Heat Transfer in the Boiling Regime

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Heat transfer in the boiling regime

Frank Mucciardi and Guohui Zheng

McGill University Department of Mining and Metallurgical Engineering

3610 University St.

Montreal, Quebec H3A 2B2

[email protected]

ABSTRACT

Numerous metallurgical systems use water cooling to control heat extraction.While water is an excellent medium in many cases, it can, nonetheless, pose problems in

high heat flux applications, especially if localized boiling is encountered. Moreover, theresult may be catastrophic if the heat transfer is dominated by film boiling.

A series of tests were devised to study the transition between nucleate (free)boiling and film boiling in closed systems. While classical studies of boiling are

configured to examine a heated solid surface in a body of fluid, the present study used anovel approach whereby the water formed the working fluid of a heat pipe. Nucleate and

film boiling were clearly discernible. Moreover, during the course of the study wediscovered an interesting strategy for averting film boiling. Heat flux measurementsshow that heat transfer can be enhanced by an order of magnitude or more with the

modification we developed. These results can have important implications in some watercooled systems currently in use. This paper briefly reviews boiling heat transfer theory

and then details the experiments that were conducted to illustrate how boiling heattransfer can be enhanced and how film boiling can be avoided.

Keywords: heat pipe, boiling, flow modification, nucleate boiling, film boiling, water,heat transfer, zinc.



INTRODUCTION

Boiling heat transfer has been and continues to be the focus of attention of

numerous researchers. Most studies and, in particular, those dealing with industrialprocesses are centered on the boiling of water. In many of these processes where water is

used for cooling, researchers have focused on how to avoid boiling in the units theydesigned. To fully appreciate why this is so, it is necessary for one to have a basicunderstanding of the boiling phenomenon. To this end, this paper begins by presenting

some background on boiling. It then goes on to describe a device known as a heat pipe,which normally operates in the boiling regime. Experimental data from severalexperiments are then presented to illustrate how boiling can be controlled and heat

extraction optimized.

Boiling Heat Transfer

Boiling heat transfer occurs when a liquid with a saturation temperature, Tsat,

contacts a surface with an interfacial temperature, Tw. The saturation temperature of theliquid is the equilibrium temperature at which the fluid develops a vapor pressure that

equals the pressure of the system. Numerical values can be determined from the well-known pressure-temperature correlation referred to as the Clausius-Clapeyron equation.

Boiling heat transfer data is normally shown plotted as the logarithm of the heatflux to the surface against the logarithm of the temperature difference, Tw-Tsat. This

excess temperature differential represents the driving force for boiling. If the walltemperature is less than the saturation temperature, boiling will not occur. However, if the wall temperature exceeds the saturation temperature of the liquid, boiling heat

transfer will be dominant. A typical boiling curve is shown in Fig. 1 (1). To fully

appreciate the boiling phenomenon, one must be aware of the regimes that comprise theboiling curve.

Consider the lower boiling curve shown in Fig. 1 and denoted by the label,

‘natural convection’. Up until point B, the excess temperature differential does not leadto the formation of vapor bubbles. Natural convection within the liquid is sufficient to

move heat from the wall to the bulk of the liquid. At point B, vapor bubbles begin tonucleate on the surface. As the wall temperature is increased, the rate of bubblenucleation increases as does the heat flux from the surface. This regime, as denoted by

the labels B-C, is referred to as the nucleate boiling regime. At point C, the maximumheat flux for nucleate boiling is reached. This is referred to as the critical heat flux

(CHF). At the CHF, the wall temperature exceeds the saturation temperature by a fixedamount. If the wall temperature is increased, the heat flux from the wall surfacedecreases until point D is reached. The reason for the declining heat flux is the formation

of a vapor film over the surface area of the wall. This film acts as a heat transfer barrierand prevents the liquid from contacting the wall. This phenomenon occurs as a

progressive event in that the greater is the wall temperature, the greater is the coverage of



the wall by the film and the more stable the film becomes. This regime, as delineated by

the labels C-D, is referred to as partial film boiling.

At point D, coverage of the surface by the film is complete and heat transfer byfilm boiling becomes dominant. The film boiling regime extends from point D to point E.The reason why heat transfer increases in this region relates to the fact that radiation

across the vapor film dominates. Given that radiative heat transfer increases by the fourthpower of temperature, the heat flux from the wall increases in the film boiling regime.

Figure 1 – Typical Boiling Curves for Natural and Forced Convection.

The set of curves in the upper left hand quadrant of Fig. 1 correspond to theboiling curves for forced convection systems wherein the liquid flows over the wallsurface. As the bulk velocity of the liquid is increased, the boiling curve is shifted

upward. Thus, increasing velocities allow for greater heat extraction for a given excesstemperature, Tw-Tsat. In addition, the forced convection set of curves is for a constant

pressure. If the pressure is increased, then Tsat also increases. As a result, one can operatein the nucleate boiling regime at higher wall temperatures without experiencing filmboiling with higher system pressures. If the operating pressure is lowered, one may

experience film boiling for an identical wall temperature.

As an illustration of natural convection boiling heat transfer, Fig. 2 presents theboiling curve for water on a horizontal, electrically heated wire (2). Also shown are thecorresponding heat transfer coefficients. Boiling is sensitive to configuration and as such

these results are only included to illustrate how the regimes of boiling interact with eachother.



Water cooling dominates many metallurgical processes. When heat fluxes arerelatively large, it is important to prevent film boiling by imposing water velocities and

pressures that correspond to nucleate boiling for the system. Otherwise, if a portion of thesystem experiences film boiling, the wall in that region will be subjected to dramaticincreases in temperature and may ultimately fail. Classical metallurgical examples where

water cooling predominates are the continuous casting of steel, the DC casting of aluminum, and rolling in general.

On the other hand the boilingphenomenon can be used as the

primary means for transferring heat.A device which uses boiling and,

specifically the vaporization and thecondensation of a working fluid, totransfer energy from one location to

another is referred to as a heat pipe.The next section gives a brief

overview of what a heat pipe is.

Figure 2 – Boiling Curve for Water on a

Heated Wire. Heat Pipe

Heat pipes were first developed in the 1940’s by Gaugler (3) of GM, however, itwas not until the early 1960’s when NASA realized their potential that rapid

development began with the work of Grover (4). In general terms, a heat pipe is a heattransfer device that utilizes the vaporization and condensation of a working substancecontained within to move energy from the evaporator section to the condenser section. It

is, in effect, a ‘superconductor’ of heat energy. Tests have shown that a heat pipe can beas effective in transporting energy as 1,000 times the equivalent quantity of copper under

similar heat transfer conditions (i.e. temperature driving force).

Typically, most heat pipe applications involve the use of heat pipes in vertical or

inclined positions. Thus, for the purpose of illustrating the operation of a heat pipe, it is

instructive to consider the simple vertical orientation as illustrated in Fig. 3. The heatpipe consists of a sealed pipe shell, circular or otherwise, containing a workingsubstance. During heat pipe operation, heat is introduced to the pipe from the heatsource. At this section of the heat pipe, the working substance evaporates. Thus, the

section of the heat pipe exposed to the heat source is termed the ‘evaporator’. The vaporflows to the heat sink section of the heat pipe (the ‘condenser’) where it condenses on the

pipe wall and returns to the evaporator by gravity in liquid form.



Numerous papers and patents

have been issued since heat pipes gainedprominence in the early 1960’s. Inaddition, a number of textbooks have

also been written on the subject. Thereader is referred to references (5-7) for

a detailed account of heat pipeprinciples. Two aspects of heat pipes areworth mentioning at this point because

they are fundamental to the successfuloperation of a heat pipe.

Figure 3 – Classical, Vertical Heat Pipe.

The first aspect of the heat pipe as depicted in Fig. 3 is that it only contains

molecules of the working substance fluid. Non-condensable gases are excluded withvacuum pumping systems. Thus, at low temperatures the heat pipe is at a vacuum, whichapproximates the partial pressure of the fluid at that temperature. The other aspect of

importance is the nature of the inner surfaces of the evaporator and condenser. It isessential that the liquid in the pipe coat all surfaces uniformly. To this end, the surfaces

are fitted with a wick comprising several wraps of fine screen (e.g. 100 mesh) tocapitalize on the capillary forces of the wick.

Boiling in a Water-Based Heat Pipe

An extensive study of boiling in a heat pipe has been carried out. Because of space limitations, only a few selected results will be presented. As a heat pipe is a closedsystem, the present authors have not found any studies that have reported on the

modification of the boiling phenomenon in a heat pipe. This paper is the first to describeattempts to enhance the boiling or burnout limit (i.e. maximum heat flux) of a heat pipe –

a parameter that permeates the heat pipe literature.

There is little agreement about the magnitude of the boiling limit in a heat pipe.

So many parameters (e.g. configuration, wick, charge) have an influence that one mustultimately carry out experimental work to determine the boiling limit for one’s particular

system. What can be said however is that the classical boiling curve for water as shownin Fig. 2 greatly overstates the critical heat flux for a conventional heat pipe. In fact, onewould be safe to assume that the critical heat flux for a heat pipe is about one order of

magnitude less (8,9). Thus, for water one may expect that the critical heat flux is severalhundred kW’s/m2 as opposed to several thousand kW’s/m2. However, the work we areabout to present dramatically changes this scenario. We have developed a new heat pipe

which is characterized by greatly increased critical heat fluxes. Subsequent sections



describe this unit and compare some results we have obtained to those of a conventional

heat pipe.

EXPERIMENTAL

To achieve both uniform and large heat fluxes we decided to use a bath of moltenzinc. Thus, two heat pipes of identical size were constructed. A schematic of the

conventional heat pipe is shown in Fig. 4. The evaporator portion of the heat pipe wasmade by drilling a hole 18 mm in diameter in a solid 304 stainless steel (SS) bar of 46mm diameter. The bottom of the bar was left with a 29 mm thickness of stainless. A

condenser, including an air cooled jacket, was welded onto the opening of the bar. Theinside of the pipe was fitted with 3 wraps of 100 mesh SS wick. The heat pipe was made

with a thermocouple well extending to within 2 cm of the bottom of the evaporatorchamber. The pipe was charged with 150 g of distilled water and evacuated.

The new heat pipe was identical with the exception that the inside of theevaporator was fitted with a twisted tape element, which made a complete turn over a

length of 5.4 cm. The thermocouple well was shortened and extended up to the top of thetwisted tape. A photograph of the twisted tape element is shown in Fig. 5.

Figure 4 – Conventional Heat Pipe forTesting in Zinc.

Figure 5 – Twisted Tape Flow Modifier.



The tests were conducted by immersing varying lengths of the leading end of the

evaporator into the molten zinc. For each immersion tested, the temperatures of the heatpipe, zinc melt and outlet cooling air were recorded as a function of time. Also recorded

was the flow rate of cooling air. The inlet temperature of the cooling air was relativelyconstant and only noted each day. Several deviations of the above procedure were alsoused. These will be described as the results are presented. All the immersion trials were

conducted in a melt of about 25 kg of commercial purity zinc with a melting point of about 420oC. The melt was contained in an alumina crucible of 15 cm internal diameter.

Unless otherwise noted, the cooling air flow rate was about 15.3 Nl/s.

RESULTS

A sampling of the results will now be presented to illustrate how the new heatpipe with the internal flow modifier compared with the conventional heat pipe. The testsare divided into 4 categories: a) immersion, b) cooling, c) heating, and d) removal from

the melt. Each of these categories is used to illustrate the effect of internal flowmodification on heat pipe performance.

Figure 6 – Staged Immersion of Conventional Heat Pipe in Zinc.

Immersion Into Molten Zinc

The conventional heat pipe with no flow modifier was immersed in molten zincin 4 stages. Initially, 2 cm were immersed. This was then increased to 3 cm and then to4.5 cm and finally to 6 cm. The results of this test are shown in Fig. 6. One can see from

these results that after the initial immersion of 2 cm, the gains in heat extraction as moreof the pipe was inserted were modest. The bath temperature changed little following the

2 cm immersion.



Figure 7 – Staged Immersion of Modified Heat Pipe in Zinc.

Figure 8 – Modified Heat Pipe WithFrozen Zinc Accretion.

Contrast these results to those

obtained under similar conditions withthe heat pipe that was fitted with an

internal flow modifier as shown in Fig.7. One can see that the heat pipeextracted substantially more heat. In

fact, the rate of heat extraction wassufficient to cause the melt to cool an

appreciable amount. Because of thedeclining melt temperature, the rate of heat extraction, as computed from the

cooling air outlet temperature, did notincrease in proportion to the length

immersed. A photograph of the heat pipeafter removal from the melt is shown inFig. 8. A layer of zinc had frozen on the

pipe because of the low superheat of themelt at the end of the test. Also apparent

is the smooth contour of the zinc layer,

which indicates that heat extraction wasuniform.

It is to be noted that the outlet temperature of the cooling air is directlyproportional to the rate of heat extraction. Clearly, the flow modifier had a profound

effect on the rate of heat extraction and thus on the heat flux the water was able toabsorb. Even though only one set of results for each pipe is presented, the tests were



repeated on numerous occasions with similar results. The difference between the heat

extraction capabilities of the 2 pipes was ascribed to the fact that the mode of boiling inthe 2 pipes differed. Whereas the conventional pipe was operating in the film boiling

regime, the new pipe with a flow modifier was operating in the nucleate boiling regime.

Freezing in Zinc

Given the different modes of boiling in the 2 pipes, it was postulated that if the

pipes were allowed to freeze in the zinc after the power to the furnace was switched off,it would be possible to determine if film boiling was a factor. Thus, the conventional heatpipe immersed to a depth of 4 cm was allowed to freeze in the zinc as the temperatures

were recorded. The results are shown in Fig. 9.

Figure 9 – Freezing of ConventionalHeat Pipe (4 cm) in Zinc.

Figure 10 - Freezing of ConventionalHeat Pipe (5 cm) in Zinc.

Figure 11 – Freezing of Modified Heat

Pipe (3 cm) in Zinc.

Figure 12 – Cooling of Conventional

Heat Pipe in Air.

An examination of the curves shows that when the zinc had cooled down to about

300oC, the heat pipe and cooling air outlet temperatures both increased sharply. Thisindicates that film boiling was prevalent prior to this point. When the film became



unstable and collapsed, the heat flux into the pipe showed a sudden increase as reflected

by the curves. In addition, the cooling rate of the frozen zinc also showed a suddenincrease.

A repeat of this test with an immersion depth of 5 cm produced the results shownin Fig. 10. Once again the presence of film boiling is discernible. At a zinc temperature

of about 250oC, the heat pipe and cooling air temperatures showed dramatic increases.This indicates the collapse of the film and the resumption of nucleate boiling.

A similar test was carried out with the heat pipe fitted with the flow modifier. Inthis case, the pipe was immersed 3 cm into the melt. The results are shown in Fig. 11. For

this case it was clear that there was no film boiling. The heat pipe and outlet airtemperatures followed the same trend as the zinc temperature. Once again the results

show that the flow modifier was successful in eliminating film boiling.

It is not necessary to solidify the pipe in the zinc to determine if film boiling is

dominant. One can simply remove the pipe from the zinc and allow the pipe to cool inthe air. This was done for the conventional pipe and the results are shown in Fig. 12.

Prior to removing the pipe, the readings were stable. When the pipe was raised from themelt, a decline in both the heat pipe and cooling air temperatures was noted. However, atsome point both temperatures began to increase until a maximum was reached. This

increase is similar to that shown in Figs. 9 and 10. Thus, this pipe had been operating inthe film boiling regime. Similar tests with the flow modified heat pipe do not exhibit this

reversal in the cooling curves.

Heating in Zinc

Given that film boiling is discernible during the cooling of the zinc, the reverseshould be true. Thus, if the heat pipe is allowed to solidify in the zinc and cool, one canthen study the reheating of the system when the furnace is switched back on.

The results from 2 immersion depths (4 and 5 cm) are reported in this paper. Alltests were carried out with a cooling air flow rate of 15.3 Nl/s. The results for a 4 cm

immersion of the conventional heat pipe are shown in Fig. 13. One can see from theseresults that as the zinc approached 400oC, the heat pipe and cooling air temperaturesshowed sudden drops. These were caused by the onset of film boiling.

Contrast this with the results for the heat pipe containing the flow modifier as

shown in Fig. 14. In this case there is only nucleate boiling. One can see that as the zincmelted and the interfacial resistance was reduced, the rate of heat extraction, as denotedby the cooling air temperature curve, increased to a new level (i.e. an increase of about

50%).A comparison of the 2 pipes for an immersion of 4 cm is shown in Fig. 15. One

can see that up to a zinc temperature of about 320oC, the 2 pipes were essentially



identical in heat extraction capability. However, as the zinc melted, the abilities of the 2

pipes to extract heat diverged dramatically.

Figure 13 – Heating of ConventionalHeat Pipe (4 cm) in Zinc.

Figure 14 – Heating of Modified Heat

Pipe (4 cm) in Zinc.

Similar tests for immersions of 5 cm were also performed. The results for theconventional pipe are shown in Fig. 16. The effect of film boiling is clear. Moreover, onecan see that even as the zinc melt temperature approached 500oC (i.e. 80oC of superheat),

the heat pipe was only at about 65oC. The heat extraction at this point was equivalent tothat when the zinc was solid and at only about 250oC.

With the heat pipe containing the flow modifier, the results shown in Fig. 17 wereobtained. Clearly, there was no film boiling in this case. In fact, heat extraction was so

intense that as the interfacial resistance between the frozen zinc and the outer heat pipewall disappeared, it was not possible to supply enough heat to the melt to sustain anincreasing melt temperature.

Figure 16 – Heating of Conventional Heat Pipe (5 cm) in Zinc.



Figure 17 – Heating of Modified Heat Pipe (5 cm) in Zinc.

The results from these 2 tests are summarized in Fig. 18. At low zinctemperatures (~250oC) one can see the onset of partial film boiling as the 2 curves start

diverging. However, as the zinc/pipe interfacial resistance is eliminated when the zincmelts, the divergence is dramatic. The beneficial effect of the flow modifier in enhancingthe boiling limit of the heat pipe is obvious.

Figure 15 – Comparison of Heat Extraction for Both Heat Pipes (4 cm).



Figure 18 – Comparison of Heat Extraction for Both Heat Pipes (5 cm).

DISCUSSION OF RESULTS

The effect of flow modification in a heat pipe was shown by the results of Fig. 7.As more of the heat pipe was inserted, the rate of heat extraction increased. Also notable

is the fact that because the melt temperature was decreasing during this period, the rate of heat extraction did not increase in proportion to the increase in area. This was expectedas the temperature driving force for convection with the zinc was decreasing. Moreover,

as the melt temperature decreased, a layer of zinc froze on the pipe. This created aninterfacial resistance, which also caused the rate of heat extraction to slow down. Theequivalent results for the un-modified heat pipe are presented in Fig. 6. One can see that

when the immersion was increased from 3 cm to 4.5 cm, the total heat extraction actuallydecreased. This was due to the production of a thicker, more stable vapor film.

The experiments dealing with the freezing of the heat pipes in the zinc (Figs. 9-11) are revealing and clearly illustrate whether a vapor film is present in a heat pipe unit.

The greater the immersed length of pipe the greater is the temperature spike when thefilm collapses as can be seen from Figs. 9 and 10. With the modified heat pipe this

temperature spike does not occur as seen from Fig. 11. This confirms that the heat pipewith flow modification did not experience film boiling.

Similar phenomena were observed when the heat pipes were first frozen in thezinc and then reheated. Figs. 13 and 16 show the results for the conventional heat pipe



for 4 and 5 cm immersions. As the zinc was heated, heat extraction proceeded smoothly

until the zinc temperature range of 250-300oC. The onset of film boiling was then notedas a slowing in the heating up of the heat pipe and the outlet air. Film boiling, however,

intensified dramatically when the zinc was around the melting temperature. This isexplained by the fact that the interfacial resistance at the zinc/pipe interface decreased atthis point. As a result, the heat flux to the pipe increased sufficiently to promote a stable

vapor film, which in turn caused the net heat flux to the pipe to decrease substantially.

The peak heat flux for the 5 cm immersion depicted in Fig. 18 was computed tobe 370.2 kW/m2. With the onset of film boiling, the heat flux dropped to about ½ thisvalue and it did so in 2 stages.

Contrast these results to those shown in Figs 14 and 17, which were carried out

under similar conditions. One will note from these results that there is no evidence of film boiling. The heat pipe and cooling air temperature curves track the zinc temperaturein a smooth manner with no abrupt changes. The maximum heat flux for the 5 cm

immersion was 519.1 kW/m2. This heat flux would have continued to increase withincreasing melt temperature, however, the test was terminated because the zinc

temperature could not be increased further. Other tests not reported here have shown thatheat fluxes in excess of 1 MW/m2 are attainable.

The results from Figs. 13 and 14 for an immersion of 4 cm are summarized inFig. 15. They are shown as the rate of heat extraction plotted as a function of the

temperature of the zinc. One can see that up to a temperature of about 300oC there is nonoticeable difference between the 2 pipes. A divergence occurs at this point and persistsuntil the melting of the zinc. As the zinc melts, the un-modified pipe shows a rapid drop

in heat extraction. However, the flow modified pipe shows the opposite effect. The

melting of the zinc causes an increase in the rate of heat extraction.

Similar results for a 5 cm immersion are presented in Fig. 18. Once again one cansee the drop in heat extraction for the conventional heat pipe as the zinc melts. On the

other hand, heat extraction increases dramatically for the modified heat pipe as the zincmelts.

The rapid increase in heat extraction for the modified pipe illustrates how muchof an interfacial resistance exists at the solid zinc/pipe interface. As the zinc is melted,

this resistance is eliminated (or dramatically reduced) with the result that heat extractionincreases greatly. Thus, it is evident that one can easily study interfacial resistances with

this technique, which includes using a modified heat pipe.

If one measures the slopes of the flow modified heat pipe results shown in Fig.

15, one finds that the rate of heat extraction is on average about 1.6 times that before theelimination of the resistance. In the case shown in Fig. 18, the slope after melting of the

zinc is about 3.7 times that before melting. Clearly, these results show that the size of theresistance is appreciable and variable.



CONCLUSIONS

Film boiling in closed, water-cooled systems can greatly limit the rate of heat

extraction. The critical heat flux (CHF) values for open systems are substantially largerthan the CHF’s for closed confined systems. Thus, one must be cautious when definingthe boiling limit (i.e. CHF) for a conventional heat pipe. If a heat pipe system attains the

critical heat flux while in transient mode (i.e. still heating up), the heat flux will startdeclining and the wall temperature will accelerate to higher values. This will continueuntil steady state is attained. Under such a condition, the heat pipe wall will run hot while

the interior of the heat pipe will run cold and the rate of heat extraction will be relativelylow.

The flow modified heat pipe, incorporating a twisted tape insert, overcomes theabove deficiencies by stripping the vapor film from the walls of the heat pipe. In this

way, the heat pipe can be viewed as operating in the forced convection domain. As aresult, this pipe can be operated at heat fluxes that can be up to an order of magnitude

greater than those typically associated with a water-based, conventional heat pipe.Comparative tests in the laboratory have confirmed these findings.

Flow modification in heat pipes has been shown to be viable and of practicalimportance. Heat pipe systems that are susceptible to film boiling can be readily

modified to allow for the extraction of heat fluxes that are much greater than thoseattainable with conventional heat pipes. Moreover, flow modification in a heat pipe canprovide an extra degree of security with respect to the integrity of the heat pipe when

operated in harsh environments.

REFERENCES

1. J. F. Grandfield, A. Hoadley and S. Instone, “Water Cooling in Direct ChillCasting: Part 1, Boiling Theory and Control, Light Metals, TMS, 1997, pp. 691-699.

2. B. Gebhart, Heat Transfer, McGraw-Hill, New York, 1971.

3. R. S. Gaugler, Heat Transfer Device, U.S. Patent 2,350,348, 1944.

4. G. M. Grover, Evaporation-Condensation Heat Transfer Device, U.S. Patent3,229,759, 1964.

5. P. D. Dunn and D. A. Reay, Heat Pipes, 4th ed., Pergamon Press, Oxford, 1994.

6. G. P. Peterson, An Introduction to Heat Pipes, John Wiley & Sons, New York,1994.



7. A. Faghri, Heat Pipe Science and Technology, Taylor & Francis, WashingtonD.C., 1995.

8. A. Abhat and R.A. Seban, “Boiling and Evaporation from Heat Pipe Wicks withWater and Acetone”, J. of Heat Transfer, Aug. 1974.

9. K. Cornwell and B.G. Nair, “Boiling in Wicks”, Proc. Heat Pipe Forum Meeting,

National Engineering Laboratory, Report No. 607, 1976.

Heat Transfer in the Boiling Regime

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