138 Philips tech. Rev. 33, 138-148, 1973, No. 5

Heat pipes

G. A. A. Asselman and D. B. Green

11. Applications

The applications of heat-pipe systems that will bedealt with in this part of the article [*1 are discussedunder four distinct headings corresponding to four ofthe main features of heat pipes. These four featuresare: the exceptionally high thermal conductivity, thesmall variation in temperature throughout the pipe, theability to give a heat-flux transformation, and the tem-perature sensitivity. The heat flux is transformed if theevaporator and condenser have different surface areas,so that the heat flux at these two parts of the pipe hasa different value. Temperature sensitivity refers to thedegree to which the mean temperature of a heat pipedepends on the heat flux, which is also a quantity ofconsiderable significanee in applications of the heatpipe. The température sensitivity of simple heat pipesis already very high, and it can be increased to excep-tionally high values in the variable-conductance heatpipes, which we shall discuss in the concluding sectionof this article.

The four features mentioned above are of courseinterdependent and are used in combination in anysingle application. The justification for discussing theapplications in groups, in each ofwhich one ofthe fourcharacteristic features is prominent, is that it mayheighten the appreciation of the peculiar advantages ofheat pipes over conventional heat-transport systems.

Heat transport

There are numerous applications employing the highheat-transfer capability of heat pipes. One that we havebeen concerned with is the transport of heat from asource of thermal energy to the heater head of a Stirlingengine. When a heat pipe is used a Stirling engine canbe combined with various types of heat source [71.

Fig. 7 shows a 10 hp Stirling engine being driven ona test bench by heat supplied along a 15 cm diametersodium-charged heat pipe, operating at about 750 oe.In this instance the heat pipe received its heat inputfrom a series of electrical heating elements (25 kW)wound around the evaporator section. In practice a

Ir G. A. A. Asselman is with Philips Research Laboratories,Eindhoven; Dr D. B. Green was formerly with Philips ResearchLaboratories.

Stirling engine will not be required to operate from anelectrical source, but from a combustion process. Theadvantage of incorporating heat pipes then lies morewith the ability to transform heat fluxes than with thehigh heat-transfer capability. With unconventionalcombustion processes both aspects can play an impor-tant role. In addition, some Stirling systems currentlyunder development are only viable because of heat-pipe technology.

Another application is a siphon for the transport ofmolten salts. As jig. 8 shows, one end of the siphon isplaced in the vessel containing the molten salt andheat is transferred from the salt and along the length ofthe siphon by heat-pipe action. In this way the siphontube may be maintained at a temperature close to thatof the molten salt in the vessel, enabling the salt to betransferred through the siphon without the danger of

Fig. 7. Test system with a 10 hp Stirling engine driven by heatsupplied along a sodium-charged heat pipe. The pipe itself iselectrically heated; at 750°C and with a temperature differenceofonly a few degrees it can transmit more than 25 kW ofenergy.The crankshaft of the Stirling engine can be seen at the bottomof the picture in the centre; above it is the engine head, envelopedin insulating material. The heat pipe protudes from the front.

Philips tech. Rev. 33, No. 5 HEAT PIPES, 11 139

;_L I'-'--

l- t-

\ I-:»:: r-lALFig. 8. A siphon heated by heat-pipe action. A siphon of thistype can be used for transporting molten salts from vessel tovessel without the danger of clogging because of solidification.The evaporator section (on the left) is immersed in the liquid tobe transported, so that the siphon tube is automatically kept atabout the same temperature as the molten salt. The liquid flow iscaused by the pressure of compressed gas admitted to the reser-voir vessel. The insulating material around the pipe is not shown.

clogging arising from solidification. We have made asiphon of this type for the transport of molten lithiumfluoride. The working fluid is sodium and the envelopeis made of stainless steel.

Elsewhere the large heat-transfer capability of heatpipes has been applied in quite different ways. Someattempts have been made to cool electronic circuits andcomponents with heat-pipe systems [81, thus eliminat-ing the need for metal cooling bars and other heatsinks. Extensive use has also been made of heat pipesin direct-energy-conversion systems [91.

Isothermal spaces

The temperature is almost the same at all pointsinside a heat pipe. This feature arises because thethermal resistances RL-V and RV-L (see I, fig. 5) aresmall, so that the temperature gradients are also small,provided that the heat fluxes are not too excessive. Aheat pipe whose basic function is the creation of anisothermal surface rather than the transport of largequantities of heat is usually referred to as an isothermalchamber. Such chambers are designed to have a mini-mum of obstruction to the vapour flow, so that pres-sure gradients in the vapour may be rapidly eliminated.Inside an ideal isothermal chamber the liquid in thewick is everywhere in equilibrium with its vapour. Aswe have seen (I, page 108/9), itfollowsfrom the relation-ship between the temperature and the pressure of thesaturated vapour that a small change in temperature ofthe liquid in the 'wick can give rise to vapour flow to-wards or away from other parts' ofthe chamber, accom-panied by condensation or evaporation of fluid and theliberation or absorption of latent heat. This continuesuntil the temperature variation is eliminated. .

Just how small the temperature differences in a heatpipe are, even when it is not specially designed as anisothermal chamber, is illustrated by fig. 9. The dia-gram shows the temperature profile measured in thevapour duct of a stainless-steel heat pipe of 1 cm diam-eter. The working medium was sodium operating at avapour pressure of about one atmosphere, and henceat a mean temperature of approximately 833 oe, theboiling point of sodium. The temperature drop along50cm of the pipe, from the beginning of the evaporatorto the end of the condenser, is only a few degrees. (Thesharp drop in temperature at the very end of the con-denser is associated with the presence of a non-conden-sable gas in the heat pipe. We shall return to this subjectin the section dealing with variable-conductance heatpipes.)

The dashed curve in fig. 9 is the temperature profile measuredafter the introduetion of a quantity of mercury into the system.One effect of adding a second component to the working fluidis evidently the loss of the spatial isothermality. However, thebehaviour of two-component systems is rather complicated, andwill not be discussed here.

The most important industrial application of iso-,thermal chambers is undoubtedly in ovens. A heat-pipeoven generally consists of two concentric cylinders be-tween which a heat-pipe process can operate. Heating

700

t---- ........",oiiii'",;;;;::~====,-883°C~'\. 1

-,-,<,\

B5at%Na \15 at %Hg \

\\\\\

T

t BOO\Na

\o 10 20 30 40

-[

Fig. 9. Temperature distribution in a sodium-charged heat pipe.The temperature T in the vapour duct is plotted against the dis-tance x between the point in question and the input end of theevaporator. It can be seen that the temperature drops only a fewdegrees over a length of 50 cm. The abrupt drop at the end isdiscussed in the final section of the article. The dashed line relatesto an experiment in which the pipe contained a second condens-able liquid, mercury, as well as sodium.

50cm

[*] Part I of this article appeared in Philips tech. Rev. 33,104-113, 1973 (No. 4). .

[7] See for example: R. J. Meijer, Prospects of the Stirlingengine for vehicular propulsion, Philips tech. Rev. 31,169-185, 1970. .. . .

[8] C. H. Dutcher Jr. and M. R. Burke, Electronics 43, No. 4,94, 16 Feb. 1970.

[9] C. A. Busse, Proc. 4th Intersociety .Energy ConversionEngng. Conf., Washington D.C. 1969, p. 861.

140 G. A. A. ASSELMAN and D. B. GREEN Philips tech. Rev. 33, No. 5

is usually by electrical resistance, or is inductive, usingradio-frequency coils. These may either surround theoven itself or deliver heat only to the evaporator sec-tion, which may be located at some distance from theoven. This permits a certain amount offlexibility, whichis particularly important when the oven is to be en-closed in some other system. We shall now discuss sometypical ovens in current use. Other types will be de-scribed in the final section of the article.

The black-body radiator

This type of oven was designed to produce black-body radiation for the calibration of pyrometers. Twoversions were made, one operating at 450 oe and em-ploying potassium as the working medium, and theother operating at about 750 oe and using sodium.Both are 13 cm long and have a diameter of 5.4 cm;they are heated by electrical resistance.

The isothermal insert

As the name indicates, this device was designed forinsertion in a conventional oven to improve the uni-formity of the temperature distribution (fig. lOa). Ithas no heating system of its own, but serves only toredistribute the heat from the surrounding oven. Ovensequipped with an isothermal insert are used at Philipsin the measurement of physical properties of glasses.The working medium is again sodium, and the operat-ing temperature lies between 700 oe and 850 oe.The battery of ovens

Fig. lOb shows a number of ovens interconnectedvia a common evaporator region, so that they have acommon temperature. Batteries of ovens are employedfor softening copper wires in a continuous process, inwhich eight wires can be treated simultaneously. Forthis application potassium is the working medium, theoperating temperature is about 450 oe and the lengthof the oven is about one metre.

Ovens with relatively high or low vapour pressure

Industrial processes often require conditions that aredifficult or impossible to reconcile with the desirabilityof operating the oven at a temperature such that thevapour pressure is approximately equal to the pressureoutside the heat pipe. In a sintering process, for ex-ample, the required temperature was 1150 oe. The natur-al choice of working medium would be lithium (see I,fig. 5 or Table Ill), but the corrosion problems asso-ciated with this metal are so great as to make the em-ployment of sodium preferable. The vapour pressure ofsodium at this temperature, however, is about 7 atmos-pheres, which introduces a new problem since above1000 oe the creep strength of most metals falls rapidly.

~

I!I '=7

a

----_._-- ---------

I I

j I1

I

l I

j

b

c

Fig. 10. Three examples of isothermal spaces operating in aspecific temperature range. They consist in principle of two con-centric cylinders, the outer one being the evaporator and theinner one the condenser; the heat-pipe process takes place in thespace between them.a) Isothermal insert. The whole pipe is placed in an oven toredistribute the heat more uniformly than is possible with theoven alone.b) A battery of eight ovens interconnected by a common evap-orator. These ovens are used for the simultaneous softening ofeight copper wires.c) A sodium-charged oven for 11 SO °C. Since this temperaturerequires a sodium pressure of about 7 atmospheres, instead ofone space acting as the heat pipe between inner and outer wall,as in (a), there are here 18 axial channels.

Philips tech. Rev. 33, No. 5 HEAT PIPES, II 141

To minimize thermal creep in the oven, we employedan oven like the one shown in cross-section in fig. lOc.The oven consists of a thick-walled steel pipe (25/20Cr-Ni steel) with channels drilled in the wall. Eachchannel contains a wick, and each works as a heat pipein the radial direction. In this way all the channels to- .gether contribute to the heat transfer from the outsideto the inside wall.We adopted a similar solution for an oven in which

the sodium vapour pressure in the space between insideand outside wall had to be much lower than the ambientpressure. This was required to be some tens of atmos-pheres for the sintering of optical fibres at a temperatureof about 800°C. The oven was constructed from 18/8Cr-Ni steel and grooves were cut in the inside wall.These ensured that even if both walls were pressedtogether by the external pressure, the result would infact be the cross-section shown in fig. lOc, and the heat-pipe function could still continue in the space left bythe grooves.

Heat-flux transformers

The surface areas of the evaporation and condensersections of a heat pipe need not be the same. Becauseof this a heat flux may be transformed from a higherto a lower value, or vice versa, since of course the totalheat-transport rate has the same value at evaporatorand condenser. This useful feature arises because therates of evaporation and condensation are determinedprimarily by local conditions, the most important onebeing the difference tl.P between the pressure of thevapour and the saturation value. As we saw in I(page 109) this depends on the heat flux q and isgiven by:

q = tl.P L (M/2nRT)t.

Since this relation holds equally for evaporation andcondensation processes, the ratio of the heat flux at theevaporator to the heat flux at the condenser - the'transformation ratio' - is:

qE/qC = tl.PE/tl.!'C,

where the subscripts E and C refer to the evaporatorand condenser sections respectively.Since the total heat transport is the same at evap-

orator and condenser, we have:

Q = AEqÈ = Acqc.

If the Clausius-Clapeyron equation is .now used torelate pressure and temperature differences, we maywrite for the limit in which these differences are small:

Since the flux-transformation ratio is equal to the ratioof two pressure differences, it may have a very largevalue evenwhen the individual pressure differences arethemselves small compared with the mean vapour pres-sure in the heat pipe.This particular feature of heat-pipe systems is being

exploited in several systems currently under develop-ment at Philips Research Laboratories. In this way it ispossible to provide a Stirling engine with a heat-pipeflux transformer between the burner and the heaterhead. This will enable the heat-transfer surface on theburner side (the evaporator) to be much larger thanthat of the engine-heater pipes on which the workingmedium will condense.

Fig. 11 shows an experimental indirect heating sys-tem fitted to a Stirling engine. The heat pipe usessodium as the working medium and operates at a meantemperature of 730°C, transporting heat at an averagerate of about 25 kW.In the test arrangement in fig. 7 the heating is elec-

trical, but in the engine itself the system is heated byatomized diesel fuel, resulting in a mean combustion-gas temperature of 1600 °C. Heat is transferred to theworking medium of the heat pipe at an average rateof about 14W/cm2• The sodium vapour flows through

Fig.H. Indirect heating system for à Stirling engine in which a so-dium-charged heat pipe HP operates as a heat-flux transformer,Combustion gases deliver theirheat to the heat pipe via a largesurface (small heat flux), but this transfers the heat to the enginevia a much smaller surface area (large heat flux). Cyl cylinder,R regenerator and H heater pipes of the engine. W gauze wick.F fuel atomizer. CC combustion ·chamber. A air- inlet. G corn-bustion gases.

142 G. A. A. ASSELMAN and D. B. GREEN Philips tech. Rev. 33, No. 5

Fig. 12. Wickless heat pipe in the form of a horizontal hollow disc, containing sodium as theworking medium. The disc is heated circumferentially by r.f. induction, and its edge thereforefunctions as the evaporator. When the disc is stationary (at the left) there can be no heat-pipe action, since the condensate does not return to the circumference. When the disc isrotated about a vertical axis (on the right), centrifugal force ensures the transport of thecondensate and the disc then operates as a heat pipe.

the heat pipe at a rate that corresponds on average toan axial heat flux of 500 Wjcm2. At the engine head,sodium vapour condenses on the heater pipes of theengine, and here the heat flux is about 23 W jcm2. Thecorresponding heat-flux transformation ratio is thus1 : 1.6, and the calculated temperature drop betweenevaporator and condenser is 2.7 "C.

Another application of flux transformation that wehave investigated concerns a wickless sodium-chargedheat pipe; the pressure head necessary for the return ofcondensed liquid to the evaporator region is obtainedby rotation of the heat pipe. This heat pipe, in theform of a hollow, rotating disc, was meant to simulatethe anode of a 'Rotalix' X-ray tube. With rotatinganodes it could be advantageous, for several reasons,if the heat generated at the small target area where theelectron beam strikes it could be distributed uniformlyover the whole anode disc and dissipated from thereas radiation. If the disc itself consists of a heat-pipesystem, and provided that the heat-pipe operatinglimits are not exceeded - an important factor in thisinstance - then the disc will function as a heat-fluxtransformer that converts a very high input flux intoa low output flux.

Fig. 12 shows a test system in which the hollow discis heated circumferentially by a small radio-frequencycoil to simulate the localized nature of the heat inputto a 'Rotalix' anode. Rotation of the disc producesheat-pipe action, with the outer edge acting as theevaporator.

Variable-conductance heat pipesA class of heat pipes not yet discussed are those

whose thermal conductance can be varied between verywide limits. The heat flow Q in these pipes depends toan exceptional extent on the mean temperature Tv-«of the vapour, or, in other words: dQjdTvm, the tem-perature sensitivity, is very high. This feature, as weshall see later, is obtained by introducing a non-con-densable inert gas into the heat pipe in addition to theworking medium.

Variable-conductance heat pipes have an enormouslywide range of potential applications, particularly insituations where the temperature is required to remainpractically constant despite considerable fluctuationsin the thermalloading. A typical example is the coolingof electronic components, whose temperature is re-quired to be maintained within a specified rangeeven though the power they dissipate during operationmay vary a great deal. Before discussing examples ofsuch heat pipes, however, we shall take a closer lookat the temperature sensitivity itself.

Temperature sensitivity of a heat pipe

To see how the temperature sensitivity of a heat pipeis related to the design parameters, it will be useful toreturn to the description of a heat pipe as a group ofthermal resistances connected in series, as shown infig. 4 (Part I). For simplicity we shalliump together allthe thermal resistances associated with the evaporatorsection and call them RE. Similarly, Rc denotes the

Philips tech. Rev. 33, No, 5 HEAT PIPES, II 143

sum of the resistances associated with the condensersection. As before, the temperature.drop in the-vapourduct is accounted for by a thermal resistance Rv. Itwill be evident that RE is inversely proportional to thearea of the evaporator, and Re inversely proportionalto the area or"the surface where the condensation oc-curs. .We now consider the case of a heat pipe delivering

an amount of heat Q to a heat sink at a fixed tempera-ture (fig. 13). The temperature drops D.TE,v,e in the

of the vapour duçt are small. Ti)~first can' be achievedby having a Iargecondenser area" or by ensuring thatthe liquid in the wick and also the envelope material,have a high. therrnakconductivity.We now consider a'{'ituation in which the condenser

resistance Re depends •.in 'one way or another: on theamount of heat transporred Q, and 'tie shall see whatthe relationship should be to obtain the highest possibletemperature sensitivity. it is easily shown that. thethermal response is now given by:

E i 0 c

I I II I II: I11.__ ~~~_'~'~~Tt~'~_~~Tc~·I,I,tr- t ;"1" _.

// / /lTvm:l :R t.( ( J~JI_ 1 c = cons.

dTvm d IJTc :I

! L,= Ro

l l" Q

Fig.13. The extent to which the mean temperature Tvm in the vapour duct varies with theheat flow Q can be considerably reduced by designing the condenser section in such a waythat its total thermal resistance Rc (see fig.4: Rc = Rw(c) + REnv(C) + REnv-S) de-creases as Q increases, and is at a minimum when Rc is inversely proportional to Q.RE thermal resistance of evaporator. Rv thermal resistance of vapour duct. D.TE,V,C

temperature drop across RE,V,C.

Q-Q+dQ-

)(

.a., jII

rQ+dQ-

heat pipe across each of these three resistances can thenbe written as three lumped thermal resistances:

D.TE= QRE; D.Tv = QRv; D.Te= QRe.

Now suppose that the heat transported by the pipeis increased by an amount D.. Q while all the thermalresistances remain constant. The accompanying changein the mean temperature of the vapour (see fig. 13)will then be given by:

dTvm = dD.Te + t dD..Tv,

and the 'thermal response' of the heat pipe by:

dTvm/dQ = dD..Te/dQ + t dD..Tv/dQ = Re + tRy.

The temperature sensitivity is the reciprocal of thisquantity, i.e.

dQ/dTvm = (Re + tRV)-l.

A high temperature sensitivity is thus obtained whenthe thermal resistance of the condenser section and that

v

Rv .<,

III

1dTvm

dTvm/dQ = dD.Te/dQ + t dD.Tv/dQ =

= Re(Q) + Q dRe/dQ + tRy.

The lowest value of the thermal response is tRy andis reached when Re(Q) = -Q dRe/dQ, or whenRe = Ro/ Q, where Ro is a constant. The maximumvalue of the temperature sensitivity is therefore:

dQ/dTvm = 2/Rv

and the temperature drop in the condenser is:

D..Te= QRe(Q) = Ro = constant.

This is the situation shown at the bottom of fig. 13.The derivative dD.Te/dQ is zero here, which impliesthat the heat flux in the condenser is independent ofthe total heat transported by the pipe. In practice thissituation will only be encountered if the effective partof the condenser surface area can be varied propor-tionately to the total heat transported.We shall now discuss the method of obtaining a con-

144 G. A. A. ASSELMAN and D. B. GREEN Philips tech. Rev. 33, No. 5

8

T

t\ \

-xFig. 14. Schematic representation (above) and temperature dis-tribution (below; temperature T as a function of space coordi-nate x) for a heat pipe whose thermal response has been reducedby connecting the condenser to a buffer space B (volume V) andadding a non-condensable inert gas to the heat-pipe system.When the pipe is i n operation, the gas is swept out of a largepart of the space by the vapour flow, and a fairly sharply definedinterface F is formed between the vapour and the gas. Only thepart of the condenser to the left of F is effective. When the heatflow is increased from Ql to Q2, the position of F shifts fromFi to F2, and the effective surface area ofthe condenser increases;the resistance Rc (see fig. 13) therefore decreases. When V is verylarge, Rc varies in inverse proportion to Q. At the interface thereis a sharp drop in the temperature (the 'heat front'). In the equi-librium situation the vapour pressure is equal to the pressure ofthe buffer gas compressed in C and B. The buffer pressure thuscontrols the operating temperature.

denser surface with a variable effective area, and weshall see that the temperature sensitivity can be givenany value between the maximum value just mentionedand the value found in a conventional heat pipe.

Gas-buffered heat pipes

The quantity Rc can be made to depend on Q byadding a non-condensable inert gas to the workingmedium in the heat-pipe system. This gas has the effectof buffering or blanketing off part of the condensersection of a heat pipe to a degree which can be madeto depend upon the heat transported along the pipe.A gas-controlled heat pipe of this kind is shown dia-grammatically in fig. 14, and we shall now explain itsoperation.

Fig. IS. Thermographs of a heat pipe containing water as theworking fluid and a non-condensable gas, taken during warm-up. The evaporator is on the right. Power consurnption was130 W. These thermographs (taken at intervals of 20 seconds)were made with an instrument that carries out a horizontallinescan of the pipe and its environment [lOl. Parts where the tem-perature is higher than 40 oe appear white, other parts black.The white curve is the temperature profile along the horizontal,which appears black in a picture of the pipe. It can be seen thatthe vapour/gas interface is fairly sharply defined and that itmoves towards the condenser as the heat pipe warms up. In thepart to the right of the interface, where heat-pipe action takesplace, the temperature along the axis of the pipe varies by onlyabout 0.1 oe.

Philips tech. Rev. 33, No. 5 HEAT PIPES, Il 145

Fig. 16. Sodium-charged heat pipes with identical electric heaters and the sarne input power.The evaporators are on the extreme right. In addition to sodium the upper pipe containsargon (approx. 200 torr); the lower one is a conventional heat pipe. At the front the insula-tion has been removed over some distance so that this part acts as the condenser. The lowerpipe dissipates the power input across the whole visible length, the other one only to the rightof the heat front, and therefore at a higher temperature.

As can be seen in the figure, the condenser section Cof the heat pipe is connected to a buffer volume B.When the pipe is not in operation, gas and vapour areof course homogeneously mixed, and the total pressurein the vapour duct is equal to the sum ofthe two partialpressures. When the pipe is in operation, however, thesituation is quite different. Owing to the flow of vapourfrom evaporator to condenser, the non-condensable gasis swept along in the vapour stream, and compressedinto the buffer space and in the adjacent part of thecondenser secti on. The interface between the part ofthe heat pipe filled with vapour and the part filled withgas is fairly sharply defined, and in this situation thevapour pressure is therefore approximately equal to thepressure of the compressed buffer gas. Since the buffergas cannot condense it cannot be recycled and henceplays no part in the heat-pipe process, which takes placeexclusively in the vapour-filled part. The effect of in-creasing the vapour flow is to compress the buffer gaseven more, causing a larger surface area to becomeavailable for condensation, so that in fact Rc decreasesas Q increases. If the buffer volume is made very large,then as we shall see in more detail below Rc is inverselyproportional to Q and the température sensitivityreaches its maximum value.

The marked separation between buffer gas and va-pour in a gas-controlled heat pipe is demonstrated injig. 15. These photographs relate to a heat pipe filledwith water and nitrogen. Fig. 16 shows that the situa-tion at higher temperatures is no different. This com-pares two sodium heat pipes, both at equilibrium, butwith one gas-controlled and the other operating in thenormal mode.

Both heat pipes transfer the same total amount of

heat from evaporator to condenser. The conventionalheat pipe, however, can give up its heat over the wholeof the condenser section, and thus operates at a lowermean temperature than the gas-controlled pipe, whichhas part of its condenser section blanketed off by argon.In the gas-controlled pipe the temperature drop at theinterface is marked by the abrupt fall in the radiationemitted from the heat-pipe wall.

An interface as sharply defined as this, in a planeperpendicular to the axis of the heat pipe, is found onlyin pipes of relatively small cross-sectional area andwith large vapour flow rates. If the pipe is upright orsloping however, with the condenser uppermost, andif the gas is heavier than the vapour, then fairly con-siderable mixing of gas and vapour is likely to occur ifthe amount of heat transported is small. This invariablymeans a blurring of the interface and also a loss of iso-thermality in the evaporator and transport sections.

A somewhat less dramatic situation is demonstratedin jig. 17, which shows a sloping stainless-steel heatpipe of 5 cm diameter, containing water as the workingfluid and helium as the buffer gas, where the interface,though inclined, is nevertheless fairly sharply defined.

An important question for the designer is of coursehow large the volume V of the buffer space connectedwith the condenser section (fig. 14) should be if themean working temperature is to remain between thelimits Tl and T2 when the heat flow is varied betweenthe limits Ql and Q2.

In the usual theoretical treatment of the gas-con-

[lOJ This equipment was developed in the Laboratoires d'Elec-tronique et de Physique Appliquée (LEP) at Lirneil-Bré-vannes, France, where we also took the photographs shownhere. A description of the equipment is given in: M. Jatteau,Philips tech. Rev. 30, 278, 1969.

146 G. A. A. ASSELMAN and D. B. GREEN Philips tech. Rev. 33, No. 5

trolled heat pipe, the heat front is assumed to lie in aplane perpendicular to the longitudinal axis ofthe pipe,and to be independent of the orientation of the pipe.Moreover the interface is assumed to be sharp. Withthese assumptions W. Bienert [11] has succeeded in ex-pressing the operation of a gas-controlled heat pipe bya differential equation.

Using a simpler treatment an expression for V canbe derived that proves to be sufficiently accurate fordesign calculations. This is:

known area of the condenser section required to dissipate thetransported heat. For a cylindrical pipe of uniform cross-section(radius a, condenser length I) the following equations apply:

Ql = Zaiaqi], Q2 = 2naQ2(1 + I::l/),

I::lI = 2~a [~22 - ~ll] ,

I::l V = na21::l1 = ~ [ ~22 - ~ll] .

Substitution in our equation for vl6. V then yields the ex-pression given above for V.

I

He.

Fig. 17. Sloping heat pipe containing water and helium with evaporator above the condenser.The interface between vapour and gas has been made visible by covering the outside witha liquid-crystal layer that gives selective reflection as a function of temporature. Betweenabout 60 DC and 65 DC the wavelength of the reflected light traverses the whole visible spec-trum. The strip ofcondenser surface where the temperature passes through this interval there-fore appears in the colours of the spectrum. It can be seen that the interface between vapourand working fluid, although askew, is still fairly sharply defined.

Here Pl,2 are the saturated vapour pressures corre-sponding to the temperatures TI,2, and QI,2 is the heatflux through the surface area of the condenser at thesetemperatures; tl,2 represents the mean temperature ofthe gas in both cases and a is the radius of the pipe.

This expression is arrived at as follows. T n the equilibriumstate, i.e. with no movement of the interface, the pressure of thegas is equal to the vapour pressure ofthe working fluid. Assumingthat the buffer gas behaves like an ideal gas, then we have thefollowing relations:

Pl( V + 6. V) = Ril for Ql,

P2 V = R/2 for Q2.

Here 6. V is the volume swept out by the interface in accornmo-dating the change of heat input from Ql to Q2. Combining theabove equations gives:

{V = [;:~: - Ir·The quantity I::l V may be independently determined from the

The above result was applied in the design of a heat-pipe oven that was not only required to be isothermalalong its length (nearly two metres), but also had tobe capable of accommodating heat-transport fluctua-tions ofup to 10% (in this case one kilowatt) with onlya 5 DC temperature variation about a mean vapourtemperature of 825 De.

The oven was designed so that the excess heat inputcould be dissipated by radiation. The vapour/gas inter-face was located in an uninsulated section of the pipe,and advanced or receded as the oven heat load varied.The oven design specification required a buffer gaspressure of 5.7 X 104 Pa and a buffer volume of aboutI Iitre. To be on the safe side, a volume of several litreswas used in practice.

The equation for the required buffer volume V isconsiderably simplified if the temperature of the buffergas can be considered constant, that is if ti = tz. Ifat the same time Tl = T2, then PI/P2 = 1, and therequired buffer volume is infinite. For practical pur-poses this means that it must be large compared withthe pipe itself. The heat pipe is then operating in the

Philips tech. Rev. 33, No. 5 HEAT PIPES, II

constant-pressure mode, which corresponds to its maxi-mum temperature sensitivity.

As mentioned earlier, this maximum temperaturesensitivity occurs when the thermal resistance of thecondenser section is inversely proportional to the trans-ported heat Q, or in other words when the effective areaof the condenser section is proportional to Q. It can

isothermal plane surface at a known temperature. Thistemperature also had to be reached quickly and thenheld constant for long periods of time in spite of pos-sible fluctuations in the power supply to the hot sur-face.

The main part of the equipment [12] (fig. 18) is anisothermal chamber Ch, which forms part of a gas-

/VIS

0S_I

tF

\Vac H

Fig. 18. Equipment for measuring the thermal conductivity of insulating material. Under-neath the sample S is an isothermal surface of virtually constant temperature. MS meas-uring space. CR thermal guard ring. Ch isothermal chamber filled with sodium vapour.W wick (steel gauze). H heater. 1 insulation. B buffer gas volume. F position of heat front.Vac evacuated space. When the equipment is operating the liquid in MS boils, giving aconstant and even temperature at the upper side of the sample. The heat flow through Sis derived from the quantity of condensed liquid flowing out of the cooler in unit time.

readily be shown that this is in fact the case for a gas-controlled heat pipe operating in the constant-pressuremode.

For heat-pipe applications in which non-flammableworking fluids are employed, it is clear that air is avery convenient buffer gas. Moreover, when a workingpressure of about I atmosphere is required, the environ-ment can provide an infinite buffer volume. The chem-ist's reflux condenser is in fact an example of this.In other instances, particularly where the working fluidis a liq uid metal, argon is generally used as the buffergas, and for constant-pressure operation a sufficientlylarge buffer volume is attached to the system. We haveused an arrangement of this type employing liquidsodium and argon in an equipment for measuring thethermal conductivity of insulating materials, which weshall now discuss.

An equipment Jar measuring thermal conductivity

To measure the extremely low thermal conductivitiesof multiple-foil insulations we needed an equipment inwhich heat could be applied to the sample through an

buffered heat-pipe system. The chamber consists of acylindrical nickel-chromium steel vessel, whose insidewalls are clad with a wick formed from severallayersof steel gauze spot-welded into position. A horizontalpipe, also containing a wick, protrudes from the vesseland is connected via a vertical arm to the gas bufferspace B.

The isothermal chamber is put into operation in thefollowing way. The pressure of the gas in the bufferspace B is set at a value equal to the vapour pressureof the working fluid at the desired chamber tempera-ture. The chamber is then heated electrically until thevapour pressure of the sodium equals that of the buffergas, and evaporation occurs at a rate sufficient to dis-place the gas from the chamber and drive it into thehorizontal pipe. Here a clear interface, or heat front,is developed between the argon and sodium vapour.[11) W. Bienert, Proc. 4th Intersociety Energy Conversion Engng.

Conf., Washington D.C. 1969, p. 1033.[12) D. B. Green and H. H. M. van der Aa, 11 th Int. Conf. on

Thermal Conductivity (extended abstracts), Albuquerque,N.M., USA, 1971, p. 31. A somewhat similar apparatus formeasuring medium to very high thermal conductivities wasdescribed by J. Schröder, Philips tech. Rev. 21, 357, 1959/60.

147

148 HEAT PIPES, II Philips tech. Rev. 33, No. 5

The sodium condenses continuously and is recycled tothe evaporator area via the wick.The position of the heat front in the horizontal arm

is determined primarily by the area required to radiatethe excess power input. As we noted earlier, the liquidbehind the heat front in the wick is everywhere in equi-librium with its vapour, and since there are only verysmall pressure differences the chamber wall acquiresalmost the same' temperature everywhere. The volumeofthe buffer vesselB is made sufficiently large to ensurethat a change in. the heat supply to the chamber Clicauses very little change of pressure, and therefore doesnot give rise to anyappreciable change of temperature.The temperature of the wall of Ch in contact with thesample drifts less than 1 "C per hour.

50 110mm

a

900°CT

t850

800

750

700

0b

___ ---------- 1040~ - 860

667

467

301

205x 102Pa

200 400 600-t

8005

c-20~r~7~50~-----8~OO-------8~5-0------9~00t

.-TFig. 19. Thermal characteristics of the isothermal chamber ofthe equipment shown in fig. 18, recorded by means of four ther-mocouples located in the upper plate.a) Position of the four thermocouples, indicated by the num-bers 1-4.b) Temperature variation at the location' 1 during warm-upmeasured at six different initial gas pressures.c) Temperature differences between the location 1 and the threeothers, plotted against the mean chamber. temperature at whichthe measurements were made.

Fig.19 shows some of the results obtained. Themeasurements were made with the aid of four thermo-couples located at the positions marked 1-4 in fig. 19a.The warm-up characteristics of the chamber (fig. 19b)were monitored by thermocouple 1for various' valuesof the buffer-gas pressure. It can be seen that the top-plate temperature rises at first until after about 5 min-utes the vapour pressure is equal to that of the buffergas; no further temperature change is then recorded.After this state has been reached, the temperature

gradients in the plate are generally less than 0.5 "Clct»,as the curves in fig. 19c show. This figure shows thetemperature differences existing between the variousthermocouples, for various temperatures between730°C and 875 "C. The maxima of these differencesbarely exceed one degree.The examples discussed above show that the high

temperature sensitivity that can be obtained for a gas-buffered heat pipe can lead to improved solutions tomany problems both in scientific instrumentation andin manufacturing processes.

In this article we have tried to give an outline of theprinciples underlying the operation of heat pipes, andwe have discussed some applications in which theemphasis was placed on those principles and featuresthat make the heat pipe so useful. When the fourcharacteristic features of heat pipes considered here aretaken together, it is clear that devices based on thempose a formidable challenge to many of the existingmethods of heat transportation, heat distribution andtemperature control.

Summary. This part of the article discusses examples of heat-pipesystems that function as transporters of heat (in Stirling-engineexperiments and in a siphon for the transfer of molten salts),as an isothermal space (black-body radiator, ovens, isothermalinserts for ovens, operating at both high and low vapour pres-sures) and as heat-flux transformers (in a Stirling-engine heatingsystem using combustion gases and in a rotating anode for X-raytubes). When a non-condensable inert gas is added to the workingmedium in a heat-pipe system, the thermal resistance of the con-denser can be made to depend on the quantity of heat Q trans-ported along the pipe, thus considerably reducing the extent towhich the mean temperature of the vapour varies with Q (tem-perature sensitivity), This reduction depends on the volume ofa buffer space connected with the condenser section. In a gas-buffered heat pipe the vapour compresses the gas into the bufferspace and the adjoining part of the condenser section, so thatthis part of the condenser section takes no part in the heat-pipeprocess. The position of the vapour/gas interface moves as theheat flow varies. The article discusses an application of thisprinciple in an equipment for measuring the thermal conductivityof insulating materials.

ERRATUM. In Part I ofthe above article, Philips tech. Rev. 33, 1973 (No. 4), the upperequation in the left-hand column of p. 110 should read: D..Pv = 41)vq//(L(!vrv2).

Volume 33; 1973, No. 5 Published 9 th August 1973pages 117-148