: Test results for HP02 in straight horizontal orientation 
0
20
40
60
80
100
120
0 1020304050607
Power (W)
C
opper Equiva
lence
0
 
Figure 5.25: Test results for HP02 in straight vertical orientation 
86 
0
20
40
60
80
100
120
140
0 5 10 15 20 25 30 35
Power (W)
C
o
pper E
quivale
nce
 
Figure 5.26: Test results for HP02 in 15? bended horizontal orientation 
0
20
40
60
80
100
120
0 1020304050607
Power (W)
C
opper Equiva
lence
0
 
Figure 5.27: Test results for HP02 in 15? bended vertical orientation
87 
0
20
40
60
80
100
120
140
0 5 10 15 20 25 30 35
Power (W)
C
o
pper E
quivale
nce
 
Figure 5.28: Test results for HP02 in 30? bended horizontal orientation 
0
20
40
60
80
100
120
0 1020304050607
Power (W)
C
opper Equiva
lence
0
 
Figure 5.29: Test results for HP02 in 30? bended vertical orientation
88 
0
20
40
60
80
100
120
0 5 10 15 20 25 30 35 40
Power (W)
C
o
pper E
quivale
nce
 
Figure 5.30: Test results for HP02 in 45? bended horizontal orientation 
0
20
40
60
80
0 1020304050607
Power (W)
C
opper Equiva
lence
0
 
Figure 5.31: Test results for HP02 in 45? bended vertical orientation
89 
0
20
40
60
80
100
120
0 5 10 15 20 25 30 35
Power (W)
C
o
pp
er Eq
uivale
n
c
e
 
Figure 5.32: Test results for HP02 in 60? bended horizontal orientation 
0
20
40
60
80
100
0 1020304050
Power (W)
C
opper Equiva
lence
60
 
Figure 5.33: Test results for HP02 in 60? bended vertical orientation
90 
0
20
40
60
80
100
120
140
10203040
Power (W)
C
o
pper E
quivale
nce
50
 
Figure 5.34: Test results for HP02 in 90? bended horizontal orientation 
0
20
40
60
80
100
120
0 1020304050
Power (W)
C
opper Equiva
lence
60
 
Figure 5.35: Test results for HP02 in 90? bended vertical orientation
91 
0
2
4
6
8
10
20406080
Bend Angle (Deg)
D
e
lta Temperatur
e (C)
10
28 W
16 W
4 W
 
Figure 5.36: ?T across HP02 for various bend angles in horizontal orientation 
0
2
4
6
8
10
12
14
16
18
20
20406080
Bend Angle (Deg)
D
e
lta Temperatur
e (C)
10
52 W
40 W
28 W
16 W
4 W
 
Figure 5.37: ?T across HP02 for various bend angles in vertical orientation
92 
84
86
88
90
92
94
96
1000 2000 3000 4000 5000 6000 7000
Time (sec)
Te
mper
atur
e (
C
)
 
Figure 5.38: Evaporator of HP02 could not attain steady state at 40W power input in 90? 
bended vertical orientation 
150
152
154
156
158
160
162
164
166
168
170
1000 2000 3000 4000 5000 6000 7000
Time (sec)
Te
mper
atur
e (
C
)
 
Figure 5.39: Heater of HP02 could not attain steady state at 40W power input in 90? 
bended vertical orientation 
93 
94 
5.4.6 Capillary Limits for HP02 
Capillary limit was calculated using the equations presented in Section 5.3.3. The 
procedure followed was similar to the one used for HP01 in Section 5.4.3. 
The capillary limit charts are presented for following cases, 
? Straight horizontal and vertical 
? 15? bended horizontal and vertical 
? 30? bended horizontal and vertical 
? 45? bended horizontal and vertical 
? 60? bended horizontal and vertical 
? 90? bended horizontal and vertical 
Vertical refers to gravity assisted operation. 
Each chart also shows steady state heat input from the tests described in previous 
section. 
 
1
10
100
20 40 60 80 100 120
Evaporator Temperature (C)
Po
w
e
r (
W
)
Capillary Limit
Heat Input
 
Figure 5.40: Capillary limit for HP02 in straight horizontal orientation 
1
10
100
1000
20 30 40 50 60 70 80
Evaporator Temperature (C)
Power (W)
Capillary Limit
Heat Input
 
Figure 5.41: Capillary limit for HP02 in straight vertical orientation 
95 
1
10
100
20 30 40 50 60 70 80 90 100
Evaporator Temperature (C)
Po
w
e
r (
W
)
Capillary Limit
Heat Input
 
Figure 5.42: Capillary limit for HP02 in 15? bended horizontal orientation 
1
10
100
1000
10000
20 30 40 50 60 70 80 90 100
Evaporator Temperature (C)
Po
w
e
r (
W
)
Boiling Limit
Capillary Limit
Heat Input
 
Figure 5.43: Capillary limit for HP02 in 15? bended vertical orientation
96 
1
10
100
20 30 40 50 60 70
Evaporator Temperature (C)
Po
w
e
r (
W
)
Capillary Limit
Heat Input
 
Figure 5.44: Capillary limit for HP02 in 30? bended horizontal orientation 
1
10
100
1000
20 30 40 50 60 70 80
Evaporator Temperature (C)
Po
w
e
r (
W
)
Capillary Limit
Heat Input
 
Figure 5.45: Capillary limit for HP02 in 30? bended vertical orientation
97 
1
10
100
20 30 40 50 60 70
Evaporator Temperature (C)
Po
w
e
r (
W
)
Capillary Limit
Heat Input
 
Figure 5.46: Capillary limit for HP02 in 45? bended horizontal orientation 
1
10
100
1000
20 30 40 50 60 70 80 90
Evaporator Temperature (C)
Po
w
e
r (
W
)
Capillary Limit
Heat Input
 
Figure 5.47: Capillary limit for HP02 in 45? bended vertical orientation
98 
1
10
100
20 25 30 35 40 45 50 55 60
Evaporator Temperature (C)
Po
w
e
r (
W
)
Capillary Limit
Heat Input
 
Figure 5.48: Capillary limit for HP02 in 60? bended horizontal orientation 
1
10
100
1000
20 30 40 50 60 70 80
Evaporator Temperature (C)
Po
w
e
r (
W
)
Capillary Limit
Heat Input
 
Figure 5.49: Capillary limit for HP02 in 60? bended vertical orientation
99 
1
10
100
20 30 40 50 60 70 80 90 100
Evaporator Temperature (C)
Po
w
e
r (
W
)
Capillary Limit
Heat Input
 
Figure 5.50: Capillary limit for HP02 in 90? bended horizontal orientation 
1
10
100
1000
10000
20 40 60 80 100 120
Evaporator Temperature (C)
Po
w
e
r (
W
)
Capillary Limit
Heat Input
Boiling Limit
 
Figure 5.51: Capillary limit for HP02 in 90? bended vertical orientation
100 
101 
40
60
80
100
120
140
160
180
200
20 30 90
Ca
pilla
ry Limit (W)
40 50 60 70 80
Temperature (C)
Straight
15 Deg
30 Deg
45 Deg
60 Deg
90 Deg
 
Figure 5.52: Effect of bending angle on capillary limit for HP02 in vertical orientation 
102 
Table 5.1: Effect of bending angle on capillary limit for HP02 in horizontal orientation 
Straight 15 Deg 30 Deg 45 Deg 60 Deg 90 Deg 
Temp 
(C) 
Capillary 
Limit 
(W) 
Temp 
(C) 
Capillary
Limit 
(W) 
Temp
(C) 
Capillary
Limit 
(W) 
Temp
(C) 
Capillary 
Limit 
(W) 
Temp
(C) 
Capillary
Limit 
(W) 
Temp
(C) 
Capillary
Limit 
(W) 
24.36  21.90 24.80 22.15 25.58 22.59 25.33 22.45 25.55 22.57 25.90 22.76
27.19  23.49 27.90 23.88 28.91 24.44 28.62 24.27 28.71 24.32 29.48 24.74
31.23  25.72 31.13 25.66 32.09 26.18 31.32 25.75 31.94 26.08 32.53 26.39
34.02  27.23 34.25 27.35 35.76 28.15 34.34 27.38 35.54 28.01 36.21 28.35
35.81  28.19 38.15 29.41 39.60 30.16 38.11 29.37 38.13 29.36 39.38 30.00
39.50  30.13 42.62 31.71 43.81 32.30 41.67 31.20 42.70 31.71 43.01 31.84
44.67  32.76 49.31 35.02 49.56 35.13 46.30 33.52 48.04 34.36 48.07 34.35
50.77  35.74 63.85 41.73 56.45 38.38 54.16 37.30 55.01 37.68 54.24 37.29
61.88   40.87 88.60 52.24 67.14 43.17 65.33 42.36 ? ? ? ? 
79.56  48.51 ? ? ? ? ? ? ? ? ? ? 
95.87  55.11 ? ? ? ? ? ? ? ? ? ? 
105.54  58.56 ? ? ? ? ? ? ? ? ? ? 
 
103 
From the above charts, it can be seen that the heat pipe was operating for all 
angles of the bending angle and the drop in the observed conductance values was because 
of the increased temperature drop along the heat pipe length. The termination of all the 
tests was either due to lack of steady state (Figure 5.38 and Figure 5.39) or stagnant 
conductance values (Figure 5.29 and Figure 5.31). As mentioned earlier for HP02, the 
bending loss was negligible and the capillary limit was mostly affected by the 
gravitational pressure drop. Hence the capillary limit variation for the horizontal 
orientation could not be plotted since all values overlap. A table is included showing the 
results (Table 5.1). It can be seen that similar to HP01, the capillary limit of HP02 in the 
vertical orientation decreases with increasing bending angle and this is mostly because of 
the decrease in the gravitational pressure drop in the axial direction. 
5.5 Results 
In the last section, the data presented showed that the heat pipe performance in 
terms of copper equivalence decreased as the input power was increased until it no longer 
maintained steady state. This can be seen during testing of HP01 in Figure 5.8 through 
Figure 5.14 and HP02 in Figure 5.24 through Figure 5.35. The increase in power coupled 
with the increasing bending angle drove down the conductance values of the heat pipe. 
This was due to the rise in the temperature difference along the heat pipe length. The 
possible causes for this were described in Section 5.2. As previously reported by 
Merrigan et al. [20], the axial temperature drop showed an increasing trend with 
increasing bending angle (Figure 5.15, Figure 5.36 and Figure 5.37) and did not 
significantly affect the operation of the heat pipe. However, with HP01, in some cases the 
104 
maximum power transferred increased with an increase in the bending angle. This was 
later traced to erroneous data recording, which was rectified during the testing of HP02. 
During tests for HP02, it was noted that the maximum power for which a steady state 
reading could be recorded decreased and the time required for attaining steady state at 
higher power levels doubled to approximately 60-90 minutes from a normal time of 30 -
40 minutes. 
The following limits are possible causes for heat pipe failures encountered during 
this work, 
5.5.1 Possible Capillary Limit 
It can be seen that the capillary limits calculated using the test data were higher 
than the input power for most of the tests carried out in Figure 5.16 through Figure 5.22 
and Figure 5.40 through Figure 5.51. When the heat pipe was in horizontal orientation the 
axial gravitational pressure drop was absent, capillary pumping pressure was the only 
driving factor. Therefore, all tests in horizontal orientation show a trend towards the 
capillary limit curve. Therefore, the possibility of encountering capillary limit in 
horizontal orientation was high.  
5.5.2 Boiling Limit Encountered 
Since the boiling limit is a radial flux limitation, it was found that the heat pipe 
was limited by boiling phenomenon in situations where the capillary limit was high and 
the operating temperatures and input heat flux were high enough to initiate nucleate 
105 
boiling (Figure 5.20, Figure 5.22, Figure 5.43 and Figure 5.51). The lack of steady state 
indicated possibility of incipient boiling in the evaporator region. 
5.5.3 Condenser Limit 
Apart from capillary and boiling limit, the third possibility was inadequate heat 
removal by the test setup. However, due to limitation of testing resources, this aspect 
could not be investigated and tubing of larger diameter was used in the water circulator to 
increase the flow rate of water over the condenser end of the heat pipe.  
5.5.4 Bending Issues 
During calculations of energy losses in the bended section of the heat pipe, it was 
found that it was very low and practically incapable in affecting the capillary limit. This 
can be explained by considering the Reynolds numbers for the vapor flow. The vapor 
flow was laminar for all the tests and Reynolds number was in the range of 10-900. The 
low density and the high viscosity minimized the expected losses due to centrifugal 
forces at the bend and hence the frictional pressure drop was negligible. The bending 
losses increased at higher powers as the Reynolds number increased due to the increased 
vapor density. 
 
106 
CHAPTER 6 
DISCUSSION 
6.1 Conclusion 
Two copper water heat pipes using sintered copper felt as the wick were 
fabricated. The aim of this investigation was to demonstrate the feasibility of bendable 
heat pipes. A thorough literature review showed that flexible heat pipes have attracted a 
lot of attention over the years. But all of the work published previously was geared 
towards making pipes which were either flexible or pre-bended during fabrication. It was 
found that no attempt was made to explore the possibility of stock heat pipes which can 
be bended or flexed in different shapes as required by the target application. 
The ongoing work on heat pipes made using sintered copper felt as the wicking 
medium was extended to explore this possibility. The results for bendable heat pipes are 
encouraging as the heat pipe was found to work well in all orientations and up to a bend 
of 90?. The effect of pressure loss due to bending was found to be negligible and three to 
four orders of magnitude smaller than the capillary pumping pressure. This shows that the 
increase in the temperature drop due to bending is because of the obstruction in the flow 
of liquid returning to the evaporator from the condenser. The investigation of wick 
separation due to bending showed a noticeable separation of the wick from the
107 
container walls. The vapor flow area was also reduced that directly reduced the heat 
carrying capacity. This lead to the build up of temperature at the evaporator end at 
constant heat input.  
The heat pipe HP02 was found to work well against gravity even though 
theoretically the capillary pumping pressure was not capable of overcoming the axial 
hydrostatic pressure drop. This indicates that the wick had a higher capillary pumping 
capacity than the one calculated. The difference was traced down to the effective 
capillary radius which was established using an empirical relation. The performance in 
adverse orientation increased with increasing bending angle, which was expected as the 
axial hydrostatic pressure drop decreased with half of the heat pipe eventually being 
oriented horizontally after the 90? bend. 
The benchmarking method used for comparing different heat pipes, which is 
designated as Copper Equivalence, was explained in detail. The usefulness and 
importance of copper equivalence was immediately recognized when the test setup had to 
be modified after testing of HP01. Copper equivalence allowed for comparing HP01 and 
HP02 even though both were tested on slightly different test setups. 
6.2 Future Work 
The possibility of multiple bends needs to be explored for this concept to be 
feasible in practice. The current heat pipes were found to be capable of working after 
multiple bends although no systematic testing was carried out. The possibility of the heat 
pipe working beyond 90? could also be explored. Even though such studies have been 
published in the past, post-fabrication bending was never investigated for these cases. 
108 
Similarly, the aspect of different combinations of working fluids and wicking mediums 
could also be explored. This will allow testing of bendable heat pipes at different 
operating temperature ranges. The effect of relative radius of curvature on the heat pipe 
performance needs further investigation. This aspect is slightly complex as once bent, the 
same heat pipe might be damaged if the bending radius is changed later. There is a 
possibility that the diameter of the heat pipe will play some role in the number of bends 
that can be introduced in the heat pipe. This could be investigated by testing a batch of 
heat pipes of different sizes. 
Wick separation studies could be performed for possible remedies including 
spring or mandrel supports during bending. The effective capillary radius for sintered 
copper felt should be measured experimentally. 
Although copper equivalence eliminates the need for knowing the contact 
resistance in the test setup, the knowledge of actual contact resistance values will greatly 
elevate the validity of such testing in the future. During higher temperature testing the 
contact resistance would play a major role as other parasitic losses are considerably 
constant due to presence of good insulation. 
 
109 
BIBLIOGRAPHY 
[1] Tohru Kishimoto, ?Flexible-heat-pipe cooling for high-power 
devices?, The International Journal of Microcircuits and Electronic 
Packaging, vol. 17, no. 2, pp. 98-107, 1994. 
[2] Shaoning Lu and His-Shang Li, ?Oscillatory mode with extremely 
high heat transfer rate in a flexible heat pipe?, InterPACK ?99: Pacific 
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