Steady and Transient Heat Transfer Characteristics
of Flat Micro Heatpipe
by Yuichi Kimura * , Yoshio Nakamura * , Junji Sotani * 2 and Masafumi Katsuta * 3

Recently, a flat micro heatpipe of slim-profile for use in electronic equipment
like personal computers is drawing attention because of its ease of mounting
and attachment to heat sources. In this paper steady-state heat transfer characteristics of thisheatpipe have been experimentally confirmed in detail, and a prediction method for its maximum
heat transfer rate is proposed. Moreover in performance measurement, transient heat transfer
characteristics due to step input have also been evaluated since actual operation of the heatpipe
itself normally starts from room temperature.
In the steady-state measurement, evaluation was carried out while the temperature of adiabatic section of the heatpipe was maintained at 50°C by adjusting the cooling capacity of a fan, andthe amount of working fluid and the lengths of evaporating and condensing sections were taken
as parameters. As the result, it has been confirmed that the maximum heat transfer rate increases as the amount of working fluid increases, and that the longer the lengths of evaporating andcondensing sections, the greater the maximum heat transfer rate. In view of these results, theequation of pressure balance has been reexamined in order to predict the maximum heat transfer rate more accurately.
In the transient-state measurement, temperature rise due to step input was held constant by
adjusting the cooling capacity of Peltier elements mounted on the condensing section of theheatpipe, and the amount of working fluid, the temperature of heatsink and the time interval ofstep input were taken as parameters. As the result, it has been confirmed that the maximum heattransfer rate measured using a step input becomes smaller than that of the steady state due tothe lowered working temperature.

ABSTRACT1.

INTRODUCTION

In recent years, laptop PCs are proceeding to havediversification of onboard devices and downsizing of
the casing, while the heat generation rate of the CPU
continues to increase —rather contradicting factors
because basically the higher the heat generation rate, thegreater the heat-dissipating space needed. Accordingly
in the near future, there will be a need for a new coolingtechnology 1) that can improve design flexibility, needed
space and heat-dissipating performance to solve these
problems.
Thus micro heatpipes (hereafter called µHP) are beginning to be used as a cooling device for laptop PCs. The
category of heatpipes generally include various new
heatpipes 2)~6) that are under extensive and detailed study
such as self-exciting mode oscillating-flow (SEMOS)
heatpipe, oscillating-flow heatpipe, pulsating heatpipe* Ecology and Energy Lab., R&D Div.
* 2 Electronics and Automotive Systems Co.
* 3 Advanced Research Institute for Science and Engineering,
Waseda Univ.

(PHP) and capillary pumped loop (CPL) heatpipe, and it
is expected that these new heat transfer devices will possibly see practical applications.
The slim-profiled flat µHP that has recently been developed is drawing attention because the heatpipe has theadvantages of ease of mounting in PCs assuring a sufficient contact surface with heat-generating devices. While
this flat µHP has geometrical features such that its crosssectional area of the vapor channel for the working fluid
is very small in comparison with cylindrical heatpipes,
the effects of this feature on the working principle andthe heat transfer performance have not been clarified yet.
Accordingly, this paper presents the basic data of this flat
µHP together with thermal characteristics that are indispensable for optimizing its inner structure.

2.

EXPERIMENTAL SETUP AND METHOD

Figure 1 shows the experimental setup for thermal
performance measurement consisting of the main test
apparatus, a power supply and a data acquisition system
combined with a personal computer. As shown in Figure
2, the µHP sample was provided with a micro ceramic

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Schematic of experimental setup.

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Detail of heater and evaporating section.

Table 1

Sample and conditions for evaluation.

Length of HP (mm)Thickness of HP (mm)

157
1.0

Length of evaporating section (mm)10, 20, 30, 40, 50

Length of condensing section (mm)40, 60, 80, 100

Amount of working fluid (vol%)20, 25, 30, 35, 40, 45

heater for heat input, whose length —marked by X in
the Figure— could be changed to make it adapted tovarious test conditions. To enhance thermal conduction
from the heater to the µHP sample, thermal compound
Nomenclatureahalf width of vapor channelAsurface areabhalf height of vapor channelddiameter of screen wireD
hydraulic diameter
fReD Poiseuille numberggravitational constanthheat transfer coefficient
Hfg latent heat of evaporationHheight of liquid channelKpermeability
Llength of heatpipeNpore numberPpressureQ
input heatR
gas constantrc
effective pore radius

rr
s
S
T
u
V+

was applied to the interface, and the evaporating andadiabatic sections were thermally insulated using athermal insulation so that all the input heat was dissipatedthrough the condensing section. At the condensing
section, a fin array with a fan was used for sufficientcooling, while the capacity of the fan was adjusted tomaintain a constant temperature of 50°C in the adiabatic
section. All the experiments for steady-state measurement
were carried out under the condition of 50°C for the
adiabatic section, and besides, all the data were taken
after the temperature of this section was stabilized.
With respect to the µHP sample, braided wire of copper
was used as wick; deionized water was used as working
fluid; the length and the thickness of all the samples were
157 mm and 1 mm, respectively, as shown in Table 1; andK-type thermocouples were mounted on the surface at aninterval of 5 mm totaling 29 in number.
The experiments were carried out, taking the amountof working fluid and the lengths of evaporating and condensing sections as parameters, with the aim of clarifying
the thermal characteristics of flat µHPs as well as of proposing a capillary force-based prediction method for the
maximum heat transfer rate that is useful for many applications.
2.1

Heat Transfer Coefficient and Maximum Heat
Transfer Rate
The heat transfer coefficient he was calculated by the The
heat transfer coefficient he was calculated by the equation������������������������
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Figure 3 shows the relationship between the heat transfer coefficient at the evaporating section and heat input.
In the Figure, dryout occurs at a point where the heattransfer coefficient shows a marked drop, and the maximum heat transfer rate is defined as the heat input at the
point just before dryout. Accordingly, as can be seen from

effective pore radius
aspect ratio
surface area
temperaturemean velocity
amount of working fluid

Greek letters∆ P pressure loss, or pressure driving forceαcoefficient of evaporation and condensationεvoid ratioζshrinkage factorθ
contact angleµ
viscosityρ
densityσsurface tensionτshearing stressφcontact angleΨnon-dimensional pressure drop

Subscripts
adadiabaticccapillary force
con condensationeevaporation
eff effective
eva evaporationggas
liquid, or liquid flowlcliquid channelsslag, or paddle
v
vapor
v'
vapor
vc
vapor channelw
wick

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2005

4

to a different channel height, the surplus fluid turns into aliquid slug at the end of the condensing section without
being dispersed over the pipe length. The condition for
liquid slug formation can be represented by the following
equation.

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Figure 3

Relationship between the heat transfer coefficientand heat input.

Figure 3, the valued of 8.5 W was taken as the maximum
heat transfer rate for this µHP.

3.

EXPERIMENTAL RESULTS ANDDISCUSSIONS

3.1 Steady-State Measurement
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Temperature distribution on µHP.

Figure 4 shows a temperature distribution on the surface
of a µHP. A marked temperature drop is observed at
the end of the condensing section, presumably caused
by a liquid slug. Thus it is thought that the effective
length of a µHP Leff representing the circulation lengthof working fluid has to be redefined as different from theconventional, taking the length of the liquid slug into
consideration as follows.
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When a µHP is placed horizontally, and if the capillary
force associated with the size of the vapor channel isgreater than the difference in the gravitational force due(4)

3.1.2. Heat Transfer Performance
Figure 5 shows the relationship between the maximum
heat transfer rate and the length of condensing sectionof µHP with braided wire wick having different amounts
of working fluid, using the length of evaporating section
as a parameter. It can be seen from the Figure that the
maximum heat transfer rate increases as the lengthof either the evaporating section or the condensing
section increases. In view of the capillary force, this is
attributable to the fact that, in either case mentioned
above, the length of the adiabatic section shortens
resulting in shortening of the effective length, in addition
to reduction of the pressure loss. When the lengths ofthe evaporating and condensing sections are equal, it isseen that the maximum heat transfer rate increases as
the amount of working fluid increases. It is suggested
that the more the encapsulated working fluid the more
surplus it becomes, so that the fluid forms a liquid slugat the condensing section end thereby bringing an effectequivalent to shortening of the effective length of theµHP. Consequently, it is assumed that the surplus amountforms a liquid slug as shown in Figure 4.
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Steady and Transient Heat Transfer Characteristics of Flat Micro Heatpipe

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Maximum heat transfer rate of µHPs with different
amount of working fluid.

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2005

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Steady and Transient Heat Transfer Characteristics of Flat Micro Heatpipe

3.1.3. Prediction Equation for Maximum Heat Transfer
Rate
Judging from the experiments above mentioned, it issuggested that the conventional model for heatpipes, i.e.
capillary force-based model, applies to this flat µHP also.
Accordingly, the following model for the braided wire wick
was used to predict the maximum heat transfer rate.
Figure 6 shows a flat µHP model with an ideal braided
wire wick, whereby the wick is assumed to be located at
the center of the pipe, and liquid channels are formed in
the space between the wires as shown in the enlarged
illustration in the Figure. Table 2 shows the dimensions of
the wick configuration.

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(7)

Each term in Equation (7) is explained in the following.
(1) Driving force due to capillary force: ∆ Pc
The capillary force of the wick acts as a driving force
for normal circulation of the working fluid 9), and is represented by:circulation circulation circulation��� ��������������� ���(8)While the contact angle θ for a combination of copper
and water is said to range generally between 33°~ 40°, avalue of 38° was adopted because this is most frequently
used 4).
(2) Pressure drop due to liquid flow: ∆ P 3)
According to Darcy's Law, ∆ P can be represented byusing the above-mentioned K value as follows.
(9)(3) Pressure drop due to evaporation and condensation: ∆ Peva and ∆ Pcon 10), 11)These can be calculated from an analysis based onmolecular dynamics using the following equations.

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Figure 6

Cross-section of flat µHP and enlarged illustrationof wick.

Table 2Dimensions of the wick configuration shown in
Figure 6.
a1.938 mmb0.250 mmd0.104 mmW

0.052 mmH

0.052 mm

Lc1

0.00697 mm

Lc2

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(10)

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(4) Pressure drop due to liquid slug: ∆ Ps 7)
When a liquid slug is formed, not only that portion
does not function as a heatpipe, but also a pressure drop
occurs due to its existence. As shown in Figure 7, a pressure difference in capillary force appears due to the slug
formation at the pipe end, lowering the air-liquid interfacepressure Pg over the vapor pressure Pv 7).

Important parameters of permeability K and effective
pore radius rc 5) are given by the following equations.
4)

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Another important parameter of Poiseille number fReD
can be uniquely determined from the geometrical configuration of the cross-section. Pressure balance is taken
into consideration to predict the maximum heat transferrate, that is, a pressure drop is generated by the working
fluid in circulation, and normal circulation of the working
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Figure 7

Configuration of liquid slug.

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Steady and Transient Heat Transfer Characteristics of Flat Micro Heatpipe

Effective pore radius r r corresponding to the vapor
space can be represented by Equation (13).
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(5) Pressure drop due to vapor flow: Pv
Although the pressure drop due to vapor flow has heretofore been calculated by a simplified equation for pressure drops for a circular cross-section using an equivalentradius, the equation is considered to be insufficient forthe calculation of flat µHPs with an extremely small ratioof b/a. Therefore, analysis of rectangular cross-section
flow 9) has been carried out to obtain a more accurate
expression for the pressure drop due to vapor flow. As
illustrated in Figure 8, the pressure drop in one of thevapor channels is calculated based on a rectangularcross-section model as follows.

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The equation is used in an iterative manner in which
the maximum heat transfer rate is calculated first without
considering the pressure drop due to vapor-liquid interaction, and subsequently, the rate is recalculated in turntaking the pressure drop into consideration using the first
result. Figure 9 shows the iteratively calculated results,
where the maximum heat transfer rates are compared
between the predicted values based on Equation (7) andthe experimental values that change, under the influenceof the lengths of condensing and evaporating sections,according to the amount of working fluid.
As can be seen from the Figure, the experimental andpredicted values show good agreement, confirming thevalidity of Equation (7), which aimed at predicting the
maximum heat transfer rate analytically based on the concept of pressure balance due to capillary force. In casethe amount of working fluid is changed, prediction can bemade accurately by introducing a suitable effective length
into the Equation.
Thus it has become clear that the pressure drop due tovapor flow near dryout accounts for a large portion of thetotal pressure drop.

Figure 8�Configuration of vapor channel with rectangularcross-section model.

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Using Equations (5) through (14), the maximum heattransfer rate can be calculated to obtain a predictive
value. It was found that, when the experimental and calculated results were compared, generally speaking the
calculated value was higher than the experimental value.
As a cause for this, it may be that the actual heat transfer process involves an additional factor of vapor-liquidinteraction, and accordingly, investigation was carried out
concerning this factor.
(6) Vapor-liquid interaction
In view of the study by Kyu Hyung Do et al. 4), it isthought that there is an interaction between the countercurrents of vapor and liquid even in the case of the
braided wire wick, although the interaction may be lesssignificant than in the case of a groove wick having alarge contact surface between the two phases of vapor
and liquid. Considering that this interaction influences thecharacteristics of flat µHP as well, the following equations

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proposed by the aforementioned authors were applied
to the µHP, where Ψ denotes non-dimensional pressure
drop 3).

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b) Amount of working fluid: 40.9 vol%Figure 9Comparison of maximum heat transfer rate between
calculated and experimental values.

Furukawa Review, No. 27

2005

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Steady and Transient Heat Transfer Characteristics of Flat Micro Heatpipe

3.2 Transient-State Measurement
The conditions for the transient-state measurement
were such that temperature rise due to step input washeld constant by adjusting the cooling capacity of
Peltier elements mounted on the condensing section;
the amount of working fluid, heatsink temperature andtime interval of step input were taken as experimental
parameters; transient data were measured from justbefore the heat input to the steady state; and thetransient-state experiments were repeated until dryout.
Figure 10 shows the temperature changes of selected
sections in response to step input, and Table 3 compares
the maximum heat transfer rates of the steady- andtransient-state measurements in conjunction with different
amounts of working fluid.
It can be seen that, although rather dependent on theworking temperature, the maximum heat transfer rate
for the transient state is generally lower than that for thesteady state, and the rate becomes lower as the cooling temperature decreases. Consequently, in practicalapplications for cooling IC chips and the like, it is neces-sary for the design to have a margin of 20 % to 30 % withrespect to the heat rate to be dissipated.

4.

CONCLUSION(1) With respect to a flat µHP with braided wire wick, theeffective length has been redefined, and a pressurebalance equation based on capillary force has been
proposed enabling the prediction of maximum heattransfer rate.
(2) Using a prediction equation for maximum heattransfer rate, it has been shown that the pressure
drop due to vapor flow accounts for a dominantportion of the total pressure drop.
(3) It has been confirmed that the maximum heat transfer
rate for the transient state is lower than that for thesteady state, and the rate becomes lower as thecooling temperature decreases.

REFERENCES
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������� ���� ���1) J. Niekawa et al.: “Introduction to Micro-Heatpipe and Heat
Dissipation Technology,” Nikkan Kogyo Shimbun Publishing,(1999). (in Japanese)2) Amir Fagri: HEAT PIPE SCIENCE AND TECHNOLOGY, (1978),Taylor & Francis.
3) Joung Ki Seo: “A Generalized Mathematical Model to Account for
the Effect of Liquid-Vapor Interfacial Shear Stress of a Heat Pipewith a Grooved Wick Structure, ”The 7th International Heat Pipe
Symposium, Jeju, Korea, (2003) 92-96.
4) Kyu Hyung Do: “Mathematical Modeling and Thermal Optimizationof a Micro Heat Pipe with Curved Triangular Grooves,” The 7thInternational Heat Pipe Symposium, Jeju, Korea, (2003) 325-331.
5) Hidehiko Noda: “Effect of Mesh Shape on Maximum Capillary
Pressure of Plain Weave Screen,” The 11th International Heat Pipe
Conference, Tokyo, vol 2 (1999) 85-89.
6) H. Kosai et al.: “Heat Transfer Characteristics of a Heatpipe with
Composite Metal Screen Wick,” Proc. 36th Japan Heat Transfer
Symposium, (1999) 653. (in Japanese)
7) M. Murakami et al.: “Heat Transfer Limit of Flat Heatpipe,” Trans.
JSME, B54-501 (1988) 1157. (in Japanese)
8) H. Kosai et al.: “Effective Pore Radius of Metal Screen Wick,”Trans. JSME, B56-521 (1990) 168. (in Japanese)
9) K. Watanabe: “Hydrodynamics —Flow and Loss—,” Maruzen
Publishing, (2002). (in Japanese)
10) Japan Association for Heatpipe: “Practical Heatpipe,” Nikkan
Kogyo Shimbun Publishing, (2001). (in Japanese)11) K. Oshima et al.: “Heatpipe Engineering,” Asakura Shoten
Publishing, (1981). (in Japanese)

Figure 10 Maximum heat transfer rates under steady- andtransient-state conditions.
Table 3Comparisons of maximum heat transfer rates understeady- and transient-state conditions.
Steady stateTransient state

Amount ofworking
fluid (vol%)Adiabatic section
temp.: 50°C

Cooling temp.:
20°C

Cooling temp.:
10°C

20.4

8.09 W

6.01 W

4.97 W

31.2

8.51 W

7.03 W

6.04 W

40.9

10.05 W

9.01 W

8.05 W

Length of evaporating section: 20 mm
Length of condensing section: 80 mm

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