Project ReportMVK160 Heat and Mass Transfer

May 7, 2012, Lund, Sweden

Heat Pipe, selection of working fluid

Per WallinDept. of Energy Sciences, Faculty of Engineering,Lund University, Box 118, 22100 Lund, Sweden

Abstract

Heat pipes are common in many application fieldsfor example cooling of electronics. The design ofa heat pipe is rather complex with many thingsto consider. In this project the focus is the getknowledge about who to select the working fluid tobe used.

Introduction

"A heat-transfer device consisting of a sealedmetal tube with an inner lining of wicklike cap-illary material and a small amount of fluid ina partial vacuum; heat is absorbed at one endby vaporization of the fluid and is released atthe other end by condensation of the vapor."Definition by McGraw-Hill Dictionary of Scientificand Technical Terms.

Heat Pipes are used in many applications allfrom cooling of the CPU in a computer, spaceapplication, energy storage for some solar thermalapplications, air conditions etc. Micro heat pipeswith diameters small as 100m, high temperatureheat pipes with silver as working fluid(temperatureup to 2300C) and low temperature heat pipeswith helium(temperature down to -271C). Thereare many different kinds of heat pipes but theworking principle is similar. The design of astandard heat pipe are illustrated in figure 1. Theliquid is evaporated at the hot end then transferedto the cool end and condensed to liquid again. Thetransfer back to the hot end is made by a capillaryforce with positive/negative contributions fromgravity. The capillary force makes it possible totransfer liquid against the gravity field.

When you design a heat pipe there are threemain selection to do, working fluid, case materialand wick. These are closely linked to each otherto achieve best conditions. In this project themain purpose is to select the working fluid butcase and wick is also briefly described to get betterknowledge of a heat pipe.

Figure 1: Standard Heat Pipe

Problem Statement

Selection of working fluid in a heat pipe

Theory

Working fluid

Selection of working fluid is directly linked to theproperties of the fluid. The properties is going toboth affect the ability to transfer heat and the com-parability with the case and wick material. Below issome things to consider when you choose the work-ing fluid.

Compatibility with wick and wall materials

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Project ReportMVK160 Heat and Mass Transfer

May 7, 2012, Lund, Sweden

Good thermal stability

Wettability of wick and wall materials

Vapor pressures not too high or low over theoperating temperature range

High latent heat

High thermal conductivity

Low liquid and vapor viscosities

High surface tension

Table 1: Working fluids

Operation Limits

To be able to choose right material, it is impor-tant to understand the operation limitations. Fig-ure 2 show the different limitations to be consid-ered. The limitations must be fulfilled both duringdesign conditions and during start up. The figureis for a specific condition and and going to changedepending on fluid and wick.

Figure 2: Operation Limitations

The viscous limit

At very low temperature the vapor pressure differ-ence between the closed end of the evaporator andthe closed end of the condenser may be very small.Viscous forces can then be dominant and limit theoperation of the heat pipe. Low temperature in theworking fluid is most common at startup and makesthe possibility to reach the viscous limit most pos-sible at startup. Expression below is a criterion forwhen the viscous limit has to be considered

PvPv

< 0.1 (1)

derived by Dunn and Reay. The concern of thislimit depend on the temperature and is of littleimportant in design of heat pipes for room temper-ature applications according to Handbook of heattransfer.

The sonic limit

The vapor velocity may reach sonic values. Asvelocity approaching sonic there is going to com-pressibility effects that affect pressure. It makes ittherefore desirable to have maximum velocity be-low sonic, which give the maximum heat flux as

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Project ReportMVK160 Heat and Mass Transfer

May 7, 2012, Lund, Sweden

equation below.

qs = vL

vRTv

2(v + 1)(2)

The entrainment limit

The liquid and vapor flows in different directions inthe heat pipe. When the vapor reach the condenserit is going to affect the liquid in the inside of thewick. If the shear force because of the vapor is bigcompared to the surface tension in the liquid thereis likelihood of entrainment of liquid drops in thecondenser. The Weber number is the ratio betweeninertial vapor forces and liquid surface tension foresand is defined as,

We =vv

2vz

2pil(3)

where index v relate to vapor, l is the surface ten-sion and z is a dimensions characterizing the vapor-liquid surface. In a wicked heat pipe, z is relatedto the wick spacing. Experiment have proved thatentrainment may occur when Weber number is oforder of one. The maximum velocity because ofentrainment is then

vc =

2pilvz

(4)

which do that the maximum heat flux is

q = vLv =

2pivL2l

z(5)

From equation 5 it can be seen that just some ofthe properties depend on the working fluid. Theseproperties can be used to form a expression of en-trainment for the working fluids.

vL2l (6)

The capillary limit

Pc Pl +Pv +Pg (7)where indexes c,l,v,g refers to capillary, liquid, va-por and gravity. If this condition is not met, thewick will dry out in the evaporator region and theheat pipe will not operate. An expression for themaximum flow rate may be obtained if it is assumedthat

the liquid properties do not vary along the pipe the wick is uniform along the pipe the pressure drop due to vapor flow can beneglected

mmax =[lll

] [KA

l

] [2re lgl

lsin()

](8)

The maximum allowed heat flux can den be spec-ified as

Q = mmaxL =[llL

l

] [KA

l

] [2re lgl

lsin()

](9)

The first group depends only on the propertiesof the working fluid and is called Merit number.

M =llL

l(10)

The capillary limit is the above limit of the heatflux for a big part of the temperature region. TheMerit number can therefore be used to evaluate theperformance of the heat pipe depending on workingfluid.

The boiling limit

At high temperature and heat flux there is going tobe nucleate boiling in the wick of the evaporator.Vapor may then block the liquid to be supplied toall parts of the evaporator. It is desirable to reducethe chance of nucleation. A working fluid degree ofsuperheat to cause nucleation is given by

T =3.06lTsatvL

(11)

where is the thermal layer thickness and is takenas a representative value of 25m to compare work-ing fluids. It is desirable to have a working fluidwith high value of superheat, T .The expressioncomes from analysis by Hsu.

Compatibility with wick and case ma-terialsCompatibility between the working fluid and ma-terial of the wick is important for the heat pipe

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Project ReportMVK160 Heat and Mass Transfer

May 7, 2012, Lund, Sweden

to work work good and have a desired service life.Problem because of non compatibility are decreasedperformance,failure or corrosion. Decomposition ofthe working fluid can lead to corrosion and forma-tion of non condensible gases through chemical re-actions between the working fluid and material, cancause problem with the operation of the heat pipe.Compatibility test by Basiulis and Busse have beenmade which the result is showed in table 2.

Table 2: Compatibility data

Case materialThe case is the heat pipes connection to the out-side environment. Heat has to be able to transferthrough the case to and from the working fluid inthe evaporator and condenser. At the same time itis desirable to have no heat transfer in the adiabaticarea and to maintain pressure differential across thewalls. Selection of the case material depends on thefollowing factors

Compatibility (both with working fluid andthe external environment)

Strength-to-weight ratio Thermal conductivity Ease of fabrication, including weldability, ma-chineability and ductility.

Wick materialThe main functions of the wick is to generate cap-illary pressure and to distribute the liquid aroundthe evaporator area. If the heat pipe has to re-turn the liquid over a distance against the gravityfield there is big requirement of the wick. Thereforthere are many different forms of wick depending of

the heat pipe and its location to be able to satisfythe two main functions. Some forms of wicks areshowed in figure below.

Figure 3: Wick Structure

Problem description

A heat pipe with minimum heat transport of 25W is going to be used for cooling electronic com-ponents. Vapor temperatures are in region 40C -120C. The inner diameter is 3 mm and wick andcase is made of copper. Select a working fluid.

Result

Working fluids that can operate in the specifiedtemperature range and are compatible with copperaccording to the known theory is acetone, methanoland water.

Satisfaction of operation limits

The operation temperature is not considered forvery low temperatures and therefore you dont haveto consider the viscous limit. The four remain-ing limits are sonic limit, entrainment limit, boilinglimit and capillary limit.

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Project ReportMVK160 Heat and Mass Transfer

May 7, 2012, Lund, Sweden

Sonic Limit

The sonic limitations has to be considered at theminimum temperature, 30C. Equation 2 is usedto evaluate the fluids. The heat capacity ratio andgas constant for the fluids are in table below

Table 3: Fluid Properties R[J/kgK]

Acetone 1.11 150Methanol 1.26 390Water 1.32 460

This give that the maximum heat flux because ofthe sonic limit is

Table 4: Sonic LimitHeat flux

Acetone 6.3 kW/cm2Methanol 11.3kW/cm2Water 2.4kW/cm2

The heat pipe have a circular cross section andare required to transport minimum of 25 W 25/0.152piW/cm2 = 0.35kW/cm2. Comparisonwith the sonic limitations, you can see that limitis not going to be reach for the fluids.

Boiling limit

T is evaluated at 120 C, as the lowest permissi-ble degree of superheat will occur at the maximumoperating temperature.

Table 5: Boiling LimitT

Acetone 0.11KMethanol 0.09KWater 1.07K

Entrainment Limit

The entrainment limit is evaluated for the temper-ature interval and are showed in figure 4. Valuesfor the fluids are taken from appendix.

Figure 4: Entrainment Limit

Capillary Limit

The performance of the working fluids can be eval-uated by the Merit Number. The Merit numberfor the different fluids are showed in figure below.Values for the fluids are taken from appendix.

Figure 5: Capillary Limit

ConclusionsThe three working fluids have been evaluated withregard to the operation limitations. Water are bestfor most of the limits compared to methanol and

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Project ReportMVK160 Heat and Mass Transfer

May 7, 2012, Lund, Sweden

acetone. Especially the capillary limit that is ameasurement for the performance is water superior.The choice is therefore water as working fluid.

ReferencesMcGraw-Hill Staff, McGraw-Hill Dictionary ofScientific and Technical Terms, 6th edition, 2002

Reay D.A and Kew P.A, Heat Pipes, 1-167,346, 348; 5th edition, Elsevier, 2007

Basiulis, A. and Filler, M. Operating charac-teristics and long life capabilities of organic fluidheat pipes. AIAA Paper 71-408. 6th AIAAThermophys. Conference, Tullahoma, Tennessee,April 1971.

Hsu, Y.Y. On the size range of active nucle-ation cavities on a heating surface. J. HeatTransf., Trans A.S.M.E., August 1962.

Warren M. Rohsenow, James P. Hartnett, YoungI. Cho, Handbook of heat transfer,12.1-12.20, 3thedition, McGraw-Hill, 1998

http://www.engineeringtoolbox.com/spesific-heat-capacity-gases-d159.html, 2012 05 04

http : //www.enertron inc.com/enertron products/heatpipeselection.php, 20120504

http : //en.wikipedia.org/wiki/Heatpipe, 2012 05 04

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Appendix