Effects of bending on heat transfer performance of axial micro-grooved heat pipe

Article (PDF Available)inJournal of Central South University of Technology 18(2):580-586 · April 2011with215 Reads
DOI: 10.1007/s11771-011-0734-2
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 wordselectronics cooling system–axial micro-grooved heat pipe–bending–heat transfer performance

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Available from: Lelun Jiang, Oct 16, 2014
J. Cent. South Univ. Technol. (2011) 18: 580586
DOI: 10.1007/s1177101107342
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 [12]. 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
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 [910], 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
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: 20100329; Accepted date: 20100629
Corresponding author: PAN Min-qiang, Associate Professor, PhD; Tel: +862087114634; Fax: +862087114634; E-mail: mqpan@scut.edu.cn
J. Cent. South Univ. Technol. (2011) 18: 580586
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
)cos1(
v
2
vv
ανρ
= AF
x
(1)
ανρ
sin
v
2
vv
AF
y
= (2)
where ρ
v
represents the vapor density of fluid (kg/m
3
),
v
ν
represents the vapor velocity of fluid (m/s), A
v
represents the vapor cross section of heat pipe (m
2
) and α
represents the bending angle.
Fig.1 Impact force from vapor to fluid
The vapor pressure drop in the bending section can
be expressed as
2
2
v
bb
ν
Kp =Δ (3)
where K
b
can be calculated as
+
=
2
sin047.2
2
sin946.0
42
b
αα
K (4)
According to the Cotter theory, the vapor pressure
drop inside the bent heat pipe is
2
π
4
8
π
4
1
2
v
b
fg
4
vv
av
2
fg
4
vv
2
4
v
ν
ρ
μ
ρ
K
hr
Ql
hr
Q
p
=Δ
(5)
where Q represents the total input heat transfer rate, μ
v
represents the vapor viscosity, l
a
represents the length of
adiabatic section, r
v
represents the radius of vapor
section and h
fg
represents the fluid latent heat of
vaporization.
According to Darcy’s law, the liquid pressure drop
can be calculated as
wl
effl
l
kA
ml
p
ρ
μ
=Δ (6)
where m represents the mass flow rate of fluid, μ
l
represents the liquid viscosity, l
eff
represents the effective
length of heat pipe, ρ
l
represents the liquid density of
fluid, k represents the liquid permeability of wick and A
w
represents the cross section of wick.
Considering the effect from the vapor impact force
and gravity, the equation of the liquid pressure drop is
w
v
2
vv
hpl
wl
effl
l
)cos1(
sin
A
A
gl
kA
ml
p
ανερ
ϕρ
ρ
μ
±=Δ
(7)
where ε (ε<1) represents a geometrical parameter
concerned with the wick structure in the heat pipe and l
hp
represents the length of heat pipe.
CHI [12] proposed the pressure balance equation in
the heat pipe:
Δp
cap
≥∆p
v
+p
l
±p
g
(8)
where Δp
cap
represents the maximum capillary pumping
press and p
g
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
effvl
hpl
e
max,ca
)(
sin
2
lff
gl
r
Q
+
±
=
ϕρ
σ
(9)
where σ represents the surface tension of wick, r
e
represents the capillary radius of the evaporator, φ
represents the angle between the heat pipe and the
horizontal plane, f
l
represents the liquid friction
coefficient and f
v
is the vapor friction coefficient.
Considering F
x
and p
b
, Eq.(9) can be modified as
effvl
2
v
b
w
v
2
vv
hpl
e
max,ca
)(
2
)cos1(
sin
2
lff
K
A
A
gl
r
Q
+
±
=
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
effvl
2
v
b
w
v
2
vv
e
bmax,,ca
)(
2
)cos1(
2
lff
K
A
A
r
Q
+
=
νανερ
σ
(11)
J. Cent. South Univ. Technol. (2011) 18: 580586
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 [1315]. 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 l
hp
=350 mm, an outside radius R
w
=3 mm, a groove
height h=0.26 mm, and a groove width w
2
=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
hpb
/llS =
(12)
where l
b
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.
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. T
1
and T
2
were
located at the two ends of the heating section, T
4
and T
5
at two ends of the cooling section, and T
3
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)
J. Cent. South Univ. Technol. (2011) 18: 580586
583
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 6070 °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 Q
in
, a smaller
input power increase, Q
in
, will make the temperature at
the evaporator end abruptly increased compared with
other temperatures at the evaporator. The input power Q
in
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
Fig.4 Effect of bending angles on wall temperature distribution
along longitudinal axis (a) and temperature difference with
different input powers (b)
in
c,avee,ave
Q
TT
R
=
(13)
where
T
e,ave
represents the average temperature of the
evaporator and
T
c,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 0.070.10 °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
J. Cent. South Univ. Technol. (2011) 18: 580586
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)
J. Cent. South Univ. Technol. (2011) 18: 580586
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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 0.0670.11 °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
J. Cent. South Univ. Technol. (2011) 18: 580586
586
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 0.0670.085 °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)
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