Applied Thermal Engineering 29 (2009) 422–430

Contents lists available at ScienceDirect

Applied Thermal Engineering

journal homepage: www.elsevier .com/locate /apthermeng

The experimental and numerical investigation of a grooved vapor chamber

Zhang Ming, Liu Zhongliang *, Ma GuoyuanKey Laboratory of Enhanced Heat Transfer and Energy Conservation, Ministry of Education and Key Laboratory of Heat Transfer and Energy Conversion,Beijing Education Commission, College of Environmental and Energy Engineering, Beijing University of Technology, Beijing 100022, China

a r t i c l e i n f o

Article history:Received 14 August 2007Accepted 8 March 2008Available online 25 March 2008

Keywords:Vapor chamberElectronics coolingGrooved structure

1359-4311/$ - see front matter � 2008 Published bydoi:10.1016/j.applthermaleng.2008.03.030

* Corresponding author. Tel.: +86 10 87798807; faxE-mail address: liuzhl@bjut.edu.cn (L. Zhongliang)

a b s t r a c t

An effective thermal spreader can achieve more uniform heat flux distribution and thus enhance heat dis-sipation of heat sinks. Vapor chamber is one of highly effective thermal spreaders. In this paper, a novelgrooved vapor chamber was designed. The grooved structure of the vapor chamber can improve its axialand radial heat transfer and also can form the capillary loop between condensation and evaporation sur-faces. The effect of heat flux, filling amount and gravity to the performance of this vapor chamber is stud-ied by experiment. From experiment, we also obtained the best filling amount of this grooved vaporchamber. By comparing the thermal resistance of a solid copper plate with that of the vapor chamber,it is suggested that the critical heat flux condition should be maintained to use vapor chamber as efficientthermal spreaders for electronics cooling. A two-dimensional heat and mass transfer model for thegrooved vapor chamber is developed. The numerical simulation results show the thickness distributionof liquid film in the grooves is not uniform. The temperature and velocity field in vapor chamber areobtained. The thickness of the liquid film in groove is mainly influenced by pressure of vapor and liquidbeside liquid–vapor interface. The thin liquid film in heat source region can enhance the performance ofvapor chamber, but if the starting point of liquid film is backward beyond the heat source region, thevapor chamber will dry out easily. The optimal filling ratio should maintain steady thin liquid film in heatsource region of vapor chamber. The vapor condenses on whole condensation surface, so that the conden-sation surface achieves great uniform temperature distribution. By comparing the experimental resultswith numerical simulation results, the reliability of the numerical model can be verified.

� 2008 Published by Elsevier Ltd.

1. Introduction

The technology of electronics cooling has become a key factorfor further improvement of the performance of various electronicdevices. Electronic devices usually dissipate heat at very high heatflux. In order to dissipate heat efficiently from the electronics de-vices to the ambient, the heat transfer area of heat sinks used isgenerally much larger than that of heat sources. This usually re-sults in a non-uniform heat flux distribution of the heat transferarea of the heat sinks. So a thermal spreader is usually placed be-tween the heat source and the heat sink to achieve more uniformheat flux distribution. The traditional solid copper plate thermalspreader can level the heat flux distribution to a certain extent,but it cannot achieve the perfect uniform distribution due to thelimited thermal conductivity of copper. Obviously, the spreadingresistance of this kind of spreader can be reduced by increasingplate thickness or higher thermal conductivity of plate. Materialswith high thermal conductivity are usually quite expensive. The in-crease of plate thickness will also increase the weight of the sprea-der, so that the performance of the traditional solid copper plate

Elsevier Ltd.

: +86 10 67391983..

spreader is restrained, especially for the large area of heat sink baseand heating power. By using a vapor chamber a nearly isothermalcooling surface can be achieved. A uniform temperature and thus auniform heat flux distribution on the cooling surface also meanmore effective heat dissipation from electronic devices.

The capillary structure can enhance performance and also makethe vapor chamber work in the reverse gravity orientations. Somany researches have been carried out on the inner capillarystructure. Vafai and Wang [1] investigated the overall performanceof an asymmetrical rectangular flat plate heat pipe. Details of thephysics of the transport processes within the heat pipe were ana-lyzed and established. They also investigated the maximum heattransfer capacity of the flat plate heat pipe based on capillary lim-itation. Kang et al. [2] described the development of radial groovedmicro heat pipes (MHPs) with a three-layer structure. The MHPswere designed to allow separation of the liquid and vapor flow toreduce the viscous shear force. Experiments were undertaken toevaluate the performance of waters with three different water fill-ing rates at different input powers. Avenas et al. [3,4] providednumerical simulations to show the thermal performance ofgrooved wick and sintered metal powder wick in power electron-ics. Heat spreaders composed of heat pipe or plain material arecompared. Gillot et al. [5] proposed the use of flat miniature heat

2

1

3

4 7

V

A

220

6

5

Fig. 1. Experimental system: 1. blower; 2. anemoscope; 3. vapor chamber; 4. PC; 5.data acquisition/switch unit; 6. transformer; 7. heating unit, and 8. heat sink.

Nomenclature

Rs spreading resistance of solid copper plate, K/WRf spreading resistance of vapor chamber, K/WR0 external resistance, K/WQ heating power, Wq heat flux, W/m2

T temperature, KTmax maximal temperature of spreader, KTc center temperature of condensation surface, KTe center temperature of evaporation surface, KTtop average temperature of top surface, KTf temperature of ambient, KTs saturation temperature, Kqinput input heat flux, W/m2

r surface tension, N/mK curvatured thickness of liquid film, md0 thickness of starting point of film, mu velocity along the x-axis, m/sv velocity along the y-axis, m/sq density, kg/m3

p pressure, Pa

pc capillary pressure, PaAp plate area, m2

As heat source area, m2

k thermal conductivity, W/(m K)t plate thickness, md diameter of heat source, mD diameter of thermal spreader, mC specific heat, J/(kg K)h heat transfer coefficient, W/(m2 K)hfg latent heat, J/kgx0 starting point of liquid film, mV filling ratioF bulk forces, N/m3

Subscriptsw wallv vaporl liquidx x-axisy y-axis

Z. Ming et al. / Applied Thermal Engineering 29 (2009) 422–430 423

pipes with micro capillary grooves to spread heat flux across a heatsink. Silicon–water heat pipes were fabricated and tested to dem-onstrate the feasibility of heat spreading with this type of heatpipes. Xuan et al. [6] studied the performance and mechanism ofa flat plate heat pipe (FPHP) in which a layer of sintered copperpowder is applied to the heated surface of the heat pipe to enhanceevaporation process. The performance of the FPHP is experimen-tally measured under different heat fluxes, orientations andamount of the working fluid in order to investigate the effects ofcharge amount of the working fluid, thickness of the sintered layer,and orientation of the heat pipe on the performance of the FPHP.On basis of some assumptions, a theoretical model is proposed tosimulate dynamic behavior and steady-state performance of theFPHP. The model and simulation method developed in this articleare verified by the experimental results. Yasushi et al. [7] carriedout a numerical analysis on a flat plate heat pipe with wick sheetsand a wick column. From the numerical results, the capillary pres-sure head necessary to circulate the working fluid is estimated andthe temperature drop inside the vapor chamber is determined.Experimental investigation is also carried out, and fairly goodagreement is obtained with the numerical results.

The capillary structures connect the condensation surface to theevaporation surface and circulate the working fluid in vapor cham-ber. Compared with the conventional heat pipe, the evaporator andcondenser sections of the vapor chambers are the opposite sides ofthe vapor chamber, so it is not easy for grooved structure to formthe capillary loop between them. The structural stability of the va-por chamber should be checked because of the big sectional areasof the top and bottom plate. This problem can be solved by increas-ing the thickness of the plate or setting a supporting framework inthe vapor chamber, the weight and the cost will however also in-crease. Though the radial thermal resistance of the vapor chambersis very small which is its main advantage compared with conven-tional thermal spreaders, its axial thermal resistance is usually atleast comparable or even larger than that of the conventional ther-mal spreaders. Therefore, it is extremely important to enhance theaxial heat transfer. Thus, we designed a novel grooved vapor cham-ber. This special structure of the grooved vapor chamber improvesboth the axial and radial heat transfer and can form the capillaryloop between condensation and evaporation surfaces. The effectsof heat flux, filling amount and gravity to the performance of this

vapor chamber are studied by experiment. A two-dimensional heatand mass transfer model was also generated. The numerical simu-lation results are presented regarding the thickness distribution ofliquid film in groove, the temperature and velocity fields in vaporchamber. By comparing the experimental results with numericalsimulation results, the reliability of the numerical model can beverified.

2. Experimental setup and procedures

The apparatus used in this study include a blower, a data acqui-sition/switch unit, T-type thermocouples, an anemoscope, a trans-former, a heating unit and a PC. Fig. 1 shows the scheme of theexperiment system. Air from a blower blows vertically onto theheat sink to cool the vapor chamber. The air velocity is measuredby an anemoscope and the air temperature is measured by a ther-mocouple which is on the side of anemoscope. The heat flux is sup-plied by a heating unit. Adjusting output voltage of the transformercan change the input power of the heating unit. The temperaturesare measured by T-type thermocouples and collected through adata acquisition system.

Fig. 2 shows the configuration of the heating unit. The heatingunit is a copper rod with four electrical rod heaters. The rod diam-eter is 60 mm at its lower part, and reduces to 20 mm at its upperpart diameter to obtain a sufficient high heat flux to the vapor

A

Insulation material

Tightening screw Vapor chamber

A

A-A

The thermocouple locations

20

215

1515

Electrical rod heaters

Copper rod

T-type thermocouples

1

2

3

4

Fig. 2. Heating unit.

424 Z. Ming et al. / Applied Thermal Engineering 29 (2009) 422–430

chamber. The copper rod is insulated by ceramic fibre and smallinsulating cushions are put between copper rod and supportingframework to reduce heat loss from supporting framework. In or-der to reduce contact resistance between the heating unit andthe vapor chamber, high conductivity grease was applied to theircontact surface. Tightening screws are also used to improve thecontact between the vapor chamber and the heating unit. r tou are the locations of thermocouples that are used to measurethe temperature distribution of the copper rod. Twelve thermocou-ples are buried inside the copper rod to measure the temperaturedistribution of the copper rod. The locations of the thermocouplesare shown in Fig. 2. These locations are in the centerline of the rod.Every three thermocouples are penetrated into one point fromthree directions which are used to measure the temperature ofone location, so that the temperatures of points r to u are themean value of temperature values from three thermocouples.The holes for burying the thermocouples are 10 mm in depth and1 mm in diameter. The four thermocouples in a row are locatedat 2 mm, 17 mm, 32 mm and 47 mm from the top surface of thecopper rod, respectively. The steady-state temperature distributionalong the axial direction is thus obtained and thereafter used tocalculate the temperature gradient. Fig. 3 shows the locations ofthermocouples on vapor chamber. In order to measure the temper-ature distributions of the evaporation and the condensation sur-face, six small holes were drilled into the bottom and top platesto bury six thermocouples. The diameters of condensation andevaporation surface are both 85 mm. Point v is at the center of

20

2

1515

15

1

2

3

4

6

5

78910

Fig. 3. The locations of thermocouples.

evaporation surface. Points w to s10 are 0 mm, 7.5 mm, 17.5 mm,27.5 mm and 37.5 mm away from the center of condensation sur-face, respectively.

Fig. 4 shows the structure of the grooved vapor chamber that ismade of copper. We use water as the working fluid. The top andbottom plates are welded together to act as the condensationand the evaporation surfaces. The diameter and the thickness ofthe condensation and the evaporation faces are 85 mm and3 mm. The filling hole is on the sidewall of the vapor chamber.The grooves are machined on the bottom plate that radiate fromthe center of the evaporation surface at every 3�. The width andthe depth of the grooves are 0.2 mm and 3 mm, respectively. Thedepths of the grooves are the same as that of the distance betweencondensation and evaporation surface, so that the top end surfaceof the grooves can touch the condensation surface. A part of heatwill therefore be transferred to the condensation surface by con-duction. The grooved structure not only forms the capillary loopbetween the evaporation and the condensation surface, but alsoacts as the supporting framework in vapor chamber. A circulargroove is at the edge of vapor chamber to act as the liquid storagechannel. The width of this channel is 1.5 mm. These radial groovescross at the center, so a boiling pool is thus formed during machin-ing process. The evaporation mainly happens in the boiling pooland its adjacent part of the grooves. The vapor flows to the conden-sation surface along grooves and condenses here. The condensedfluid is then transported to the boiling surface under the effect of

Fig. 4. Grooved vapor chamber: 1. top plate; 2. filling hole; 3. boiling pool;4. grooves; 5. bottom plate; 6. liquid storage channel.

Z. Ming et al. / Applied Thermal Engineering 29 (2009) 422–430 425

the capillary pressure of these micro grooves. The liquid storagechannel can store or discharge the working fluid when the liquidis superfluous or insufficient.

The measure equipments in our experiment include anemo-scope, pressure transducer and thermocouples. The uncertaintiesof the experimental results mainly depend on the precisions ofthese equipments. The precision of anemoscope is 5% and the pre-cision of pressure transducer is 0.25% which had been determinedby producers. Before experiment, all of the thermocouples havebeen measured with standard thermometer. After the calibrationof thermocouples, the precision of thermocouple is 0.2%. In ourexperiment, we inserted these thermocouples into the small holesto measure the temperatures. The measure errors are caused bythe contact thermal resistance. To reduce contact resistance andtemperature measurement errors, high conductivity grease wasapplied into these holes. In our experimental rig, the heating powerof heating surface is not equal to the heating power of electricalrod heaters in heating unit. A part of heat will be dissipated fromthe walls of the heating unit, though we have placed small insulat-ing cushions between the copper rod and the supporting frame-work to reduce heat losses. Therefore, we use 12 thermocouplesto measure the temperatures of 4 points on the axis of copperrod. Every three thermocouples measure the temperature at onepoint to reduce the measure error. Then the heat flux of the heatingunit is deduced from Fourier’s law of heat conduction.

Before filling the vapor chamber, it must be weighed. Then avacuum pump is used to bring the vapor chamber to vacuum con-dition and the working fluid is filled into it. The filling amount is alittle bit over the expected value. After that, the vapor chamber isvacuumized again. But this time, it is heated by hot water duringthe vacuumizing process in order to extract as much residual airas possible and also to assure the vapor chamber is full of vaporof the working fluid. At this moment a pressure transducer in thefilling system indicates that the pressure value in the vapor cham-ber is 30 Pa. When the weight of the vapor chamber reaches the ex-pected value, the vacuum valve which connects with vaporchamber is closed to keep the vacuum condition.

Heating input

Thin liquid film region

Vapor

Evapora

Conden

Fig. 5. Liquid film dis

Heat source

42.5

10

Evaporation

CondensationInterface

y (mm)

Fig. 6. Physic

3. Model of the grooved vapor chamber

A proposed liquid film distribution model in the groove isshown in Fig. 5. Due to the local boiling and the effect of capillarypressure of the micro grooves, the liquid film at the heat input re-gion is much thinner than that at the other region. The phasechange heat transfer is thus the strongest within the heat input re-gion. The heat flux and the filling ratio of working fluid are the keyfactors affecting the thickness of liquid film in the micro grooves,so it is very important to find out the optimum values for main-taining the thin liquid film near the heat input region. The thermalresistance of the phase change heat transfer will also increase withthe thickness of the liquid film. On the other hand, a steady liquidfilm cannot form in the heat input region if the working fluid isinsufficient, and the vapor chamber will dry out easily.

Needless to say, the above liquid film model is only a possibleapproximation of the true liquid film distribution. The interface be-tween vapor and liquid in the grooves is not as sharp as shown inFig. 5. Some of the condensed fluid will adhere on the wall andsome others will drip to the evaporation surface directly. Of course,most of the condensed fluid will be pushed into the liquid storagechannel by vapor flow. Therefore, in our numerical simulation, wesuppose that all of the vapor condenses at the condensation surfaceand all of the liquid to the evaporation surface is from the liquidstorage channel. We also suppose that the vapor and liquid flow in-side the grooves are laminar.

Since the grooves in vapor chamber radiate from the center ofthe evaporation surface, we suppose that the heat and mass trans-fer processes in these grooves are independent of other groovesand identically the same in all the grooves. Our study mainly fo-cuses on the heat and mass transfer process in a single groove,so that the effect of boiling pool is neglected in this model. Further-more, since the heat and mass transfer happens mainly in the ra-dial and thickness directions, a two-dimensional model isproposed as shown in Fig. 6.

The dimension of the numerical model is the same as that of thevapor chamber that we design. The initial vapor–liquid interface is

Liquid film

tion surface

sation surface

tribution model.

3 3

3

plate

plate

x (mm)

al model.

426 Z. Ming et al. / Applied Thermal Engineering 29 (2009) 422–430

uniform and presents a horizontal line. The initial position of theinterface also denotes the filling ratio of the working fluid. Theboundary condition of the interface is set as the dynamic boundaryin FLUENT software. The properties of the liquid and vapor are cal-culated from the international standard for properties of water andsteam IAPWS-IF97.

Eqs. (1)–(9) represent conservation of mass, momentum andenergy of the solid, liquid and vapor region.

For the solid wall region, conduction is the only mode for heattransfer:

o2Tw

ox2 þo2Tw

oy2 ¼ 0 ð1Þ

Vapor region:

ouv

oxþ ovv

oy¼ 0 ð2Þ

qv uvouv

oxþ vv

ouv

oy

� �¼ qvFx þ

opxx

oxþ

opxy

oyð3Þ

qv uvovv

oxþ vv

ovv

oy

� �¼ qvFy þ

opyx

oxþ

opyy

oyð4Þ

qvCv uvoTv

oxþ vv

oTv

oy

� �¼ kv

o2Tv

ox2 þo2Tv

oy2

!þ / ð5Þ

Liquid region:

oul

oxþ ovl

oy¼ 0 ð6Þ

ql uloul

oxþ vl

oul

oy

� �¼ qlFx þ

opxx

oxþ

opxy

oyð7Þ

ql ulovl

oxþ vl

ovl

oy

� �¼ qlFy þ

opyx

oyþ

opyy

oyð8Þ

qlCl uloT l

oxþ vl

oT l

oy

� �¼ kl

o2T l

ox2 þo2T l

oy2

!þ / ð9Þ

where / is the dissipation function, which can be simply neglecteddue to the very low velocity. At the liquid–vapor interface, the pres-sure difference between the vapor and the liquid phase is due to thecapillary pressure when we neglect the disjoining pressure [8]. Thecapillary pressure is defined as the product of interfacial curvatureK, and surface tension r, which is given by the following equation:

pv � pl ¼ pc ¼ rK ð10Þ

The curvature of the interface K can be expressed as

K ¼ d2ddx2 1þ dd

dx

� �2" #�1:5

ð11Þ

where d is the thickness of the liquid film. From Eqs. (10) and (11),one can easily obtain

d2ddx2 ¼

pv � pl

r1þ dd

dx

� �2" #1:5

ð12Þ

Eq. (13) shows the mass balance. The total mass of vapor andliquid in vapor chamber equals to the filling amount of the workingfluid,Z 42:5

x0

dðxÞdxþ 3� 42:5�Z 42:5

x0

dðxÞdx� �

qv=ql ¼ V � 3� 42:5

ð13Þ

where x0 is the starting point of the liquid film and V is the fillingratio of working fluid. At the initial time, the position of the startingpoint of film is uncertain. It has two possible states for the startingpoint. If the liquid film starts from x = 0, it can be shown as

x0 ¼ 0; y ¼ 3þ d0 : d ¼ d0;dddx¼ 0; pl ¼ pv ¼ ps ð14Þ

If the starting point of liquid film is backward, it can be shownas

x ¼ x0; y ¼ 3 : d ¼ 0;dddx¼ 0; pl ¼ pv ¼ ps ð15Þ

x ¼ 0 :ovox¼ 0; u ¼ 0;

oTox¼ 0 ð16Þ

y ¼ 0; 0 6 x < 10 : �kwoTw

oy

� �¼ qinput ð17Þ

y ¼ 0; 10 6 x 6 42:5 : �kwoTw

oy

� �¼ 0 ð18Þ

x ¼ 42:5; 0 6 y 6 3 or 6 6 y 6 9 : �kwoTw

ox

� �¼ 0 ð19Þ

x ¼ 42:5; 3þ d 6 y 6 6 : �kvoTv

ox

� �¼ 0;

ovv

ox¼ 0; uv ¼ 0

ð20Þ

In this model, we suppose that all of the vapor condenses at thecondensation surface and all of the liquid to the evaporation sur-face is from the liquid storage channel. Eq. (21) shows that themass of vapor which flows to the condensation surface is equalto that of the liquid which flows to the evaporation surface.

x ¼ 42:5; 3 6 y 6 3þ d :

ql

Z 3þd

3ulðyÞx¼42:5 dy ¼ qv

Z 42:5

0vvðxÞy¼6 dx ð21Þ

y ¼ 3 : kwoTw

oy

� �¼ kl

oT l

oy

� �ð22Þ

y ¼ 6 : kwoTw

oy

� �¼ kv

oTv

oy

� �ð23Þ

y ¼ 9 : �kwoTw

oy

� �¼ hðTw � T f Þ ð24Þ

Eqs. (25) and (26) are applied to the liquid–vapor interface andthe condensation surface to found the relationship between vaporvelocity and heat flux:

y ¼ 3þ d : T l ¼ Tv; vvðxÞ ¼kv

oTvðxÞoy � kl

oTlðxÞoy

qvhfgð25Þ

y ¼ 6 : kvoTvðxÞ

oy� kw

oTwðxÞoy

¼ vvðxÞqvhfg ð26Þ

Eqs. (12) and (13) with the above boundary conditions aresolved numerically to obtain the thickness distribution of liquidfilm using the Runge–Kutta method. The dynamic interface willbe adjusted at each iteration step. The temperature, velocity andpressure fields are therefore obtained numerically by FLUENT forthis new vapor–liquid interface. Obviously, the adjusted interfaceposition and geometry will influence the temperature, velocityand pressure results, and thus the new film thickness after eachiteration step is obtained. The iteration will be carried on untilthe convergence achieved.

4. Results and discussion

4.1. Experimental results

Fig. 7 shows the steady-state temperature in the vapor chamberversus heat fluxes. The working fluid of the vapor chamber is waterand the filling amount of the working fluid is 1.6 g. The room airtemperature is 19 �C and the air velocity that impinges on the heatsink is 9.7 m/s. The experimental results show the good perfor-mance of axial and radial heat transfer of the vapor chamber. Thetop end surface of the grooves can touch the bottom surface ofthe condensation surface, so a part of heat will be transferred to

0 5 10 15 20 25 30 35 4020

30

40

50

60

70

80

T (º

C)

Heat flux ( W / cm2 )

PointPointPointPointPointPoint

5

6

7

8

9

10

Fig. 7. Steady-state temperature of the vapor chamber versus heat fluxes.

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.020

30

40

50

60

70

80

Heat flux 30.5 W/cm2

Point Point Point PointPoint Point

T(º

C)

Working fluid amount (g)

5

7

9

6

8

10

Fig. 8. Steady-state temperature of the vapor chamber versus working fluidamount.

20

30

40

50

60

70

condensation surface on top

Heat flux 15.346 W/cm2

Point Point

Heat flux 30.459 W/cm2

Point Point

T(º

C)

evaporationsurface on top

6

6

5

5

Fig. 9. Steady-state temperature of the vapor chamber at different installationlocation.

Z. Ming et al. / Applied Thermal Engineering 29 (2009) 422–430 427

the condensation surface by conduction. The axial heat transfer ofthe vapor chamber will not only include the phase change heattransfer but also include the conduction of copper. The steady-state temperature of the vapor chamber versus working fluidamount is shown in Fig. 8. When the working fluid amount is0 g, it shows that the vapor chamber is empty. The maximal work-ing fluid amount is 3.54 g. The experimental results show that thevapor chamber maintains good performance when the workingfluid amount is between 1.0 g and 2.0 g. It proves that the liquidstorage channel can store or discharge the working fluid whenthe liquid is superfluous or insufficient in some extent. When theheat flux is 3.05 � 105 W/m2, the results show the best optimalworking fluid amount is 1.43 g which is 40.4% of the maximalworking fluid amount. Fig. 9 shows the steady-state temperatureof vapor chamber at different installation locations. The experi-mental results show that the vapor chamber can work in the re-verse gravity orientations, though the temperature differencebetween evaporation and condensation is bigger when the vaporchamber is installed at the reverse gravity orientations.

The geometry dimension of heat sink is generally much largerthan the heat source, so a spreader is usually placed between theheat source and the heat sink to level the heat flux distribution.

The traditional spreader is a solid copper plate. But the thermalspreading performance of a solid copper plate deteriorates withthe increasing of the heat flux and the base area of the heat sink.So it is important to study the minimal heat flux that is necessaryto use the vapor chamber.

The solid copper plate spreader is supposed to be a disk-shapeflat plate and the heat source is under the center of the spreader.The spreading resistance Rs is used to describe the heat flow outfrom a narrow region into a larger cross-sectional area. It can bedefined as follows:

Rs ¼Tmax � T top

Qð27Þ

where Tmax is the maximal temperature of spreader which is usuallyat the center of the plate bottom surface. T top is the average temper-ature of the spreader top surface.

This definition can also be used for vapor chamber. Song et al.[9,10] used the method of separation of variables to solve the en-ergy equation in a two-dimensional coordinate system. They pre-sented the simple approximation for the dimensionless spreadingresistance. The dimensional equation can be written as follows:

Rs ¼ffiffiffiffiffiffiAp

p�

ffiffiffiffiffiAsp

kffiffiffiffiffiffiffiffiffiffiffiffiffipApAs

p � kkApR0 þ tanhðktÞ1þ kkApR0 tanhðktÞ ð28Þ

where k ¼ p3=2ffiffiffiffiffiAPp þ 1ffiffiffiffiffi

Asp ð29Þ

As reported by Song et al., the above correlations agree with theanalytical solutions in other papers well within 10% consideringthe range of parameters commonly found in microelectronicsapplications. From Eqs. (28) and (29), we can see that the spreadingresistance can be determined from the heat source area As, platearea Ap, plate thickness t, thermal conductivity k and externalresistance R0.

R0 can be defined as follows:

R0 ¼T top � Tamb

Qð30Þ

where Ttop is the average temperature of the top surface and Tamb isthe air temperature.

When we use the same definition as solid copper plate to calcu-late the spreading thermal resistance of vapor chamber, the aver-age temperature Ttop of the top surface can be replaced by thecenter temperature Tc of condensation surface because of the uni-

0.00 0.01 0.02 0.03 0.043973.8

3974.0

3974.2

3974.4

3974.6

3974.80.00 0.01 0.02 0.03 0.04

6942.6

6942.8

6943.0

6943.2

6943.4

6943.6

p (Pa

)

x (m)

Heat flux 5 W/cm2

liquidvapor

p(P

a)

Heat flux 10W/cm2

liquidvapor

Fig. 11. The pressure of the vapor and liquid phases at the vapor–liquid interface inthe groove.

428 Z. Ming et al. / Applied Thermal Engineering 29 (2009) 422–430

formity of temperature in condensation surface. And the maximaltemperature Tmax can be replaced by the center temperature ofevaporation surface Te. The spreading resistance of vapor chambercan be defined as follows:

Rf ¼Tmax � Ttop

Q¼ Te � Tc

Qð31Þ

So we can use Eqs. (28) and (29) to calculate the thermalspreading resistance of solid copper plate and compare it withthe experimental results of vapor chamber. The thermal resistanceof solid copper plate will not change along with the heat flux. Andwe also suppose that the thermal resistance of vapor chamber willnot change along with the thickness and diameter in tested range.

Fig. 10 shows the spreading resistance ratio of vapor chamber tosolid copper plate. When the spreading resistance ratios are grea-ter than 1, the vapor chamber has worse performance than solidcopper plate. From this figure, we can see that the ratio increaseswith the thickness and decreases with the heating power and thearea of spreader, so that the vapor chamber should be appliedwhen it has the large underside area of heat sink and high heatingpower. For example, when the R0 is 0.127 K/W, d is 0.02 m, t is0.005 m and D is 0.1 m, the flat plate heat spreader should be ap-plied when the heating power is more than 60 W. The spreadingresistance of solid copper plate spreader can be reduced by increas-ing plate thickness, so that the vapor chamber should be manufac-tured in small thickness, otherwise, the vapor chamber will presentworse spreading performance than that of solid copper plate insame dimension. From Fig. 10, we can see that when the R0 is0.127 K/W, d is 0.02 m and D is 0.1 m, and, if the thickness is in-creased from 0.005 m to 0.01 m, the ratio will be greater than 1in all tested range.

4.2. Numerical results

Fig. 11 shows the pressure of the vapor and liquid phases at thevapor–liquid interface in the groove at different heat fluxes andFig. 12 shows the thickness of the liquid film in the groove. The fill-ing ratio of working fluid is 33.3% and the temperature of ambientis 20 �C. As indicated by Eqs. (14) and (15), saturated pressure is as-sumed for the vapor and liquid phases at the starting point of li-quid film. Therefore, from Fig. 11 we can see that the pressurecurves of the vapor and the liquid phase meet together at the start-ing point of liquid film. The vapor flows from the central to theedge region, and the liquid flows from the edge to central region

0 20 40 60 80 100 120

-0.4-0.20.00.20.40.60.81.01.21.41.61.82.02.22.42.62.8

Rf

/Rs

Q ( W )

R0= 0.127 K / W d =0.02 mt = 0.005 m D = 0.08 mt = 0.005 m D = 0.1 mt = 0.005 m D = 0.15 mt = 0.01 m D = 0.1 m

Fig. 10. Spreading resistance ratio of vapor chamber to solid copper plate.

in the groove. As a result, the pressure of the vapor decreases withx, while the pressure of the liquid increases. The increased heat fluxenhances the circulation of the working fluid and the velocities ofthe vapor and the liquid will also increase. This in turn results inthe increases of the capillary pressure and the friction loss. Thepressure difference between the vapor and liquid phases is actuallyresulted from the capillary pressure. Therefore, we can see thatfrom Fig. 11 the magnitude of variations of the vapor and liquidpressure and the pressure difference between vapor and liquidall increase with heat flux.

The thickness of liquid film depends on the pressure of the va-por and the liquid at the interface. From Fig. 12, we can see thatinterfacial curvature of the liquid film increases with the heat fluxand also increases with x for a given heat flux. The radius of theheat source is 0.01 m. The boiling and evaporation thus mainly ex-ist in the heat source region, so that the thickness of the liquid filmin this region dramatically influences the performance of the vaporchamber. From Fig. 12, we also can see that the thickness of the li-quid film in the heat source region decreases with the heat flux. Inorder to show the thickness variation of the liquid film in the heatsource region more clearly, we enlarged the figure of the heatsource region. From this enlarged figure we can see that whenthe heat flux is 10 W/cm2, a very thin liquid film forms in the heatsource region whose thickness is about 2.5 � 10�6 m. When theheat flux increases to 12.5 W/cm2, there is not liquid film on theheat source region and the starting point position of the liquid filmmoves backward. If the starting point of the liquid film is out of theheat source region, the vapor chamber will dry out and very hightemperature may appear. At low heat fluxes, the whole heat sourceregion is covered with a complete liquid film of the working fluidand the liquid film thickness is much larger than that of the highheat fluxes, no dry out happens. However, the thick liquid film atthe heat source region will deteriorate the performance of vaporchamber. Therefore, there exists an optimal filling ratio for main-taining a steady thin liquid film in the heat source region of the va-por chamber.

Fig. 13 presents the temperature distribution of the groove witha heat flux of 7.5 W/cm2 and a working fluid filling ratio of 33.3%.The heat flows from a heat source of a small area into the evapora-tion plate of a large cross-sectional area, so that the evaporationplate shows a remarkable temperature change in the x direction,which indicates a large radial thermal resistance of the evaporationplate. At the center of the evaporation surface the phase changeheat transfer is strongest because of the thin liquid film and the

0.00 0.01 0.02 0.03 0.040.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.000 0.002 0.004 0.006 0.008 0.0100.000000

0.000005

0.000010

0.000015

0.000020

0.000025

0.000030

δ ( m

)

x (m)

heat flux 5 W/cm2

heat flux 7.5 W/cm2

heat flux 10 W/cm2

heat flux 12.5 W/cm2

δ ( m

)

x ( m )

Fig. 12. Liquid film thickness distribution in the groove at different heat fluxes.

Fig. 13. Temperature distribution of the vapor chamber.

Z. Ming et al. / Applied Thermal Engineering 29 (2009) 422–430 429

high heat flux. The vapor flows from the central to the outer regionin the vapor region and condenses on the entire condensation sur-face. The vapor flow and the condensation on the condensationsurface will certainly cause a uniform temperature distributionon the condensation surface. And the vapor flow also results in a

Fig. 14. Velocity distribution

sudden change in gradient of the isothermals at the vapor–liquidinterface as shown in Fig. 13.

Fig. 14 shows the velocity distribution in the vapor chamberwhose heat flux is 7.5 W/cm2 and filling ratio is 33.3%. The negativevelocity of the liquid means the liquid flows opposite the x direc-tion and the liquid and the vapor form a countercurrent flow insidethe groove. The largest liquid velocity happens in the thin liquidfilm region. Because of the large density difference between liquidand vapor, the liquid velocity is much smaller than the vaporvelocity.

Fig. 15 shows the comparison between the experimental andnumerical results when the filing ratio of working fluid is 45%.The temperatures of numerical results are a little bit higher thanthat of the experimental results. That is because we set the wallsof vapor chamber as the adiabatic boundary condition in ournumerical simulation, but in reality no surface can be insulatedabsolutely.

in the vapor chamber.

0 10 20 3020

30

40

50

60

70

80

T (º

C)

Heat flux (W / cm2)

Experimental resultscenter of evaporation surface center of condensation surface

Numerical results center of evaporation surfacecenter of condensation surface

Fig. 15. Comparison of the experimental and numerical results.

430 Z. Ming et al. / Applied Thermal Engineering 29 (2009) 422–430

5. Conclusions

A novel grooved vapor chamber was designed in this paper. Theeffects of heat flux, filling amount and gravity to the performanceof this vapor chamber are studied by experiment. From experi-ments, the best filling amount of this grooved vapor chamber is ob-tained. By comparing the thermal resistance of a solid copper platewith that of the vapor chamber, it is suggested that the critical heatflux condition should be considered when using vapor chamber asefficient thermal spreaders for electronics cooling. A two-dimen-sional heat and mass transfer model for the grooved vapor cham-ber is founded in this paper. The numerical simulation resultsshow the thickness distribution of liquid film in the groove is notuniform. The thickness of the liquid film in the groove is mainlyinfluenced by pressure of vapor and liquid beside liquid–vaporinterface. At the vapor–liquid interface, then magnitudes of varia-tions of the vapor and liquid pressure and the pressure differencesbetween vapor and liquid increase with the heat flux. The liquidfilm in heat source region is very thin and this can enhance the per-formance of vapor chamber. But if the starting point of the liquid

film out of the heat source region, the vapor chamber may dryout. The heat flux spreads along with the flow of vapor. The vaporcondensates on whole condensation surface, so that the condensa-tion surface achieves a very uniform temperature distribution. Theoptimal filling ratio should maintain a steady thin liquid film inheat source region of the vapor chamber. The agreement betweenthe experimental results and numerical simulation results verifiesthe numerical model.

Acknowledgements

This work is supported by Beijing Education Committee project(No. KM200510005002) and Beijing Outstanding Scholar Program(2006).

References

[1] K. Vafai, W. Wang, Analysis of flow and heat transfer of an asymmetrical flatplate heat pipe, Int. J. Heat Mass Transfer 35 (9) (1992) 2087–2099.

[2] Shung-Wen Kang, Sheng-Hong Tsai, Hong-Chih Chen, Fabrication andtest of radial grooved micro heat pipes, Appl. Thermal Eng. 22 (2002)1559–1568.

[3] Y. Avenas, C. Gillot, A. Bricard, C. Schaeffer, On the use of flat heat pipe asthermal spreaders in power electronics cooling, in: Proceedings of the IEEE33rd Annual 2002 Power Electronics Specialists Conference, vol. 2, 2002, pp.753–757.

[4] Y. Avenas, M. Ivanova, N. Popova, C. Schaeffer, J.L. Schanen, Thermal analysis ofthermal spreaders used in power electronics cooling, in: Proceedings of theIndustry Applications Conference, 37th IAS Annual Meeting, vol. 1, 2002, pp.216–221.

[5] C. Gillot, A. Id, M. lvanova, Y. Avenas, C. Schaeffd, E. Foumid, Experimentalstudy of a flat silicon heat pipe with micro capillary grooves, in: Proceedings ofthe 2004 Inter Society Conference on Thermal Phenomena, 2004, pp. 47–51.

[6] Yimin Xuan, Yuping Hong, Qiang Li, Investigation on transient behaviors of flatplate heat pipes, Exp. Thermal Fluid Sci. 28 (2004) 249–255.

[7] Yasuahi Koito, Hideaki Imura, Masataka Mochizuki, Yuji Saito, Shuichi Torii,Numerical analysis and experimental verification on thermal fluid phenomenain a vapor chamber, Appl. Thermal Eng. 26 (2006) 1669–1676.

[8] Kyoungwoo Park, Kwan-Joong Noh, Kwan-Soo Lee, Transport phenomena inthe thin-film region of a micro-channel, Int. J. Heat Mass Transfer 46 (2003)2381–2388.

[9] S. Song, S. Lee, Au Van, Closed-form equation for thermal constriction/spreading resistances with variable resistance boundary condition, in:Proceedings of the International Electronics Packaging Conference, Atlanta,Georgia, 1994, pp. 111–121.

[10] S. Lee, S. Song, Au Van, Constriction/spreading resistance model for electronicspackaging, ASME/JSME Thermal Eng. Conf. 4 (1995) 199–206.