fundamental experiments and numerical analyses on heat

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Fundamental Experiments and Numerical Analyses on Heat

Transfer Characteristics of a Vapor Chamber∗(Effect of Heat Source Size)

Yasushi KOITO∗∗, Hideaki IMURA∗∗, Masataka MOCHIZUKI∗∗∗,Yuji SAITO∗∗∗ and Shuichi TORII∗∗

A vapor chamber is used as a novel heat spreader to cool high-performance MPUs (mi-croprocessor units). The vapor chamber is placed between small heat sources and a large heatsink. This paper describes the effect of heat source size on the heat transfer characteristics ofthe vapor chamber. First, by the experiments, the effect of heat source size on the temperaturedistribution of the vapor chamber is investigated, and the validity of the mathematical modelof the vapor chamber is confirmed. Secondly, by the numerical analyses, the effect of heatsource size on the thermal resistances inside the vapor chamber is discussed. It is found thatthe heat source size greatly affects the thermal resistance of the evaporator section inside thevapor chamber. Although the thermal resistance is hardly affected by the heat generation rateand the heat flux of the heat source, it increases as the heat source becomes smaller.

Key Words: Heat Transfer, Heat Pipe, Thermosyphon, Vapor Chamber, Heat Spreader,Heat Source Size

1. Introduction

In recent years, a flat-plate type heat pipe called “Va-por Chamber” is widely used as a novel heat spreader tocool high-performance MPUs (microprocessor units) inpersonal computers, workstations and servers. The MPUsare high-heat-flux heat sources of small sizes, and the va-por chamber is placed between the small MPUs and a largeheat sink to spread the heat from the former to the lat-ter, resulting in the low thermal resistance between them.The principle of operation of the vapor chamber is basi-cally the same as a conventional cylindrical heat pipe. Thelatent heat of evaporation and condensation of the work-ing fluid is utilized and two-dimensional heat transfer isallowed inside the vapor chamber. Effectiveness of thevapor chamber has been already confirmed(1), (2), and theother advantages of the vapor chamber are that it is fabri-

∗ Received 14th June, 2006 (No. 05-0538). Japanese Orig-inal: Trans. Jpn. Soc. Mech. Eng., Vol.72, No.714, B(2006), pp.404–411 (Received 16th May, 2005)

∗∗ Department of Mechanical System Engineering, Kuma-moto University, 2–39–1 Kurokami, Kumamoto 860–8555, Japan. E-mail: [email protected]

∗∗∗ Thermal Technology Division, Fujikura Ltd., 1–5–1 Kiba,Koto-ku, Tokyo 135–8512, Japan

cated easily with low cost, the thickness is less than 5 mm,and it is lighter than the solid copper heat spreader of thesame size.

The current vapor chamber works effectively withoutencountering any problems, but the improvement of thethermal performance of the vapor chamber is indispens-able for cooling next generation MPUs. This is becausethe heat flux dissipated from the MPUs is increasing year-by-year resulting from the progress of data processing per-formance and the downsizing of the MPUs. In view ofthe above-mentioned fact, some experimental studies werealready carried out on the heat transfer characteristics ofthe vapor chamber, and the useful data were presented forthe improvement of the vapor chamber(3) – (6). Moreover, amathematical model of the vapor chamber was developedto analyze the thermal-fluid transport phenomena occur-ring inside the vapor chamber and to predict the thermalperformance of the vapor chamber in a short calculationtime(7) – (9).

This paper describes the effect of heat source sizeon the heat transfer characteristics of the vapor chamber.From previous studies of conventional heat pipes, it isconsidered that the heat source size is one of the impor-tant parameters to dominate the heat transfer characteris-tics of the vapor chamber; nevertheless, very few stud-

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ies have been published in this respect. Moreover, thiskind of study is required currently because the downsiz-ing of the MPUs is ongoing. First, by using three kinds ofheat sources having different sizes, the fundamental exper-iment is carried out to investigate the effect of heat sourcesize on the temperature distribution of the vapor cham-ber. Secondly, by using the mathematical model of thevapor chamber developed by the authors(7) – (9), numeri-cal analysis is moreover carried out to discuss the effectof heat source size on the thermal resistances inside thevapor chamber. Similar to conventional cylindrical heatpipes, the thermal resistance of the vapor chamber is di-vided into two parts of evaporator and condenser sectionsinside the vapor chamber. Each of them is discussed inthis paper.

2. Nomenclature

A : area cm2, m2

cp : specific heat J/(kg·K)hfg : latent heat of evaporation and condensation J/kg

K : permeability m2

k : thermal conductivity W/(m·K)p : pressure PaQ : heat generation rate Wq : heat flux W/cm2, W/m2

R : thermal resistance K/Wr : radial coordinate mm, m

r∗ : radius mm, mT : temperature ◦C

<T> : average temperature ◦CV : velocity vector = (v, w) m/sv : radial velocity m/sw : axial velocity m/sz : axial coordinate mm, mε : porosityµ : viscosity Pa·sρ : density kg/m3

Subscripts1, 2, · · ·, 5 : positions indicated in Fig. 2

air : cooling airb : bottomc : condenser section

cal : calculatede : evaporator section

eff : effectiveexp : experimental

l : liquid-wick regions : solid wall region

sat : saturatedsink : heat sinksou : heat source

t : topv : vapor regionvc : vapor chamber

Fig. 1 Photograph of the vapor chamber; dimensions inmillimeters

3. Vapor Chamber

Figure 1 shows a photograph of the vapor chambermounted on the base plate of the heat sink. This is thesame vapor chamber as described in the authors’ previouspaper(5). This paper addresses the extended study of thisvapor chamber on the effect of heat source size. The va-por chamber is essentially a flat-plate type heat pipe madeof copper. Water is enclosed as the working fluid. Sin-ter sheets (thickness: 0.5 mm) and sinter columns (diame-ter: 8.5 mm) made of small copper powders (powder size:100 – 200 mesh, porosity: 40%) are used as the wick tocirculate the working fluid. The sinter sheets are attachedto the upper and lower internal surfaces, and then the sin-ter columns are set inside the vapor chamber to ensure thecirculation of the working fluid.

The vapor chamber is placed between small heatsources and a large heat sink. Inside the vapor chamber,the working fluid receives the heat from the heat sourceand evaporates. The generated vapor spreads and flowsto the upper internal surface, where it condenses, and thecondensate returns to the lower internal surface throughthe wick to continue the circulation of the working fluid.Based on this principle of operation, the vapor chamberspreads the heat continuously from the heat source to theheat sink.

4. Experimental Apparatus and Procedure

Figure 2 shows a schematic illustration of the experi-mental apparatus. It consists of a wind tunnel, a heat sinkwith a vapor chamber, a heater used as a heat source, ablower, an orifice manometer setup and a damper. Thewind tunnel is 890 mm long and its cross section is rectan-gular (height: 31.0 mm, width: 78.0 mm). The heat sinkis placed in contact with the internal surface of the windtunnel so as not to cause the airflow deviation along thegap between the heat sink and the wind tunnel. The va-por chamber is mounted on the base plate of the heat sink.

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Fig. 2 Experimental apparatus (left) and measuring points of temperature at the top of thevapor chamber (right); dimensions in millimeters

Table 1 Specification of the heaters

The bottom surface area of the heat sink (= 76.2 mm ×88.9 mm) is equal to the top and bottom surface areas ofthe vapor chamber, and they are much larger than the heat-ing surface area of the heater (see Table 1). The heater isin the form of a square block and is attached to the cen-ter of the bottom of the vapor chamber, where the thermalgrease (thermal conductivity: 0.64 W/(m·K)) is applied.The damper is used to control the air velocity. The windtunnel, the vapor chamber and the heater are covered withthe thermal insulators made of foamed plastic and glasswool to minimize any heat loss from them to the atmo-sphere.

In the experiment, three kinds of heaters, H1, H2and H3, having different heating surface areas, Asou, asshown in Table 1, are used. The heat generation rate, Q, ischanged as Q=24, 48, 72 W, · · ·, while the air temperatureand the apparent air velocity inside the wind tunnel, whichis 0.73 of the pore velocity in the heat sink, are maintainedat 25◦C and 1.5 m/s, respectively. The temperature distri-bution of the vapor chamber in a steady state condition ismeasured by K-type thermocouples. The temperature atthe center of the bottom of the vapor chamber in contactwith the heater, Tb, is measured by a thermocouple fixedin a small groove machined on the top of the heater. Thetemperatures at the top of the vapor chamber, Tt,1, Tt,2, · · ·,Tt,5, are measured by five thermocouples located at the po-sitions indicated in Fig. 2. Five small holes are drilled intothe base plate (thickness: 2.5 mm) of the heat sink and thethermocouples are inserted into them. The air velocity ismeasured by the orifice manometer setup.

Similar to conventional heat pipes, the vapor cham-ber also has a maximum heat transfer rate. If Q is inputtedover this limitation, a part of the wick in the evaporatorsection inside the vapor chamber dries out, resulting inthe degradation of the thermal performance of the vapor

chamber. As mentioned above, the present experiment iscarried out by increasing Q, but to avoid this problem, it isstopped before Q reaches the maximum heat transfer rateof the vapor chamber. The heat input from the heater ismeasured by a wattmeter, while the heat output from theheat sink inside the wind tunnel is calculated from the air-flow rate and the temperature difference between the inletand outlet of the heat sink. Because the measured heat in-put agrees within 5.5% with the calculated heat output, theformer value is adopted as Q.

5. Mathematical Modeling and Numerical SolutionProcedure

Because the details of the mathematical model of thevapor chamber and its numerical solution procedure werealready contained in the authors’ previous papers(7) – (9),only their summaries are presented here.

Figure 3 shows the mathematical model of the va-por chamber, which consists of three regions of a vapor,a liquid-wick and a solid wall. For simplicity, the va-por chamber is modeled as an axisymmetric disk-shapedone and the numerical analysis is carried out in a cylindri-cal coordinate by using the following equivalent radii, r∗vc,r∗sou.

r∗vc= (Avc/π)1/2 (1)

r∗sou= (Asou/π)1/2 (2)

where Avc is the top surface area (= bottom surface area)of the actual vapor chamber, and Asou the heating surfacearea of the actual heat source (= contact area of the actualheat source at the bottom of the vapor chamber). The heatflux, q, is applied from the heat source and the top of thevapor chamber is entirely cooled by the heat sink.

The following assumptions:a) A steady state condition is established inside the

vapor chamberb) The vapor flow is laminarc) The wick is isotropicd) The circulation of the working fluid is ensurede) The vapor condenses and the liquid evaporates

only at the interface between the vapor and liquid-wickregions


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Fig. 3 Mathematical model and boundary conditions

Table 2 Governing equations

are made in conducting the analysis, and the governingequations for the vapor, the liquid-wick and the solid wallregions are given respectively as shown in Table 2, whereV is the velocity vector = (v, w), p the pressure, T thetemperature, ρ the density, µ the viscosity, cp the specificheat, k the thermal conductivity, ε the porosity, K the per-meability. Subscripts v, l and s stand for the vapor, theliquid-wick and the solid wall regions, respectively. Equa-tions (6) – (8) are derived by using the pore velocity, andkeff is the effective thermal conductivity in the liquid-wickregion.

The boundary conditions are also indicated in Fig. 3,where hfg is the latent heat, Tair the temperature of coolingair. The temperature along the vapor-liquid interface istaken as a saturated temperature, Tsat, corresponding to thepressure inside the vapor chamber. The authors have theexperimental result(5) on the heat transfer characteristicsof the heat sink shown in Fig. 1, so the value of the thermalresistance of the heat sink, Rsink, is obtained from them(Rsink =0.249 K/W).

The control volume method and the SIMPLE algo-rithm(10) are employed to solve the governing equationswith the boundary conditions. Because Tsat cannot be de-termined from the above equations, the numerical results

Table 3 Specification of the vapor chamber

are obtained with Tsat as a parameter, and then the one re-sult is selected based on the following steady-state energybalances within 0.1%: the evaporative heat transfer rateinside the vapor chamber agrees with the rate of conden-sation, and the heat input to the vapor chamber agrees withthe heat output from the vapor chamber.

The specification of the mathematical model is de-termined as shown in Table 3 based on the actual vaporchamber shown in Fig. 1.

6. Results and Discussion

6. 1 Temperature distribution inside the vaporchamber

Figure 4 shows the experimental results of the tem-perature at the center of the bottom of the vapor chamber,Tb, and the temperatures at the top of the vapor chamber,Tt,1, Tt,2, · · ·, Tt,5. Tt,5 is found to be slightly lower thanTt,1, Tt,2, Tt,3 and Tt,4 because it is located near the air in-let of the heat sink. However, the small differences in Tt,1,Tt,2, · · ·, Tt,5 implies that the heat applied from the heater tothe vapor chamber is spread almost uniformly to the heatsink. In the following discussion, the average of Tt,1, Tt,2,· · ·, Tt,5 is used and expressed as <Tt>. Figure 5 shows the


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Fig. 4 Temperatures at the top and bottom of the vaporchamber

Fig. 5 Relation between temperatures of the vapor chamberand heat generation rate

experimental results of the relation between Tb, <Tt> andQ. It is confirmed that Tb is greatly affected by the heatsource size, Asou, while the difference is not observed in<Tt>.

Concerning Tb and <Tt>, the experimental results,Tb,exp, <Tt,exp>, are compared in Fig. 6 with the numericalresults, Tb,cal, <Tt,cal>. The agreement between <Tt,exp>

and <Tt,cal> is very close because the value of the ther-

Fig. 6 Correlation between experimental results and numericalresults

mal resistance of the heat sink, Rsink, is obtained fromthe authors’ previous experimental results(5) as mentionedabove. The agreement between Tb,exp and Tb,cal, on theother hand, is known to depend on the estimation of theeffective thermal conductivity, keff , in the liquid-wick re-gion(9), and in the present numerical analysis, the excel-lent agreement is obtained as shown in the figure whenkeff = 4.0 W/(m·K) is given. This value of keff is consid-ered to be valid because the published equations by Chi(11)

and Yagi-Kunii(12), which were both presented for estimat-ing keff of sintered metal powder wicks, give keff = 3.36 –3.61 W/(m·K) and keff = 7.93 – 8.40 W/(m·K) respectively,and the present value of keff = 4.0 W/(m·K) lies betweenthem. This value of keff is used in the following furthercalculations.

Figure 7 shows the numerical results of the temper-ature distribution inside the vapor chamber. The dashedlines represent the interfaces between the vapor and liquid-wick regions, and the liquid-wick and solid wall regions.In addition, the numerical result of the vapor velocity dis-tribution inside the vapor chamber is shown in Fig. 8. In-side the vapor chamber, the liquid in the liquid-wick re-gion receives the heat from the heat source and evaporates.The generated vapor spreads through the vapor region andthen condenses at the upper interface between the vaporand liquid-wick regions. The condensate returns from theupper to the lower wick to continue the circulation of theworking fluid. Because the latent heat of evaporation andcondensation of the working fluid is utilized to transportthe heat, it is found that the temperatures in the vapor re-


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(a) Asou=1.5 cm2 (b) Asou =6.0 cm2

Fig. 7 Temperature distribution inside the vapor chamber for Q=144 W and Tair =25◦C

Fig. 8 Vapor velocity distribution inside the vapor chamber for Asou =6.0 cm2, Q=144 W andTair =25◦C

(a) Effect of heat flux for Asou =6.0 cm2 (b) Effect of heat source size for q=24 W/cm2

Fig. 9 Thermal resistances inside the vapor chamber

gion and therefore at the top of the vapor chamber are al-most uniform. The numerical results also indicate that thetemperature gradient near the heat source becomes largeras Asou decreases, because the decrease in Asou causes toincrease the heat flux, q, from the heat source; while thetemperature at the top of the vapor chamber is hardly af-fected by Asou, which is similar to the experimental re-sults shown in Figs. 4 and 5. Because the effective ther-mal conductivity in the liquid-wick region is considerablylow compared to the thermal conductivity in the solid wallregion, the temperature gradient in the former region ismuch larger than that in the latter region.

For the cases of Fig. 7 (a) and (b), the heat trans-fer rates through the bottom surface (r = 0 – 4.3 mm, z =2.0 mm) of the centered wick column are calculated at10.4 W and 5.1 W, respectively. This heat transfer rate isfound to increase as Asou decreases. However, becauseboth the values are much smaller than the heat input,Q = 144 W, it is confirmed that the heat flow through the

centered wick column is very small. Most of the heat ap-plied from the heat source is transferred through the vaporregion utilizing the latent heat of evaporation and conden-sation of the working fluid.

6. 2 Thermal resistance inside the vapor chamberThe thermal resistance of the vapor chamber, Rvc, is

defined by the following equation:

Rvc= (Tb−<Tt>)/Q (10)

and, by using the saturated temperature, Tsat, correspond-ing to the pressure inside the vapor chamber, Rvc is dividedinto two parts, namely, the thermal resistances of the evap-orator section, Re, and the condenser section, Rc, inside thevapor chamber. Re and Rc are expressed respectively as

Re = (Tb−Tsat)/Q (11)

Rc = (Tsat−<Tt>)/Q (12)

The heat generation rate, Q, in Eqs. (10) – (12) is ex-pressed as Q=q×Asou, and the effects of q and Asou on Rvc,Re and Rc are examined numerically in Fig. 9. Irrespective


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Fig. 10 Effect of heat source size on thermal resistances forQ=72 and 144 W

Fig. 11 Effect of centered wick column on thermal resistances

of q and Asou, it is found that Rc is very small and Re isnearly equal to Rvc, implying that Re is dominant insidethe vapor chamber. The numerical results also indicatethat Re and Rvc are hardly affected by q, but they increasewith the decrease in Asou. Figure 10 shows the numericalresult of the relation between Re, Rvc and Asou. It is alsorevealed that even when Q is constant, Re and Rvc increaseas Asou decreases.

6. 3 Effect of centered wick columnThe numerical results are moreover obtained when

the centered wick column inside the vapor chamber is re-moved, and the effect of centered wick column on Rvc, Re

and Rc is shown in Fig. 11. The purpose of the centeredwick column is to ensure the circulation of the workingfluid and to resist the external forces squashing the vaporchamber. Irrespective of Asou, it is found that Re and Rvcwith the centered wick column are about 13% higher thanthose without the centered wick column. This is becausekeff is comparatively low and the centered wick columnstops the evaporation of the working fluid at the vapor-liquid interface at r = 0 – 4.3 mm, z=2.0 mm. Because the

small amount of heat is transferred through the centeredwick column as mentioned above, a slight decrease in Tsat

is observed when the centered wick column is placed. Rc

is very sensitive to this change in Tsat due to the very smallvalue of (Tsat –<Tt>), and therefore Rc with the centeredwick column is about 10% lower than that without the cen-tered wick column. Although the vapor chamber used inthis study has the centered wick column above the heatsource, it is better to place it at the position except justabove the heat source inside the vapor chamber to decreasethe thermal resistance and to increase the thermal perfor-mance of the vapor chamber.

7. Conclusions

Experimental and numerical analyses were carriedout to investigate the effect of heat source size on theheat transfer characteristics of the vapor chamber, whichis used as a novel heat spreader for cooling high-heat-fluxMPUs. It was found that the thermal resistance of the con-denser section inside the vapor chamber was very small,and that of evaporator section was nearly equal to the to-tal thermal resistance of the vapor chamber, implying thatthe thermal resistance of the evaporator section was dom-inant inside the vapor chamber. It was also revealed thatthe thermal resistance of the vapor chamber was hardly af-fected by the heat flux applied from the heat source, whileit increased as the heat source became smaller. The wickcolumn is placed inside the vapor chamber to ensure thecirculation of the working fluid and to resist the externalforces squashing the vapor chamber. However, the numer-ical results also showed that irrespective of the heat sourcesize, the thermal resistance of the vapor chamber was in-creased by 13% by the centered wick column placed justabove the heat source inside the vapor chamber. There-fore, the wick column should be placed at the position ex-cept just above the heat source inside the vapor chamber todecrease the thermal resistance and to increase the thermalperformance of the vapor chamber.

References

( 1 ) Mochizuki, M., Nguyen, Th., Mashiko, K., Saito, Y.,Nguyen, Ti., Wu, X.P. and Wuttijumnong, V., LatestTechnology Using Micro Heat Pipes and Vapor Cham-ber for Cooling Personal Computer, Proc. 1st Int. Sym-posium on Micro & Nano Technology, XXXV-C-02(CD-ROM), (2004).

( 2 ) Mochizuki, M., Nguyen, Th., Mashiko, K., Saito, Y.,Nguyen, Ti., Wuttijumnong, V. and Wu, X., PracticalApplication of Heat Pipe and Vapor Chamber for Cool-ing High Performance Personal Computer, Proc. 13thInt. Heat Pipe Conf., (2004), pp.448–454.

( 3 ) Mochizuki, M., Mashiko, K., Goto, K., Saito, Y.,Nagata, M., Eguchi, K., Nguyen, Th. and Ho, P.,Cactus-Type Heat Pipe for Cooling CPU, Proc. 5th Int.Heat Pipe Symposium, (1996), pp.194–198.

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Sauciuc, I. and Nguyen, Th., The Optimum WorkingFluids Ratio for Vapor Chamber, Proc. 6th Int. HeatPipe Symposium, (2000), pp.159–163.

( 5 ) Koito, Y., Motomatsu, K., Imura, H., Mochizuki, M.and Saito, Y., Fundamental Investigations on HeatTransfer Characteristics of Heat Sinks with a VaporChamber, Proc. 7th Int. Heat Pipe Symposium, (2003),pp.247–251.

( 6 ) Agata, H., Kiyooka, F., Mochizuki, M., Mashiko, K.,Saito, Y., Kawahara, Y., Nguyen, Th. and Nguyen,Ti., Advance Thermal Solution Using Vapor Cham-ber Technology for Cooling High Performance Desk-top CPU in Notebook Computer, Proc. 1st Int. Sympo-sium on Micro & Nano Technology, XXXV-C-01 (CD-ROM), (2004).

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( 8 ) Koito, Y., Imura, H., Mochizuki, M., Saito, Y. andTorii, S., Numerical Analysis on Thermal TransportPhenomena in Plate-Type Heat Pipes, Proc. 10th APC-ChE Congress, 3I-06 (CD-ROM), (2004).

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(11) Chi, S.W., Heat Pipe Theory and Practice, (1976), p.48,Hemisphere Pub. Corp., Washington.

(12) Japan Association for Heat Pipes (JAHP), JitsuyouHeat Pipe, (in Japanese), 2nd Ed., (2001), p.31, NikkanKogyo Shimbun, Ltd., Tokyo.


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