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J. Cent. South Univ. Technol. (2011) 18: 580−586

DOI: 10.1007/s11771−011−0734−2

Effects of bending on heat transfer performance of

axial micro-grooved heat pipe

JIANG Le-lun(蒋乐伦), TANG Yong(汤勇), PAN Min-qiang(潘敏强)

School of Mechanical and Automotive Engineering,

South China University of Technology, Guangzhou 510640, China

© Central South University Press and Springer-Verlag Berlin Heidelberg 2011

Abstract: Heat pipe is always bent in the typical application of electronic heat dissipation at high heat flux, which greatly affects its

heat transfer performance. The capillary limit of heat transport in the bent micro-grooved heat pipes was analyzed in the vapor

pressure drop, the liquid pressure drop and the interaction of the vapor with wick fluid. The bent heat pipes were fabricated and tested

from the bending angle, the bending position and the bending radius. The results show that temperature difference and thermal

resistance increase while the heat transfer capacity of the heat pipe decreases, with the increase of the bending angles and the bending

position closer to the vapor section. However, the effects of bending radius can be ignored. The result agrees well with the predicted

equations.

Key words: electronics cooling system; axial micro-grooved heat pipe; bending; heat transfer performance

1 Introduction

Heat pipe is a highly efficient heat transfer

component, and is widely used in electronics cooling,

such as the CPU of desktop and laptop [1−2]. With

higher integration of electronic components, heat pipe

always needs to be bent in the thermal structure design of

electronic cooling system because of the restriction of

the geometrical structure and its limited space. So far,

many researchers have investigated on the heat transfer

performance of bent heat pipe. BLISS et al [3] designed

a flexible heat pipe and found that bending little

influenced the heat transfer performance. MERRIGAN

et al [4] tested the heat pipe with bending angles of 0°,

90° and 180°, and found that the distribution of axial

temperature was associated with bending but the heat

pipe could work normally after being bent by 180°.

SHAUBACH and GERNERT [5] made comparisons on

the heat transfer performances of sintered felt heat pipe,

mesh heat pipe and V-grooved heat pipe before and after

bending. The results indicated that the heat transfer limit

of sintered wick is the best while the thermal resistance

of V-grooved heat pipe is the least. DHANANJAY and

DANIEL [6] theoretically analyzed and tested mini bent

sintered heat pipe, and found that with bending angle

Foundation item: Project(U0834002) supported by the Joint Funds of the National Nature Science Foundation of China and Guangdong Province; Project

(2009ZM0134) supported by the Foundational Research Funds for the Central Universities in China

Received date: 2010−03−29; Accepted date: 2010−06−29

Corresponding author: PAN Min-qiang, Associate Professor, PhD; Tel: +86−20−87114634; Fax: +86−20−87114634; E-mail: mqpan@scut.edu.cn

increasing, temperature became different between the

evaporator and condenser, and the heat transfer capacity

decreased. TAO et al [7] found that the heat transfer limit

of axial grooved heat pipes after bending by 90° is lower

than that of the straight one. WANG et al [8] researched

the start-up performance of different bending angles in

axial grooved heat pipes and found that the bending heat

pipe was more sensitive to the inclination.

A lot of work about bending heat pipe have been

done in the 1970s and 1980s [9−10], but little research

has been completely made on the heat transfer

performance of the axial micro-grooved heat pipe at

different bending position and bending radius. In this

work, the capillary limit of the bent axial micro-grooved

heat pipes was analyzed. Then the bent heat pipes were

fabricated and an experimental platform was set. Finally,

the experimental data were analyzed and discussed based

on the bending angle, the bending position and the

bending radius. These results can also be used as the

basic data of bent heat pipe to guide the thermal structure

design of electronic cooling system.

2 Theory analysis

The heat pipe has several performance limits, such as

sonic limit, boiling limit, entrainment limit and capillary

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J. Cent. South Univ. Technol. (2011) 18: 580−586

581

limit. However, it is bent at the adiabatic section, so only

the capillary limit is affected [11]. Therefore, only the

effects of bending on capillary limit were discussed in

this work.

Three simple hypotheses were set before the

analysis of the bent axial micro-grooved bending pipe:

1) Steady fluid flow and heat transfer,

2) The vapor phase and fluid phase in the state of

laminar flow, and

3) Constant fluid properties.

According to the hydrodynamics, the impact force

equation of the vapor to the wall and the wick fluid in the

adiabatic section as shown in Fig.1 can be deduced as

)cos 1 (

vvv

ανρ−=

AFx

(1)

ανρ

sin

vvv

AFy=

where ρv represents the vapor density of fluid (kg/m3),

ν

represents the vapor cross section of heat pipe (m2) and α

represents the bending angle.

2

2

(2)

v

represents the vapor velocity of fluid (m/s), Av

Fig.1 Impact force from vapor to fluid

The vapor pressure drop in the bending section can

be expressed as

2

v

bb

Kp

−=Δ

where Kb can be calculated as

⎞

⎜

⎝

2

According to the Cotter theory, the vapor pressure

drop inside the bent heat pipe is

4

1

av

2

fgvv

ρρ

rhr

where Q represents the total input heat transfer rate, μv

represents the vapor viscosity, la represents the length of

adiabatic section, rv represents the radius of vapor

section and hfg represents the fluid latent heat of

2

ν

(3)

⎟

⎠

⎞

⎜

⎝

⎛

+

⎟

⎠

⎛

=

2

sin047. 2sin946. 0

42

b

αα

K

(4)

2

π

4

8

π

2

v

b

fg

4

vv

4

2

4

v

νμ

K

h

Ql

Q

p

−−

⎟

⎠

⎞

⎜

⎝

⎛−

−=Δ

(5)

vaporization.

According to Darcy’s law, the liquid pressure drop

can be calculated as

ml

p

ρ

where m represents the mass flow rate of fluid, μl

represents the liquid viscosity, leff represents the effective

length of heat pipe, ρl represents the liquid density of

fluid, k represents the liquid permeability of wick and Aw

represents the cross section of wick.

Considering the effect from the vapor impact force

and gravity, the equation of the liquid pressure drop is

ml

p

ϕρ

ρ

where ε (ε<1) represents a geometrical parameter

concerned with the wick structure in the heat pipe and lhp

represents the length of heat pipe.

CHI [12] proposed the pressure balance equation in

the heat pipe:

Δpcap≥∆pv+∆pl±∆pg ( 8 )

where Δpcap represents the maximum capillary pumping

press and ∆pg represents the hydrostatic pressure due to

gravity.

Ignoring the vapor pressure drop of the straight pipe,

the calculating equation of capillary limitation can be

expressed as

2

gl

r

Q

+

where σ represents the surface tension of wick, re

represents the capillary radius of the evaporator, φ

represents the angle between the heat pipe and the

horizontal plane, fl represents the liquid friction

coefficient and fv is the vapor friction coefficient.

Considering Fx and ∆pb, Eq.(9) can be modified as

2

gl

r

Q

=

wl

eff

kA

l

l

μ

=Δ

(6)

w

v

A

2

vv

hpl

wl

eff

kA

l

l

) cos 1 (

sin

A

gl

ανερ

μ

−

−±=Δ

(7)

effvl

hpl

e

max,ca

)(

sin

lff

±

=

ϕρ

σ

(9)

effvl

2

v

b

w

v

A

2

vv

hpl

e

max,ca

)(

2

)cos1 (

sin

lff

K

A

+

−

−

−±

νανερ

ϕρ

σ

(10)

The capillary limitation of the heat pipe in this

experiment was tested in the horizontal orientation,

therefore, the influence from its gravity on the heat

transfer performance can be ignored, and Eq.(10) can be

simplified as

2

vv

1 (

2

Ar

Q

+

effvl

2

v

b

w

v

e

bmax,,ca

)(

2

)cos

lff

K

A

−

−

−

=

νανερ

σ

(11)

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582

3 Experimental

3.1 Fabrication of bent heat pipes

The rectangular grooves in the axial micro-grooved

heat pipe were fabricated by oil-filled high-speed spin

forming process [13−15]. This fabrication method has

the advantages of high depth to width ratio of the

grooves, adjustable tear number and different pipe radii.

The experimental heat pipes were cylindrical ones with a

length lhp=350 mm, an outside radius Rw=3 mm, a groove

height h=0.26 mm, and a groove width w2=0.18 mm, as

shown in Fig.2. Heat pipes were charged with 0.91 mL of

the purified water as the working fluid.

Fig.2 SEM image of wick structure

The bending position (S) can be expressed as

b/llS =

(12)

where lb represents the length from the heating end.

The heat pipes could be identified by the bending

position (30%, 50%, 70%) and bending radius (R15.0,

R17.5, R20.0), as shown in Table 1, and every sample

could be bent from 0° to 135° with increment of 45° at

each testing.

hp

Table 1 Bending parameters of heat pipes

Pipe number Position, S/% Bending radius, R/mm

1 30 20.0

2 50 20.0

3 70 20.0

4 30 17.5

5 50 17.5

6 70 17.5

7 30 15.0

8 50 15.0

9 70 15.0

3.2 Experimental setup

An experimental setup was designed for testing heat

transfer performance of bent heat pipes, as shown in

Fig.3. It was mainly composed of heating module,

cooling module and data collecting module. The

experimental setup was placed on a horizontal platform

with ambient temperature 25 °C, and the adiabatic

section of the heat pipe was exposed in the air.

The heating module was used to heat the heat pipe

as the vapor section at different input power, while the

cooling module was designed to cool as the condenser

section of heat pipe at a constant temperature. The data

collecting module consisted of five pieces of thermal

resistor Pt100, data collecting module (NI Compact

DAQ and data collecting card USB-9217), and NI

labview data acquisition program. The position of

thermal resistor was marked in Fig.3. T1 and T2 were

located at the two ends of the heating section, T4 and T5

at two ends of the cooling section, and T3 at the adiabatic

section, which were all pressed tightly to the heat pipe

wall with spring force and insulated from environment.

Fig.3 Schematic diagram of experimental setup (mm)

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J. Cent. South Univ. Technol. (2011) 18: 580−586

3.3 Experimental procedure

The experimental test was performed to investigate

the heat performance of the bent heat pipes. The constant

temperature bath was adjusted at (50±0.5) °C and the

flux of glass rotameter at (200±1.5) L/h to keep the

working temperature of heat pipe at 60−70 °C, which

was a reliable temperature value for general electronic

components. Load power was varied from 25 W with

increment of 5 W, and the test would be stopped when

the temperature at the evaporator end cap increased

drastically due to dryout. The wall temperature of the

heat pipe was recorded at the steady state by each

thermal load step. The results of the test included the

errors in the measurement, such as tolerance of the input

power (±0.5 W) and temperature fluctuation error

(±0.1 °C).

4 Results and discussion

4.1 Effects of bending angle

When the input power reaches a value Qin, a smaller

input power increase, ∆Qin, will make the temperature at

the evaporator end abruptly increased compared with

other temperatures at the evaporator. The input power Qin

can be defined as the heat transfer limit [16].

Fig.4(a) presents the effect of bending angles on the

wall temperature distribution along the longitudinal axis

of pipe 2 with the input power of 30 W. The temperature

difference is below 3 °C, which indicates that the heat

pipe still has good isothermal characteristics with

different bending angles. Fig.4(b) presents the effect of

bending angles on the temperature difference with

different input powers of pipe 2. When the input power is

below heat transfer limit, the temperature difference is

small, which means that the thermal equilibrium, namely

isothermal property of the bending pipe from the

evaporator to the condenser is well accomplished.

However, the temperature difference is increased with

the increase of the bending angle at the same input power.

According to Eqs.(4), (5) and (7), the vapor pressure

drop and liquid pressure drop increase as the bending

angle increases, and the pressure drop may largely affect

the temperature distribution of the heat pipe [17]. When

the input power exceeds the limit of the bent heat pipe,

temperature difference will increase dramatically. This is

because the pressure drop balance, as presented in Eq.(8),

is broken and the capillary force of working fluid is not

enough to flow from the condenser to the evaporator.

There is not enough working fluid to wet the top part of

the vapor section, and the bent heat pipe is dry.

The thermal resistance of heat pipe is defined as

583

Fig.4 Effect of bending angles on wall temperature distribution

along longitudinal axis (a) and temperature difference with

different input powers (b)

TT

R

=

in

c,avee,ave

Q

−

(13)

where Te,ave represents the average temperature of the

evaporator and Tc,ave is the average temperature of

condenser.

Fig.5 presents the effect of bending angles on the

thermal resistance under different input powers of pipe 2.

When the input power is below heat transfer limit,

thermal resistance is 0.07−0.10 °C/W, which indicates

that heat pipe works well at a relatively steady thermal

resistance value with different bending angles. However,

the thermal resistance increases with the increase of

bending angle at the same input power. Pressure drop

increases as the bending angle increases at the same heat

flux, and the returned flow of the condensed liquid to

evaporator decreases, therefore, the thermal resistance

increases by a relatively thick liquid film of the

condenser. When the input power exceeds the heat

transfer limit, the thermal resistance abruptly increases,

due to the fact that the end cap of the evaporator is dry,

which means that the heat transfer of the heat

pipe is only the heat conduction by the wall without high

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584

Fig.5 Effect of bending angles on thermal resistance under

different input powers

speed vapor.

Fig.6 presents the effect of bending angle on the

heat transfer limit of pipe 2. The heat transfer limit

decreases greatly with the increase of the bending angle,

and almost 30% at the bending angle of 45° compared

with that of the straight heat pipe. However, heat transfer

limit decreases especially fast at the bending angles

between 0° and 45° and is slowed down above 45° with

increasing the bending angle. According to Eq.(11), the

capillary limit decreases as the bending angle increases,

so Eq.(11) agrees with Fig.6. According to Eq.(2), the

high-speed flowing vapor impacts the working fluid in

the grooves and disperses part of working fluid in the

bending section, which further affects the heat transfer

limit of heat pipe.

Fig.6 Effect of bending angles on heat transfer limit

4.2 Effects of bending position

In the heat dissipation design of electronic

products，the adiabatic section of heat pipe is not

virtually adiabatic but always exposed to the air, so the

adiabatic section in this experiment is placed in the air.

Therefore, there is temperature difference between the

adiabatic section and environment, so fluid condensation

also happens in the adiabatic section and the vapor flow

velocity in the adiabatic section is not a constant value

but decreases with the increase of the length.

Fig.7(a) presents the effect of bending position on

the wall temperature distribution along the longitudinal

axis of pipes 4, 5 and 6 at the bending angle of 90° with

input power of 30 W. The temperature difference is less

than 2.5 °C, which indicates that heat pipes have good

isothermal property with different bending positions.

Fig.7(b) presents the effect of bending position on the

temperature difference under different input powers at

the bending angle of 90° of pipes 4, 5 and 6. When the

input power is below heat transfer limit, temperature

difference increases with the input power. This is due to

the fact that the vapor flow velocity increases with

increasing input power. According to Eq.(5), the vapor

pressure drop also increases, therefore, the temperature

difference increases [16]. The temperature difference

generally increases as the bending position value, S,

decreases at the same input power. It is because the vapor

flow velocity and the vapor pressure drop at different

bending positions are various. When the input power

exceeds the limit of the heat pipes, the heat transfer

performance is sharply deteriorated.

Fig.7 Effect of bending position on wall temperature

distribution along longitudinal axis (a) and temperature

difference under different input powers (b)

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585

Fig.8 presents the effect of bending positions on the

thermal resistance under different input powers at

bending angle of 90° of pipes 4, 5 and 6. When the input

power is below the limit of the heat pipes, the thermal

resistance increases with decreasing bending position

value, S, and the thermal resistance is 0.067−0.11 °C/W.

According to Eq.(7), the vapor flow velocity affects the

liquid pressure drop at different bending positions, and

thickness of the liquid film at the condenser changes,

which causes the variety of thermal resistance.

Fig.8 Effect of bending position on thermal resistance under

different input powers

Fig.9 presents the effect of bending position on the

heat transfer limit of pipes 4, 5 and 6. The heat transfer

limit of pipes 4, 5 and 6 is about 55 W in their straight

state. However, compared with the straight heat pipe, the

maximal decrease of heat transfer limit is about 40% at

the bending position value of 30%, while the minimal

decrease is about 15% at the bending position value of

70%. So the heat transfer limit is increased obviously

with the increase of the bending position value, S. The

vapor flow velocity in the adiabatic section decreases

with the increase of the bending position value, S. In

accordance with Eq.(11), the vapor flow velocity will

Fig.9 Effect of bending positions on heat transfer limit

decrease the capillary limit in the heat pipe by

influencing the vapor pressure drop and fluid pressure

drop.

4.3 Effects of bending radius

Fig.10(a) presents the effect of bending radius on

the wall temperature distribution along the longitudinal

axis of pipes 1, 4 and 7 at the bending angle of 90° with

the input power of 30 W. The temperature difference is

less than 2.5 °C, so heat pipes have good isothermal

property under different bending radius. Fig.10(b)

presents the effect of bending radius on the temperature

difference under different input powers at the bending

angle of 90° of pipes 4, 5 and 6. The temperature

difference is always less than 3 °C when the input power

is below the heat transfer limit. As shown in Fig.10, the

bending radius has little effect on the temperature

difference. This is because the bending radius of the axial

micro-grooved heat pipe is always larger than 15 mm

due to the restriction of the bending technique, and large

radius results in little influence on bending pressure loss,

as a result, the effects of bending angle on the

temperature difference can be ignored.

Fig.11 presents the effect of bending radius on the

Fig.10 Effect of bending radiuses on (a) wall temperature

distribution along longitudinal axis; (b) temperature difference

under different input powers

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Fig.11 Effect of bending radiuses on thermal resistance under

different input powers

thermal resistance under different input powers at

bending angle of 90° of pipes 1, 4 and 7. The thermal

resistance is 0.067−0.085 °C/W and its fluctuation is

little under different bending radius compared with the

straight heat pipe. This indicates that bending radius

shows little effect on thermal resistance of heat pipes.

Fig.12 presents the effect of bending radius on the

heat transfer limit of pipes 1, 4 and 7. Fluctuation of the

heat transfer limit is within 5 W under different bending

radius. The possible reason lies in the fact that the

bending has little damage to the grooves in the heat pipe,

so the capillary force is almost the same at different

bending radius. The vapor pressure drop at different

bending radius can be ignored, so the capillary limit

varies little.

Fig.12 Effect of bending radiuses on heat transfer limit

5 Conclusions

1) Heat pipe can still keep good isothermal property

after being bent. But the temperature difference increases

with increasing the bending angle and decreasing the

bending position value, S. The bending radius shows

little effect on the temperature difference.

2) The thermal resistance of the bending heat pipe

keeps below 0.11 °C/W. The bending angle and bending

position shows great influence on the thermal resistance,

but the effect of the bending radius can be ignored.

3) The bending of the heat pipe has very great effect

on the heat transfer limit. The overall heat transfer

coefficient is decreased by almost 30% at the bending

angle of 45° and by about 40% at the bending position of

30% compared with that of the straight heat pipe.

However, the bending radius affects little on the heat

transfer limit of the heat pipe.

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(Edited by LIU Hua-sen)