miniature heat-pipe thermal performance prediction tool – software development

Miniature heat-pipe thermal performance prediction tool ±software development

V. Maziuk a, A. Kulakov a, M. Rabetsky a, L. Vasiliev a,*, M. Vukovic b

a Luikov Heat and Mass Transfer Institute, Academy of Science, P. Brovka 15, 220072 Minsk, Belarus, Russian

Federationb Nortel Networks, Ottawa, Ont., Canada

Received 26 October 1999; accepted 12 May 2000

Abstract

The software for ¯at miniature heat-pipe parameters (Qmax, Rhp, temperature ®eld along the pipe surface,heat transfer coe�cients in the evaporator and condenser zones he, hc, etc.) prediction and numericalmodeling was developed. The experimental data received for the ¯at miniature heat pipe (2.5±4 mmthickness, 50±250 mm length, 8±11 mm width) with a copper sintered powder wick saturated with waterwere compared with the data of numerical analysis and results showed that experimental veri®cation tes-ti®es the validity of the software application. Ó 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Miniature heat pipe; Metal powder wick; Two-dimensional numerical analysis

1. Introduction

The recent design of desktop and notebook computer performance necessitates higher per-formance processors to be developed. The miniature ¯at heat-pipe applications for cooling tele-com boots and notebook computers were started in the last ten years. Conventional miniatureheat pipes and miniature ¯at heat pipes now are used in 80% of notebook PCs. Heat pipes havebeen appreciated by thermal designers for their small size and e�ective cooling capacity. Innotebook PCs, several applications of the heat pipe cooling technology are put to practical use inlarge quantities [1,2]. The high heat ¯uxes typical for the electronic equipment need to use thee�ective heat pipes with high heat transfer capabilities at any inclination. Hence, we need to use

Applied Thermal Engineering 21 (2001) 559±571www.elsevier.com/locate/apthermeng

* Corresponding author. Tel.: +375-17-284-2133; fax: +375-17-284-2133.

E-mail addresses: [email protected] (L. Vasiliev), [email protected] (M. Vukovic).

1359-4311/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved.

PII: S1359-4311(00)00066-1

Nomenclature

r liquid surface tensiond wick thicknesskcs e�ective thermal conductivity of the wickql liquid densityll liquid viscosityqv vapor densitylv vapor viscosityTv vapor temperature at the end of the evaporatorA vapor channel thicknessdT temperature di�erence at the mHP endsdTe temperature di�erence of the evaporator end and the adiabatic zoneg gravity constantk wick permeability coe�cientK 0 speci®c capacity ratio Cp=Cv

L, l heat-pipe length�l heat-pipe e�ective lengthmHP miniature heat pipepc maximal capillary pressurepv vapor pressureQ heat ¯owR mHP thermal resistance, calculated using the temperature di�erence between the

mHP endsr* latent heat of evaporationRb vapor bubble radius (near 2:54� 10ÿ7 m)Rc, Re the thermal resistance of the condenser and evaporator, calculated using the mean

temperature of the condenser and the evaporatorReff e�ective mHP thermal resistance, calculated using the mean temperature di�erence of

the evaporator and the condenserRg gas constantRm meniscus radiusScs the square of a heat-pipe wick cross-sectionSe evaporator cross-section squareSv vapor channel cross-section squareT1, T2, . . ., Tn temperature of mHP surface (thermocouples data)Te, Tc, Ta temperature of the evaporator, condenser and adiabatic zoneTv vapor temperatureTw;in temperature of the cooling water at the entranceTw;out temperature of the cooling water at the exitW vapor channel widthX coordinate (mm)

560 V. Maziuk et al. / Applied Thermal Engineering 21 (2001) 559±571

miniature heat pipes with improved wick structures due to their operation at top heating modetypical for most of the notebook manufacturers with a decrease of 30±40% of the thermal re-sistance over conventional cooling systems. High speed CPUs with a heat loading of 35 W areused in notebook PCs [3±8]. The e�ciency of the developed software tool was compared with theexperimental data received during the experiments with a ¯at miniature heat pipe made fromcopper (copper sintered powder wick).

The ¯at miniature heat pipes with thickness 2±4 mm are used on electronic components coolingin small cabinets. The evaporating section is installed between each package, and condensersection is attached to the cabinet wall directly. The cabinet wall is used as a cooling heat sink. Themain advantage of the ¯at miniature heat pipes as the electronic components cooler is a possibilityto ensure a good thermal contact with the chips and have a symmetric heat input from both sidesof the heat pipe, like in the cylindrical heat pipes. In both cases, the liquid motion inside thecapillary wick and the temperature distribution along the heat pipe can be considered as one-dimensional. If the heat input to the ¯at miniature heat pipe is ensured from one side, the liquidand temperature distribution in the heat pipe is considered as two-dimensional and we need tomodify the software to calculate the heat transfer coe�cients in the evaporator and condenserzones, the heat pipe thermal resistance, temperature distribution along the heat pipe and to de-termine Qmax along the heat pipe. The goal of this work is to develop a software to calculate the¯at miniature heat-pipe parameters and experimentally validate this software [9±11].

2. Experimental setup

The experimental setup (Fig. 1) to determine the miniature heat-pipe's (¯at and cylindrical)parameters was designed and made. The general goal of this setup application was to

· determine the temperature distribution along the heat pipe for di�erent heat loads,· estimate the heat-pipe's maximum capacity in horizontal and vertical, and inverted position,

and· evaluate the dependency between a heat-pipe thermal resistance and heat dissipation.

This setup was done in a way as to reproduce the mode of heat-pipe applications close torealistic. Heat-pipe heating was done by the electric heaters (¯at or circular), and heat-pipecooling by the air ¯ow (forced or natural convection) and water ¯ow. Three small fans wereinstalled inside the experimental setup. Heat-pipes thermal control was done with the help of the

Indexa adiabatic zoneamb ambiance temperatureavg averagec condensere evaporator

V. Maziuk et al. / Applied Thermal Engineering 21 (2001) 559±571 561

heat ¯ow measurements in the evaporator (qmax � 40±50 W/cm2, Qmax � 100 W), heat-pipe sur-face temperature measurements were performed by thermocouples and heat-pipe tilt measure-ments (�90° to 0° to ÿ90°) were performed by an automatic system of the tilt deviation.

A miniature heat pipe is disposed in a thermally insulated chamber inside the experimentalsetup. This chamber is divided into three zones and comprises four components ± the basement towhich heat pipe is attached, two lids covering the bottom, the chamber and one movable partition(wall). This thermally insulated chamber is ®xed on the turning device to ensure heat-pipe tiltchanging.

The heat ¯ux in the evaporator is regulated following the computer program. Thus, the lengthof the evaporator, adiabatic zone and the condenser zone of the heat pipe can also be regulatedfollowing the program of testing. The most typical case is when the length of the heat-pipeevaporator is 15±30% and the length of the heat-pipe condenser is 40±60% of the heat-pipe's totallength. To measure the temperature ®eld along the heat pipe some thermocouples d � 0:2 mm aresoldered on the heat-pipe surface. Three thermocouples were ®xed on the evaporator surface, twoon the adiabatic zone surface and three on the condenser zone surface (Fig. 2).

The heat ¯ux qmax can be determined as follows: the heat ¯ow supplied to the heat-pipeevaporator increases step by step with the temperature ®eld measurements. The heat ¯ow in-creases in steps of 1±2 W.

Fig. 1. Experimental setup schematic: 1. heat pipe disposed inside the reinforced polymer chamber, 2. electric cartridge

heater, 3. the platform for the heat pipe inclination, 4. wattmeter, 5. electric source of energy, 6. electric signals recorder

with the thermocouples, 7. electric tension meter, 8. IBM PC computer, 9. thermostat, 10. water rate recorder, and 11.

ampermeter.

Fig. 2. Heat pipe schematic with the thermocouples on its surface.


The miniature heat-pipe thermal resistance RHP (and the heat transfer coe�cients in theevaporator and condenser zones) is calculated when the temperature drops in the evaporator andcondenser zones and the heat ¯ow transfer through the heat pipe are known:

RHP � �Te ÿ Tc�=Q:

The computer program is developed to determine the heat ¯ow Q, heat-pipe temperature dropDT and heat transfer coe�cient in the evaporator zone:

he � q=�Te ÿ Tsat�;and heat transfer coe�cient in the condensation zone,

hc � q=�Tsat ÿ Tc�:The graphic data and ®gures of qmax, Qmax, RHP, he and hc as a function of heat-pipe tilt are

received for di�erent heat load and heat-pipe orientation in the space. A computer program wasdeveloped to determine Qmax for the ¯at miniature heat pipes (Fig. 3).

3. The methodology of the experiment

The heat load of the heat pipe is guided by the computer program depending on the electricheater electric resistance.

Qmax is determined as follows. After the ®xed heat-pipe orientation in space, the electric heateris switched-on when the temperature ®eld along a heat pipe is stationary and recorded in the ®le.Then, the heat-pipe heat load increases on DQ and the temperature ®eld along a heat pipe ismeasured once more. The Qmax value is ®xed when there is a non-proportional dependency be-tween the temperature change (thermocouples data disposed below the electric heater) and the

Fig. 3. Heat transfer limits for the ¯at miniature heat pipe with a sintered metal powder as a wick.


heat load change. In this case, we could see a sharp increase of the temperature. For the precisemeasurement of the heat-pipe crisis Qmax value, a small step of heat load DQ � 1 W increasing wasensured.

Heat-pipe thermal resistance is determined using the data of the vapor temperature in theadiabatic zone, and the mean temperature value in the evaporator and in the condenser. Twodi�erent modes of heat-pipe cooling were used during these experiments. Initially, we used the airforced convection cooling (by fans), but this mode of cooling did not give us an opportunity toapproach the critical situation (Qmax) due to a high heat-pipe temperature (more than 120°C). Forthe second set of experiments, we were obliged to use a water forced convection cooling of theheat-pipe condenser (thermostat application with the temperature measurements accuracy lessthan 1°C). The liquid motion was directed from the heat-pipe condenser end to the adiabatic zoneat a constant rate.

During the experiments, the temperature of the adiabatic zone and of the cooling water weremaintained constant.

A special computer program for the miniature heat-pipe experimental data analysis was de-veloped and tested, which permits ®xing and analyzing of all the experimental data in a steadystate and transitional mode. The ®rst ®le is developed for a steady state heat ¯ow along the heatpipe. The second ®le is used to analyze the experimental data in the transitional mode (®xed timeintervals).

This program guarantees automatic de®nition of the stationary heat transfer in the heat pipe.After this, the next command is sent (electric heater is switched-on) to change the heat ¯ow valuetransferred through a heat pipe. The experimental data of the temperature ®eld along the heatpipe are automatically visualized on the display screen (Fig. 4).

The heat-pipe physical model is based on some assumptions:

(1) The evaporation of the working liquid from the capillary structure of the wick occurs onlywhere the wick temperature is higher than the vapor temperature. The condensation of the vaporon the wick structure occurs only where the wick temperature is lower than the vapor tempera-ture.

Fig. 4. Temperature distribution along the heat pipe.


(2) The liquid motion occurs through the whole capillary structure (wick) under the capillaryaction. Due to one side heat-pipe heating, the evaporation zone is also situated on one side of a¯at heat pipe and the liquid movement inside the wick is considered as two-dimensional.

(3) The heat and mass transfer e�ciency in the heat pipe is mostly dependent on the wickproperties and the wick saturation by liquid. When the liquid saturation in the evaporation zonereaches a critical value, there is a limit of the capillary suction by the wick and for further de-creasing of the liquid saturation inside the wick a strong increase of the heat-pipe thermal re-sistance takes place. The heat-pipe heat load increase is also a reason for its thermal resistanceincreasing. When a wick is completely dry the heat transfer is realized only by thermal conduc-tivity of the heat-pipe envelope and the wick. In this case, the heat-pipe thermal resistance of thispart of the heat pipe increases several times.

The heat transfer coe�cients in the evaporators and condensers of heat pipes are directly re-lated with a wick thermal conductivity. The ratio between the axial heat ¯ow transferred along theheat-pipe envelope and radial heat ¯ow transferred as a liquid evaporation in the pores is di�erentfor di�erent heat pipes.

For the heat pipes with a metal sintered powder wick, the heat ¯ow transferred in the radialdirection by the liquid evaporation up to Qmax is several times more than the heat ¯ow transferredalong the heat-pipe envelope, because the e�ective thermal conductivity of the wick is high (up to40 W/m K). As a result, we have an isothermal temperature pro®le along the evaporator.

These heat-pipe features are included in the software through the wick e�ective thermal con-ductivity. The heat transfer coe�cient in the condenser zone depends on the wick e�ective thermalconductivity, wick thickness and the liquid ®lm thickness under the wick surface. This liquid ®lmthickness is varied along the condenser ± the heat transfer coe�cient also varies along the con-denser length.

Fig. 5. Cross-section of the ¯attened copper miniature heat pipe with sintered metal powder wick (received from the

cylindrical heat pipe ¯attening): 1. HP envelope (3:7� 8 mm), 2. porous wick, and 3. vapor channel.

Fig. 6. Cross-section of the copper±water ¯at miniature heat pipe with sintered metal powder wick (rectangular cross-

section): 1. HP envelope (2:2� 9 mm), 2. porous wick, and 3. vapor channel.


Experimental samples of the ¯at miniature heat pipe were chosen as copper/water heat pipewith a copper sintered powder as a wick. Two di�erent samples were tested. The ®rst sample was a¯attened cylindrical heat pipe (Figs. 5, 7±13). The second sample was a heat pipe with a rect-angular cross-section (Figs. 6 and 14). Heat-pipe heat transfer limit is Qmax.

Usually, the heat transfer limit in heat pipes is determined experimentally as a fast temperaturerise in the evaporator. This temperature rise is not proportional to the heat ¯ow increase. In ourexperiments, the temperature on the surface of the evaporator was controlled by the thermocoupledisposed on the opposite side of the electric heater (electric heater was joined to the opposite sideof a ¯at heat pipe). Basically, the temperature rise on the surface of a heat pipe in contact with anelectric heater was di�erent from the temperature rise on the opposite side of heat-pipe evaporator(a faster temperature increase occurred).

Fig. 7. Heat ¯ow Qmax as a function of saturated vapor temperature inside the copper±water ¯attened miniature heat

pipe with copper sintered powder wick.

Fig. 8. Temperature distribution along the ¯at miniature heat pipe: 1. experimental data and 2. numerical modeling of

the heat pipe data.


The calculations show that the temperature drop between these ¯at surfaces of the evaporatorcould be essential (Fig. 13), so a real heat transfer limit starts earlier, when Qmax is few watts lessthan that we can estimate by the thermocouple no. 1 temperature data. Analyzing the data of Qmax

(Fig. 14), we can conclude that the heat transfer limit for two di�erent orientations of a heat pipein space (vertical and horizontal) is essentially di�erent. To verify the reliability of the computerprogram, we need to compare the computer data with some of the experimental data ± thetemperature ®eld along the heat pipe for di�erent heat ¯ows transferred. We can conclude that thetheoretical and experimental data coincides within the limit of 10% for large range of heat ¯owtransferred through a heat pipe.

Fig. 9. Temperature distribution along the ¯attened mHP for various powers supplied (Le � 20 mm, Lc � 100 mm,

La � 30 mm, experimental data, horizontal position).

Fig. 10. Temperature distribution along the ¯attened mHP for various powers supplied (Le � 20 mm, Lc � 100 mm,

La � 30 mm, experimental data, vertical, inverted position).


Fig. 11. Relationship between the thermal resistance R and power dissipation Q in the ¯attened mHP (metal sintered

powder): horizontal position, 20°C cooling water, experimental data, Le � 20 mm, Lc � 100 mm, La � 30 mm.

Fig. 12. Relationship between the thermal resistance R and power dissipation Q in the ¯attened mHP (metal powder):

vertical, inverted position, 20°C cooling water, experimental data, Le � 20 mm, Lc � 100 mm, La � 30 mm.

Fig. 13. 1. Non-heated opposite side of the evaporator and 2. heated surface of the evaporator, theoretical data.


The equation to calculate heat-pipe limit Qmax due to capillary forces limitation is

Q � pc ÿ qlgl

lllqlr�Scsk

� 12lvlqvr�A3W

:

The ®rst part of this equation is the liquid pressure drop and the second part of this equation isthe vapor pressure drop in the heat pipe.

Heat-pipe boiling limit Qcr and sonic limit Qcr were analyzed following [1±3]. The heat-pipeboiling limit Qcr is determined as

Qcr � kcsSe

dRgT 2

v

r�ln 1

�� 2r

pv

1

Rb

�ÿ 1

Rm

�� 2rqv

pvRbq1

�:

Heat-pipe sonic limit is determined as

Qcr � Svqvr�K 0RgTv

2 K 0 � 1� �� 0:5

:

A ¯at long miniature heat pipe is considered for the numerical analysis of its action. A com-prehensive two-dimensional steady-state mathematical model for predicting thermal perfor-mances (maximum transport capacity, thermal resistance, heat-pipe temperature axial pro®le,temperature drop between a heat source and heat sink) is the goal of this research program. Thismodel needs to predict a heat-pipe performance within �=ÿ10%. Actually, we analyze a ¯at heatpipe which has an isotropic capillary structure (metal sintered powder wick) on the inner heat-pipesurface. The heat-pipe orientation in space is in the limits of ÿ90° to �90°. A long heat-pipe axis isconstantly in a horizontal position and we consider the heat-pipe rotation on its axis. Heat-pipeperformance depends upon a heat-pipe thermal resistance, while the thermal resistance dependsupon the heat-pipe ¯uid transport limit, wick structure, permeability limitation, input power andoperating temperature, etc.

Fig. 14. Capillary limit Q of a miniature rectangular heat pipe with dimensions 2:2� 9� 150 mm and Le/La/Lc ± 20/70/

60 mm.


The main (principal) particularity of the metal sintered powder wick is the possibility offunctioning with a partially dry porous structure in the heat-pipe evaporator. The degree of wicksaturation with the liquid has an in¯uence on the heat transfer across the wick. For such sinteredpowder wicks, the heat transfer crisis (Qmax) beginning is soft and the heat-pipe works in a certainrange of DQmax (from Qmax1 up to Qmax2). Within this DQmax range, the wick capillary propertieschange: liquid permeability decreases (some pores are occupied by the vapor), and capillarypressure increases (small pores are responsible for a liquid capillary suction). The heat-pipeevaporator works as the porous structure with the ``inverted'' meniscus of the evaporation and theheat transfer increases. When Qmax2 is reached full drying in the evaporator's wick occurs and theheat pipe stops functioning [10].

Therefore, the heat transfer coe�cient in the evaporator basically is a function of the wicke�ective thermal conductivity, wick thickness and the degree of the wick saturation with theliquid.

Therefore, in such cases, the surface of the liquid ®lm evaporation in the pores increases and thewick e�ective thickness decreases. These two phenomena are the reasons for the heat transfercoe�cient he increase. Evidently, he is a function of the evaporator length and the heat-pipe tilt.

The heat transfer coe�cient in the heat-pipe condenser zone depends on the wick e�ectivethermal conductivity, wick thickness and the liquid ®lm thickness on the wick surface.

During the evaporator partial drying (Qmax), the excess of the liquid is accumulated on the wicksurface in the heat-pipe condenser. The liquid ®lm thickness increases and the heat transfer co-e�cient in the condenser zone decreases. The local value of the heat transfer in the condenser zoneis a function of the condenser length which can be estimated [11].

The vapor channel thickness inside the ¯at miniature heat pipes usually does not exceed 1 mmand the vapor pressure drop is comparable with the liquid pressure drop inside the wick. Thisvapor pressure drop DPv can be determined as the pressure drop for the gas ¯ow in the thinrectangular channel [12]:

DPv � 12lv�l

qvr�A3W:

The heat and mass transfer analysis in the ¯at miniature heat pipe gives the possibility ofdetermining the meniscus diameter distribution along the wick surface, wick saturation, capillarypermeability and heat transfer coe�cients in the evaporator and condenser zones.

To utilize the software for the ¯at miniature heat-pipe numerical modeling, we need to use someexperimental data related with the real pore distribution in the wick (mercury pore distributioncheck technology).

4. Conclusion

Heat transfer coe�cients in the evaporator and condenser of the ¯at miniature heat pipe de-pend on two-dimensional hydraulic (pore saturation, capillary permeability, capillary pres-sure) and thermal (temperature distribution along the heat-pipe envelope) parameters of suchdevices.


(1) The temperature in the middle of the heated surface of the envelope (evaporator) can exceedthe symmetric point temperature on the opposite (non-heated) surface of the envelope (evapo-rator) by nearly 10°C.

(2) The technology of heat pipes with the metal sintered powder wick development stronglyin¯uences the heat-pipe parameters (¯attened heat pipe or rectangular heat pipe).

(3) Experimental veri®cation of the ¯at miniature heat-pipe parameters testi®es the validity ofthe software application.

Acknowledgements

The authors would like to show their appreciation to Nortel Networks Ltd. for ®nancingsoftware development, Contract No. 642817, ``Thermal performance prediction algorithm for ¯atminiature heat pipe''.

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miniature heat-pipe thermal performance prediction tool – software development

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