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International Journal of Thermal Sciences 45 (2006) 1–15www.elsevier.com/locate/ijts

How to create an efficient surface for nucleate boiling?

J. Mitrovic∗

Institut für Energie- und Verfahrenstechnik, Thermische Verfahrenstechnik und Anlagentechnik, Universität Paderborn, 33095 Paderborn, Gery

Received 2 February 2005; received in revised form 3 May 2005; accepted 24 May 2005

Available online 23 June 2005

Abstract

From a brief historical overview of the ideas on bubble generation, some directives for developing of efficient structures withboiling are deduced in the first part of the paper. Then, starting from the survival conditions of a vapour bubble in a liquid with a temgradient, a criterion is obtained for the creation of such structures. The efficiency of a heater surface covered with a structure is cideal if the driving temperature difference does not change with the heat flux. Experiments show that constancy of the wall supebe realized on surfaces provided with an appropriate micro-structure. The required properties of the structure are: It must be geneidentical elements which are arranged in a mono-pattern on the heating surface, the structure elements (protrusions) must trap vbubble detachment and generate a possibly long three-phase-line (TPL) formed by intersection of the vapour–liquid interface with tsurface. 2005 Elsevier SAS. All rights reserved.

Keywords:Nucleate boiling; Efficient surfaces; Heat transfer

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1. Introduction

Nucleate boiling of liquids has been the subject maof a number of studies, which cover questions ranging frformation of stable bubble nuclei in metastable liquids,bubble growth and departure to boiling heat transfer unvarious conditions. The state of the art can be obtained fseveral review articles and monographs, e.g., by Westw[1], Nesis [2], Carey [3] and Collier and Thome [4], to namonly a few. The capillarity theory is mostly used to descrthe bubble equilibrium in a superheated liquid. This therequires a liquid–vapour interface of macroscopic propties to exist and is, therefore, not applicable to the vstart of bubble formation. The processes preceding fortion of a stable vapour bubble are still poorly understoconsequently, there is not a theory that could describe tprocesses successfully. The existence of the heating sumakes the system heterogeneous and the boiling phmuch more complicated in comparison to homogeneous

* Tel.: +49 5251 60 2409; fax: +49 5251 60 3207.E-mail address:[email protected] (J. Mitrovic).

1290-0729/$ – see front matter 2005 Elsevier SAS. All rights reserved.doi:10.1016/j.ijthermalsci.2005.05.003

e

tems. Particularly the effect of surface structure of nano-micro-sizes on formation of premature bubble embryosbubble growth are still to be explored.

Despite these facts considerable effort has been untaken in the last decades to develop efficient boiling surfaThe guiding idea is to provide the surface with a structthat increases the heat flux in comparison to technicalfaces at the same surface superheat. The achievemethis direction are considerable, as may be taken, e.g.,Thome [5]. The boiling characteristics of such surfacesqualitatively similar to the ones of technical surfaces shing a dependency of the heat flux on the surface superThis behaviour allows the conclusion that the potentialvapour generation on structured surface is still available

In the present paper a relationship originally develoby Hsu and Graham [6] is used to deduce some direcon how to create an efficient heat transfer surface forcleate pool boiling. This equation specifies the conditionbubble grow under the conditions of a temperature grent and leads to a relationship for the surface structureof bubble cavity) in dependence of process parameterswill be shown, a surface having an appropriate monost

2 J. Mitrovic / International Journal of Thermal Sciences 45 (2006) 1–15

Nomenclature

A interface areaC constantd pin diameter�h enthalpy of phase changeL lengthm massn pin number densitynL surface density of TPLq heat fluxQ heat flow rateR thermal resistancer radiusT temperature�T temperature differencet timeu velocityy coordinate, wall distanceα heat transfer coefficient

δ distance to wallλ thermal conductivityρ densityκ thermal diffusivityσ surface tensionTPL three-phase-line (solid, liquid, vapour)

Subscripts and superscripts

B bubbleC cavityCR criticalL liquid, length TPLI interfaceV vapourW wall∞ far from wall− average

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ture results in a boiling characteristic that is different frothe ones of technical surfaces. Namely, in a certain rangthe process parameters, the heat flux is largely indepenof the wall superheat.

The paper begins with a short historical overview maifocussing on the evolution of the ideas and growth ofknowledge at the beginning of the research in the arebubble formation.

2. Early studies on bubble generation

Like in many fields of science, also the beginning of boing physics in written form cannot be stated very precisbut the following text seems to shed some light on thesue [7]:

“The well-known incident of the failure of the pumto suck water from a deep well occurred when GaliGalilei (1564–1642) retired to his villa at Alcetri and hlife was drawing to a close. All the ingenuity of the GraDuke’s artisans failed to make the water rise more thabout 30ft in the suction pipe.1 When asked for his advice, Galileo replied that it would be well to find out whthe water rose at all, and to the suggestion that Natabhorred a vacuum, he answered that it was appareonly a vacuum less than about 30ft that Nature wasaverse to.”

The above remark by Galilei probably stands at the vbeginning of experiments withliquids under tension. Obvi-

1 Grand Duke of Tuscany, Ferdinand the IInd.

t

ously, he had in mind the difference of the pressuresing on the free water surface (in the well) and in the stion pipe expressing his wondering about the water staing such a tension. This remarkable thought occurrea time where the atmospheric pressure was still to becovered.2

Some twenty years later,Christiaan Huygens(1629–1695) [8] made public the discovery oftensile strength owater. He observed that water can resist a considertension when filled in a tube that is arranged verticaand open at its lower end. In 1669 he also demonstrbefore the Royal Society of London columns of air-frwater to not subside in the tube. The studies byRobertHook (1635–1703), who originated the idea of mechacal strength of materials,Denis Papin(1647–1712), whoinvented the digester (pressure cooler), and of manyers, were guided by the desire to mainly understandTorricelli empty [9]. Since then, the vapour nucleationliquids has attracted the attention of physicists and eneers both as a natural phenomenon and from a pracpoint of view. In this context it is also interesting that areadyAristotele[10] was aware of transition of phases athatsee-water can be rendered potable by distillation. As itseems,experimentson boiling andcondensationwere firstperformed not with pure liquids but withmixtures, whilemaking liquors [11].

2 Evangelista Torricelli is supposed to have been present to this mrable occasion, and thus, being drawn to consider the question, he conthe happy idea of making a vacuum in a tube by means of a liquid hethan water [7].

J. Mitrovic / International Journal of Thermal Sciences 45 (2006) 1–15 3

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2.1. Historical development of the ideas on bubblenucleation

Important in several respects, the question of bubblemation in liquids has been debated extensively in the pbut a satisfactory answer to the question does not seeexist in the literature. In modern publications in this aof engineering science one usually takes a bubble as gformed somehow. In the following, a brief historical devopment of the ideas is presented, aiming at keepingsupporting discussion on this important and interesting sject.

Edmé Mariotte(1620–1684), well know from the isothemal pressure—volume relationship of gases, supposedwater contains air, which escapes during boiling thus asisting in bubble formation. As boiling continues after tair has completely escaped, he assumed the existencean-other matter which appears only in connection with boilin.In 1690,Edmund Halley(1656–1742) [12], the discoverer oa comet which bears his name, held

“that warmth does separate the particles of Water aemit them with a greater and greater Velocity as the h(temperature) is more and more intense.”

At about the same time,Denis PapinandGottfried WilhelmLeibniz (1646–1716) argued that the effect of superheawater, the fulmination, is caused by the water itself. Asnow appears, the vapour pressure was meant by thisIn addition, Leibniz ascribed theboiling soundto beating offluid particles against the heating wall.

Some 70 years later,Henry Cavendish(1731–1810) [13],discriminated betweenevaporation(in presence of a gasandboiling with bubble formation:

“Water as soon as it is heated ever so little above thatgree of heat which is acquired by the steam of water. . . ,is immediately turned into steam, provided it is in contwith steam or air; this degree I shall call the boiling heaor boiling point. It is evidently different according to thpressure acting on the water. If the water is not in contwith steam or air, it will bear a much greater heat witout being changed into steam, namely that which Decalls the heat of ebullition.”

Cavendish also gave an explanation of the chief phenomof boiling:

“When water is set on the fire and begins to boil, the laina of water in contact with the bottom of the pot is heatill either small particles of air are detached from it, or tibubbles of steam are produced by ebullition. As theseticles or bubbles ascend, the water in contact with themat all hotter than the boiling point is immediately turneinto steam. . . . though the coat of water immediatelycontact with the bubbles during their passage is not h

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ter than the boiling point, yet the rest of the water hastime to communicate much of its heat to that coat bethe bubble is past. For this reason when the water bwith a vast number of small bubbles its heat ought in geral to exceed the boiling heat less than when it boils wlarge bubbles succeeding one another slowly.”

Regarding the heat of ebullition (boiling inception),Cavendish says:

“The excess of the heat (temperature) of the water abthe boiling point is influenced by a great variety of ccumstances. The quantity of air in the water has a vgreat influence; for the more air it contains, the less hewill the water in contact with the bottom be capablereceiving, and the greater number of bubbles will be dcharged. It is this which seems to be the reason of theference between water beginning to boil and long boile

In addition, a Committee appointed by the Royal Sociconcerning the fixed points of thermometers that was chaby Cavendish recommended [14]:

“. . . not to dip the thermometer into the water, but to epose it only to the steam, . . . ”

in order to exclude the wall effect on boiling temperatureDoubtlessly, the notions of Cavendish could fill lines

an actual publication.De Luc (1727–1817) [15,16] stated that boiling is pr

duced bybubbles of the air which the heat disengages frthe liquid.3 Deprived of air, water can boil only on the uppor free surface, he concluded.

By a number of experimentsAchard(Franz Carl Achard1753–1821) [19], much more known as the inventor ofPrussian Sugar and who was the first to built up a factorymaking sugar from sugar-beet, arrived in 1785 at the cclusion that theboiling point of water varies much moremetallic than in glass vessels. He also noticed that a drachof iron-filings or some other insoluble solids added to wter lowers its boiling point, and that there were considerabdifferences in the lowering degree, depending on whethesolid is in powder or in lump.

In 1812 and 1817,Gay-Lussac(Joseph Louis, 17781850, well known from the isobaric temperature-volumelationship of gases) [20,21], supposed the boiling poinvary in different vessels according to the nature of their sfaces and the materials, the variation depending on both thconducting power of the materialfor heat and on thepolishof the surface. According toMarcet [22] the lower boiling

3 De Luc (Jean André De Luc, or John Andrew de Luc, frequently wriDELUC) was a member of the above mentioned Cavendish’s committewas for many years Reader to Queen Charlotte, and was engaged infield of science of the late eighteenth century [17]. For an account oLuc’s achievements see Emeis [18].


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temperature of water on metallic surfaces in comparisoglass surfaces is caused by a corresponding weakeradhesionof water particles to the wall. Bubble generation is expecwhen therepulsive action of heatovercomes thecohesion ofthe liquid along with the atmospheric pressure. He alsoticed the dependence of thebubble departure diameterandthe bubble frequencyon thestrength of heat source(heatflux).

It is interesting that some basic studies of boiling pnomena were originated from the development of thmometers and explosions of steam boilers. To the forgroup of works belong at least by part also the studiesCavendish [14]. In a paper byRudberg[23] there are considerations of liquid evaporation during bubble rise throuthe liquid and expansion of vapour making the bubble.

First precise experiments on anegative pressure in liquidwere performed byBerthelot(1827–1907) [24] at constanvolume, showing that liquids can sustain a considerablesion (water 50 bar, ether 150 bar, approximately). Howefor the present purposes of much greater interest is thebaric liquid superheat.Dufour [25] seems to be the first whinvestigated the superheat ofwater droplets suspended in othus avoiding a direct contact between the test liquid andsolid wall. By this method, he was able to obtain waterperheats up to 70 K at atmospheric pressure. He termestate of the superheated liquidmetastable. Dufour’s exper-iments aimed at clarifying the cause of explosion of steboilers. At high superheats, he observed a vapour gention in the whole liquid mass.Krebs[26] reported on similarboiling behaviour, which he calledexplosive boiling. As itappears, both authors reached in their experiments neahomogeneous vapour nucleation.

Two further classical contributions to the understandof bubble nucleation are worth mentioning.Tomlinson[27]stressed that formation of bubble nuclei depends noton thestate of the surface(clean, unclean) but also on iporosity. He gave a very interesting definition of a liquid neor at its boiling point:

“A liquid at or near its boiling point is a supersaturatesolution of its own vapour, constituted exactly like sowater, champagne, and solution of some soluble gase

Tomlinson’s ideas have sharply been criticized byAitken[28], remarking, we cannot imagine a porous body whileder the same conditions both to absorb vapour from the wand give it out again in a constant, never-ceasing flow. Aitcontinues to describe the boiling supposing a free surfacexist. The free surface is formed by adsorption of gaseswere dissolved in the liquid. He says:

“. . . bubbles have sprung from certain points wherewater is not in contact with the vessel, but is separafrom it by a small quantity of gas or vapour; into thisgas or vapour the water vaporises till it grows to suchsize that part of it breaks away and rises to the surfa

-

-

leaving part still attached to the vessel to form a cetre from which another bubble grows, to be thrown offturn, and while the bubbles rise in rapid successionroot remains fixed.”

Aitken also discussed theeffect of roughnessand ofsurfaceactive substanceson bubble generation, but he assumednuclei for formation of vapour bubbles, which was not a nidea.

From this short review of the literature we may drawfollowing conclusions concerning the state of the art inarea of nucleate boiling (bubble nucleation) at the end19th century:

(1) Bubble generation is intimately connected with ingases, either dissolved in the liquid or adsorbed onsurface of the wall.

(2) The boiling temperature (liquid superheat) dependsthe amount of the dissolved gases, the surface roness/porosity and the interaction liquid–solid wall.

(3) The state of a superheated liquid is instable and bble formation in such a liquid can be initiated in varioways. At a strong superheat the boiling manifests itexplosively.

The papers referred to so far are scarcely mentioned inrent literature. The notions about bubble formation descrin these old and vastly forgotten publications are interesnot only from a historical point of view.

2.2. Theoretical speculations

The conclusions above are mainly based on experimeobservations. Besides, there are also theoretical modethis area aiming at deeper insights into the boiling phenena. The model connecting the separation of liquid partiby action of heat was originally proposed by Halley [12].Query 31,Isaac Newton(1642–1727) [29] has drawn the atention to particles, released from and beyond the attracof a body, receding from it and from one another with grstrength. The idea developed byAntoine Lavoisier(1743–1794) [30] unifies the notions of Halley and Newton. Hassumed that the particles of all bodies are subjected toattractive and repulsive forces. When removed beyond thlimits of attraction, a change of state (phase) might bepected. This idea has already been developed byDesaquliers(1683–1744) [31] andBoskovic(1711–1787, Roger JospBoscovich, or Rudjer Josip Boškovic)) [32]. Desaqulierspostulated that in liquids there exists both arepulsiveandanattractiveforce between the particles. The former woube augmented and suppress the attraction if the temperis increased and elastic fluid formed. Boskovic [32] spein his Theoria (§462), appeared in 1763, ofevaporationandebullition. According to Boskovic,a slow evaporation willtake place when the repulsive force does not greatly exthe attractive force. An ebullition is expected when the ma


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The theoretical contributions of fundamental importanin this area byWilliam Thomson(Lord Kelvin, 1824–1907) [33],J.W. Gibbs(1839–1903) [34], andJ.J. Thomson(1856–1940) [35], resulting in analytical relationships,mained unrecognized for decades. This might be due tocomplexity of the ideas, particularly by Gibbs, as may beduced from the foreword to the German translation of Gibstudies byW. Ostwald4 [36]:

“Anmerkungen und Erläuterungen hinzuzufügen hatVerfasser nicht die Zeit und der Übersetzer nicht den Mgehabt.”

On the basis of a thought experiments, W. Thomsonquantified theeffect of curvatureof the interface onvapourpressure,while Gibbs [34] introduced anenergy barrierequal to thework of bubble formation. The other ThomsonJ.J., derived an equation for theliquid superheat arising fromthe interface curvature[35,37].

More recent works in the area of bubble formation aboiling heat transfer mostly deal with specific phenomsuch asfluctuation of state parameterspreceding bubble nucleation, an issue, which can be traced back to the timvan der Waals[38], and even ofBoskovic[32]. The heattransfer to a growing bubble, adhering to a heater surfoccurs mainly in the region where all the phases invol(liquid, vapour, solid wall) are interacting and the heat flmay change its direction [39]. The detection of this pnomenon makes the boiling process by no means simbut contributes to understanding the boiling events ocring around a growing bubble. The issue becomes mmore complicated if the heater surface is provided witmicro-structure that should enhance boiling kinetics, se.g., Thome [5] and Webb [40].

3. Efficient boiling surfaces

3.1. Vapour trapping and ideal boiling surface

The above short overview of the literature shows thateffect of wall on boiling temperature has been recognialmost three centuries ago. First systematic investigatof the wall effect on nucleate boiling heat transfer wseemingly performed by Jakob and Fritz [41]. Corty aFoust [42] reported heat transfer data obtained with difent liquids boiling on surfaces of various polish. Dependon the pair liquid–surface, Corty and Foust [42] observedheat transfer coefficient to be almost independent of the

4 “The author had no time and the translator no courage to provide cments and explanations”. W. Ostwald was one of the leading scientisphysical chemistry of his time.

-

,

superheat. As they noticed, the micro roughness of theing surface was one of the fundamental factors governingheat transfer:

“It may be postulated that there exist cavities in tmetallic surface and that in these cavities vapourtrapped after an earlier bubble has broken loosely. Ttrapped vapour then acts as the nucleus for the next bble from the same spot.”

“A vapour-filled cavity may act as nucleus for bubble fomation as long as the superheat in the surface is henough to support the vapour phase inside the caagainst the constrictive effect of surface tension inphase boundary.”

These findings by Corty and Foust in 1955 (PhD dissetion of C. Corty 1951) concerning thevapour restactingas a nucleus for the next bubble are perfectly in agreemwith the ideas developed by Aitken [28] in 1878. Corty aFoust applied an expression for the equilibrium temperaof a concave interface to a bubble in a cavity. This seembe for the first time to specify theminimum wall superheain nucleate boiling required by thermodynamics for a sble vapour bubble. This idea has been extended by Hsu aGraham [6,43] tonon-isothermal systemsand refined in themean time by many others. We will use the Hsu and Gham relationship in a slightly modified form further beloto estimate the cavity size of an efficient surface for nucleboiling. Prior to this, however, it seems appropriate to dean ideal surface regarding the boiling heat transfer:

A heat transfer surface in nucleate boiling is consideto be ideal if the variation of the heat flux does not resin any change of the driving temperature difference.

Fig. 1 illustrates typical shapes of boiling curves.schematically shown in Fig. 1(c) and (d), the heat fluxq

is independent of the wall superheat�T . This heat flux in-dependency requires a change of the thermal resistanceR tonucleate boiling according to the expression

q · R = �T = const (1)

which means that any increase in the heat flux results in acrease in the thermal resistance thus keeping the heat trapotential unchanged. This relationship follows the genTheorem of Moderation(Le Chatalier Principle, as a particular case):

Any system in a steady state undergoes, as a resua variation in one of the factors governing this statecompensating change in a direction such that, hadchange occurred alone it would have produced a vation of the factors acting in the opposite direction.


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Fig. 1. Some shapes of boiling characteristics: (a) Partial activation ofble sites after boiling inception; (b) Simultaneous activation of bubble safter boiling inception; (c) Simultaneous activation of bubble sites followby independency of wall superheat on heat flux; (d) Ideal boiling surfaczero inception superheat.

What could be the nature of these factors in case of nucboiling in accordance with Eq. (1)?

To answer this question requires an analysis of the manisms of boiling heat transfer. These mechanisms havediscussed in several publications dealing with the boilingcommon, technical surfaces, and a recent paper by YuCheng [44] should be mentioned in this context, insteagiving a literature review. According to the well-acceptfigure of nucleate boiling, the bubble density increases wrising heat flux. Consequently, thestirring effectof growingand detaching bubbles should principally be included wdiscussing Eq. (1). However, considering that an improment of the stirring effect requires a corresponding increin bubble frequency and/or bubble density, the stirringfect does not represent a direct event in the chain of buevents and the reduction of the thermal resistance withcreasing heat flux according to Eq. (1) seems less probby this effect. The same holds for other transfer mechanlike Marangoni convectionor displacement of hot liquidbygrowing bubbles. They all depend on the wall superheathat an increase in the heat flux necessitates a rise of thetemperature [44].

A direct heat transfer event in nucleate boiling wouldevaporation at an existing vapour–liquid interface whichteracts with the heating surface, if the molecules leavthe liquid phase receive the necessary energy jump (action energy) immediately from the heating wall. This idimplies that the wall heat flux is completely consumedvapour generation directly on the wall surface, as it occur

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-

the three-phase-line (TPL, liquid, solid, wall). For the idto be realistic, the bubble frequency and/or the activaof further bubble cavities must take place without anyditional increase in the wall temperature. One possibilityaccomplish this is to adopt the ideas of Aitken [28] and Coand Foust [42] and topostulatea permanent existencethe vapour–liquid interface on the heating surface. Anoone could be based on an appropriate surface structureacting with the bubble–induced liquid flow in a way whiassists in bubble generation. We will return to this quesfurther below.

3.2. Criterion of bubble growth

From the above, we may draw the conclusion that aface efficient in nucleate boiling should be able to genevapour bubbles at (nearly) zero waiting time. This implievapour rest to remain in the surface cavity at the bubbletachment. The existence conditions of this vapour rest wthen formulate a criterion for bubble growth. This criterimust not be confused with the condition of boiling incepti

Like Corty and Foust [42] also Griffith and Wallis [45proposed a relationship between the cavity size and thesuperheat:

rCR = 2σT∞

�hρV (TW − T∞)(2)

HererCR denotes the radius of the cavity mouth,σ the sur-face tension,�h the evaporation enthalpy,T the tempera-ture, andρ the mass density. The indicesV , W and∞ referto vapour, wall and to liquid at a large distance from the wrespectively.

The temperature differenceTW −T∞ in Eq. (2) representthe minimum wall superheat required by the thermodynaequilibrium conditions for a concave interface of the radrCR. Being derived by J.J. Thomson in 1886 for the first timit would be safe to name this equationThomson’s(J.J.) nu-cleation criterion.

As noted above, the conditions of bubble existencesystem with temperature gradient was apparently firstmulated by Hsu and Graham [6,43]. Their analysis stfrom the (J.J. Thomson) equation for a bubble in a liqof homogeneous temperature,

TB = T∞ + 2σT∞

�hρV rB(3)

which is identical to Eq. (2); the indexB refers to the bubbleThe fate of a bubble in a liquid of an inhomogeneous te

perature will depend both on its size and place with regto the temperature distribution near the wall. As illustrain Fig. 2 for a liquid of a linear temperature distribution,bubbles of the temperatureTB and the radiusrB are thermo-dynamically stable in the layerδ adhering to the wall. Bycontrast, bubbles above the lineTL (outsideδ) were instableand would condense [46]. Analogously, another bubble tperatureTB would require a corresponding bubble radius


ano oc

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Fig. 2. Illustration of bubble survival conditions.

Fig. 3. Illustration of bubble growth criterion.

If the line TL in Fig. 2 intersects the bubble interface,evaporation–condensation process may be expected tcur, and the conditions of bubble growth would demand

dmV

dt= −

∫A

ρL(uLI − uI )dA � 0 (4)

wheremV is the mass of the vapour,uLI the radial velocityof the liquid at the interface moving at the velocityuI , andA

the interfacial surface area. This equation requires the eoration to balance or overcome the condensation; the litemperatureTL at the distanceδ + rB must at least be equato the bubble temperatureTB , as stated by the nucleation cterion (3).

For a semi-spherical bubble attached to the mouthcavity of the radiusrC = rB , the temperatureTB in Eq. (3)can be plotted as a function of the wall distancey = rB ,Fig. 3 [47]. A linear temperature distribution in the liqunear the wall,

dTL

dy= − q

λL

(5)

and the requirement of tangency aty = rCR give

dTL

dy= TB − TWCR

rCR= − q

λL

= −α(TWCR − T∞)

λL

(6)

TWCR − T∞ = 2σT∞

�hρV rCR

/(1− αrCR

λL

)(7)

wereλL denotes the liquid thermal conductivity,α the heattransfer coefficient, and the index CR refers to the critbubble (cavity) radius. The structure of this equation is idtical to the one reported by Howell and Siegel [48].

-

-

Fig. 4. Effect of wall temperature on critical bubble radius.

Because ofTWCR − T∞ > 0, Eq. (7) requires

α < αmax= λL

rCR(8)

and the critical radiusrCR according to Eq. (7) lies in thrange 0< rCR < λL/α, Fig. 4. At the minimum of the curve

rCR = 1

2

λL

α(9)

we have

TWCR,min − T∞ = 8σT∞α

�hρV λL

= 4σT∞

�hρV rCR(10)

For a wall temperatureTW > TWCR, the spectrum of bubblradii able to grow falls betweenrCR1 and rCR2. The exis-tence of the two critical radii at the same wall temperatis associated with the thermodynamic equilibrium condit(regionr < rCR1) and by condition of heat transfer (regior < rCR2) that can cause large bubbles to condense.

3.3. Creation of an efficient surface

For a givenrCR within the rangerCR1 < rCR < rCR2, thetemperature difference

TW − TWCR = TW − T∞ − 2σT∞

�hρV rCR

1

1− αrCRλL

(11)

represents the wall superheat above the thermodynamicimum (equilibrium), and by this temperature differencesystem (wall, liquid and bubble) is shifted from its eqlibrium state. Taking the temperature as a system coonate, the temperature differenceTW − TWCR defines a forcedriving the system towards the thermal equilibrium.

The driving force is different for different bubble cavitieAs follows from Fig. 4, it is zero forrCR = rCR1 andrCR =rCR2, but maximum forrCR given in Eq. (9),

TW − TWCR,min = TW − T∞ − 4σT∞ (12)

�hρV rCR


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ot inionainouldle

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As is obvious from Fig. 4 and Eq. (11), any increase inwall superheat above the thermodynamic minimum couldsult in an activation of surface cavities in the rangerCR1 <

r < rCR2. Because the size of the cavities is a fractal quanany increase in the wall temperature would, at least thretically, correspond to activation of certainfraction of thecavity size, and by this process also the heat flux couldfractioned. As discussed by Yu and Cheng [44], a relatship between the wall superheat (or heat flux) and the fradimension of cavities would result. Such a behaviour, hever, would not be in accordance with the definition ofideal boiling surface stated above, Eq. (1), because antivation of new cavities (other fractal level) would requsurmounting the energy barrier as a measure of the theresistance.

The expression given in Eq. (11) shows us a way howcreate an efficient boiling surface. Namely, in order to kthe temperature difference constant,the cavity radiusrCRmust be fixed, that is, all the cavities must have the sradii. In this way we would exclude the existence of cavitof other sizes thus generate amono-cavity-pattern. As a con-sequence, the thermodynamic wall superheat corresponto this cavity pattern would be the same for the whole sface.

In the case of a mono-cavity-pattern all the cavitiesexpected to become activated simultaneously at the samperheat. An increase in the wall temperature beyond therequired by the thermodynamic equilibrium would resultfaster vapour production on the heating surface, and nactivation of further bubble sites. As the vapour productmainly occurs at the TPL, the wall superheat would remunchanged whereas the heat flux (evaporation rate) wrise. In other words,a rise in the heat flux would be possibwithout increasing the wall temperature.

This notion requires two further conditions to be fulfille

(a) Bubble formation at (nearly) zero waiting time, whimeans a viable vapour rest in the cavity after the bble detachment. A vapour rest able to grow immediaafter the bubble break-off could be realised in an apppriately formed structure.

(b) The mutual distance of the cavities must also bescribed in a certain manner for the surface to be efficiFor this reason, the pattern of the cavities must be csen so that (ideally) no heat is transferred from the hing surface to the liquid, but at the same time any sincavity be supplied sufficiently with the heat requiredbubble growth.

The mutual distance of the cavities could be estimated ftheir thermal interaction through the wall. Distributed onheating surface in a way that the surface area thermallycupied by one cavity just touches the ones of the neighbing cavities, would largely prevent the heat transfer frthe wall to the liquid and the heat would be consumedmost completely by vapour generation directly on the w

-

l

-

surface. Because of vapour rest remaining in the caon bubble detachment, the energy barrier of bubble nuation would be reduced considerably and the temperaof the wall surface would approximately remain constaThis would change the boiling characteristic substantibecause the increase in the wall temperature with risingflux in nucleate boiling on common surface is associawith the nucleation barrier of cavities having different bosize and shape. In this context the reader may be referrthe studies dealing with surface roughness, e.g., [48–53the review paper by Fujita [54].

4. Experimental evidence

Corty and Foust [42] observed boiling characteriswith n-pentane and diethyl ether on polished copper surfawith wall superheat largely independent of the heat flascribing the micro roughness of the heater surface a fumental role. Similar behaviour have been reported by Yoal. [55] on particle-layered surface, see also Bar-Cohen [More than two decades ago, the present author conduboiling experiments with the Refrigerant R11 (CF2Cl3) ona flat heater surface provided with artificial nucleation siFig. 5. The surface cavities (diameter 180 µm, depth 120density 460 cm−2, approximately) were arranged hexagnally.5 They were generated by photo-etching techniqfirst used by Messina and Park [57]. The experimental fiings have been presented at a meeting in 1988 [58], bupublished yet. As the results seem to be still interestFig. 6 shows the boiling characteristics obtained with Rat nearly atmospheric pressures. In the region of develoboiling, the experimental uncertainty of the heat flux wastimated to be less than 2% and of the temperature differebelow 1.5%.

The constancy of the wall superheat is observed oat relatively high heat flux. In the case of increasing hflux, the surface cavities were activated at nearly the sheat flux. The bubble detached almost simultaneously onwhole surface, resulting in a piston-like boiling oscillatioThis boiling behaviour was observed only in the horizonposition of the heating surface.

Recently, Wei and Honda [59] published very interestresults on boiling FC-72 using chip surfaces provided wdifferent micro-pin fins. The boiling characteristics were oserved to depend on the liquid subcooling and fin geomSome surfaces show almost constant wall superheat inrange of the wall heat flux. At the same time, the hysterat boiling inception was practically zero.

A novel microstructure. As a further example, a paper bMitrovic and Hartmann [60] dealing with nucleate pool boing of the Refrigerant R141b should be mentioned. T

5 It should be noted that the walls of the cavities were not smoothcovered with a fine structure that largely governed the wall superheat.


used

re.r to1b,

t.by

s aressentro-er oion

en-oresingins

Thetro-teentrmitns.

tersfromomd

ro-the

truc-duc-ition

i-ted

allon-thed

entbepar-allre-

ed

Fig. 5. Photograph showing the pattern of cavities on the heating platein the experiments with R11.

used a horizontal tube provided with a novel microstructuFig. 7 shows an example of the surface structures. Priopresenting some experimental result obtained with R14the main steps of generating the structure are given nex

The microstructure shown in Fig. 7 is generatedelectro-deposition in a galvanic process. The basic stepillustrated in Fig. 8. A thin polycarbonate foil (thicknebelow 100 µm) is irradiated by heavy ions. This treatmcreates ion-tracks in the foil which can be widened to micpores in an etching process. The density and the diametthe pores can be altered by variation of ion density in theray and the etching duration, respectively.

The treated foil is then affixed to the specimen and thesemble subjected to a electrolytic process, in which the pbecome filled by material deposition. In a further etchprocess, the foil is completely removed leaving behind pmetallically connected to the surface of the specimen.height of the pins can be varied by the duration of the elecdeposition, but is limited by the foil thickness. Appropriamanaging of the galvanic deposition may result in differshapes of the top of the elements. The whole process pean almost continuous variation of the structure dimensio

f

s

Fig. 6. Boiling characteristic of the surface shown on Fig. 5.

The height of the pin-shaped elements, having diamebetween 1 µm and 25 µm, can be realized in the range10 µm to 100 µm, while the pin density can be varied fr1× 104 cm−2 to 1× 107 cm−2. The structure can be createon cylindrical specimens like tubes in almost all electchemically depositable materials. For the purposes ofpresent investigations, both specimen (tube) and the sture are made of copper because of its high thermal contivity and the advantages regarding the electro-deposprocess.

Fig. 9 shows the boiling characteristic of the novel mcrostructure on a single horizontal tube (OD 18 mm, healength 180 mm) with pool boiling. The heat fluxq is taken tobe independent of the circumferential position, but the wtemperature was obtained in the vertical and the horiztal planes of symmetry. The experimental uncertainty ofheat flux and the wall superheat�T was less than 2% an1.5%, respectively.

The different boiling characteristics observed at differcircumferential positions of the tube are considered tocaused by free convection that affects the heat transferticularly at the bottom of the tube. At the tube top, the wsuperheat is practically independent of the heat flux, asquired by Eq. (1). The slight reduction in�T with rising q

is not fully understood yet, but it could basically be causby pins protruding the bubble surface.


be,fromheaeatthe

oly-ess;hing

aurure,

meserytly

ingex-

e ifbble

h ain-PL

ary

Fig. 7. Examples of surface structures consisting of micro pins.

Fig. 9(b) compares the novel structure with a plane tuboth investigated at the same apparatus. As is obviousthis Figure, the wall superheat increases with increasingflux for the plane tube. On the contrary, the wall superhof the structured surface remains practically constant inregion offully developednucleate boiling.

t

Fig. 8. Generation steps of a novel microstructure: (a) Ion-perforated pcarbonate foil; (b) Foil affixed to specimen; (c) Electro-deposition proc(d) Structure elements with torospherical tops; (e) Structure after etcprocess; (f) Structure after etching process with torospherical tops.

Isothermality of the boiling surface.An explanation of thesurface isothermality given in the following is based onsimple idea. As illustrated in Fig. 10, a growing vapobubble interacts with several pins at a low system pressFig. 10(a). The liquid layer underneath the bubble becothinner as the heat flux increases, Fig. 10(b). At a vhigh (near-critical) pressure, a growing bubble if sufficiensmall interacts with only a few pins, Fig. 10(c). Dependon system pressure, that is, on the bubble size it may bepected that different number of pins pierce the interfaca liquid wedge is assumed sandwiched between the buand the wall, thus creating a TPL at any single pin witstrong evaporation, Fig. 11(a). In case of a motionlessterface for a time period, the liquid evaporated at the Tis replenished by a cross flow originating from the capillaction of the pins and by gravity, Fig. 11(b).


ro-

es-ngIn a

etate

r-

ins:ure.

c-nglecuts

thenta-

-e

ting

Fig. 9. Preliminary results of pool boiling of R141b on a tube surface pvided with micro pins (a) and comparison with plain tube (b).

By this model, processes taking place at the TLP aresential for boiling kinetics. The TPL is the place of strovapour production acting simultaneously as a heat sink.first approximation, the relationship

LTPL ∼ Q (13)

is expected to hold, whereLTPL denotes the length of thTPL andQ the heat flow rate under common steady-sconditions; the bar refers to the averaged value.

The ratioLTPL/A, whereA is the area of the heating suface, represents the surface densitynL of the TPL,

nL = LTPL

A(14)

thus

q ∼ nL (15)

Fig. 10. Sketch of a vapour bubble growing on a surface with micro-p(a) Low pressure and/or low heat flux; (b) High heat flux; (c) High press

with q = Q/A as the wall heat flux.The lengthLTPL of the TPL depends on the surface stru

ture, the number of growing bubbles, the size of each sibubble, and the angle the surface of the liquid wedgethe pins, Fig. 11(a). The quantityLTPL of each single bubbleis expected to change with time. Since its calculation forwhole surface is impossible, we will consider a represetive vapour bubble.

Taking the bubble at the timet as semi-spherical of a radius r = r(t) without a dry-spot, Fig. 10(a), we obtain thlengthLTPL

LTPL = π · n · d · A = π2 · n · d · r2 = f (t) (16)

wheren is the number density andd the diameter of thepins;A is the bubble surface area projected onto the heasurface,A = A(t) = π · r2(t).


cingour-

rned

bble

theme

e

the

thef the

notour

er-s

blel re-

r theom-fluxses.

cle.es isbub-in

ace,uper-

Fig. 11. Illustration of the effects of micro-pins on heat transfer: (a) Pierthe interface by pins results in a large TPL; (b) Cavity formed by neighbing pins.

Furthermore, assuming the bubble growth to be goveby heat diffusion, we may expect a relationship6

r(t) = C(κt)1/2 (17)

whereC is the growth constant andκ the thermal diffusivity,thus

LTPL = (Cπ)2κ · n · d · t (18)

which gives a constant growth rate of the TLP, dLTPL/dt =(Cπ)2κ · n · d , Fig. 12. The quantityLTPL,min correspondsto the vapour rest remaining in the structure after the bubreak-off.

This interesting result shows by the relation (13) thatheat flowQ increases during the bubble growth at the sarate as the length of the TPL,

Q ∼ LTPL = (Cπ)2κ · n · d · t (19)

Relating the lengthLTPL to the projected bubble surfacarea,A = A(t) = π · r2(t), we get the surface densitynL

of the TPL and the heat fluxq for a single bubble,

nL = πnd (20)

q ∼ πnd (21)

showing that the both quantities remain constant duringbubble growth time.

6 This equation is usually derived by assuming the evaporation onwhole bubble surface. As can be shown, it is also valid for any part osurface, thus also for the interline region.

Fig. 12. Time history of TLP. After bubble detachment, the TLP doesdisappear; its lengthLTPL,min corresponds to volume and shape of vaprest for given structure.

Fig. 13. Increase in bubble density at the same wall superheat.

To obtain an estimate of the quantitynL we may set:n = 105 cm−2, d = 20 × 10−6 m. Then, nL = 2π =6.28 m·cm−2, which is surprisingly large; even ford =1× 10−6 m, we getnL = (π/10) = 0.314 m·cm−2.

Eq. (21) leads to the conclusion that the driving tempature difference�T for any single bubble linearly dependon the thermal resistanceR,

�T = q · R (22)

However, the growth of the TPL associated with bubgrowth seems to act against the change in the thermasistanceR thus giving a constant wall superheat�T . Thisinteresting interplay does, however, not suffice to answequestion asked in connection with Eq. (1) regarding the cpensation of the wall heat flux rise. With increasing heatboth the frequency and the density of the bubbles increaBy Eq. (21), the heat flux is constant during a bubble cyThe constancy of the wall superheat at various heat fluxdecisively governed by the corresponding change in theble density, Fig. 13. As the activation of further bubblesthe structure is equally probable at any place of the surfnew bubbles become generated at the same surface sheat.


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Despite its simplicity, this analysis provides an explation of the independency of the wall superheat on the hflux. Within the Theorem of Moderation, thegrowth of theTPL, associated with bubble density and bubble growthduces the thermal resistance thus leading to a constantsuperheat.

The pins do not only act as generators of the TLP. Talso tend to prevent (by capillary action) the formationa dry spot beneath the bubble thereby improving thetransfer. When a bubble detaches from the heater surfacexpected that the necking and break-off of the bubble ocin the outer part of the capillary structure. The vapour rremaining in acapillary formed by neighbouring pinsactsas nucleus for the next bubble which drastically reducesthe waiting time and the energy barrier of bubble formatin comparison to a plane surface, Fig. 11(b).

Regarding the optimum distance of active bubble sithe pin structure possesses someself-regulating potential.In contrast to artificial cavities that are fixed on the heing surface, the pin structure allows bubble formationany place of the surface having a sufficient superheat. Fthis model it becomes obvious that the shape and numdensity of the pins will strongly affect the heat transfIt is generally expected that, for pure liquids under opmal conditions, the number density of the pins mustincreased with the pressure. This quantity could basicbe connected with the bubble equilibrium [60], but itsliable determination would require precise experimentsthis way, we could tailor boiling structures in dependenof the system parameters that largely behaves accordinEq. (1).

This idea is basically not new. In 1963 J.W. Westwter [61] wrote in a very remarkable contribution entitlThings We Don’t Know About Boiling Heat Transfer:

“. . . in principle, it is possible to produce a tailor-madesurface which will have a predetermined distributionpore sizes and thus a predetermined boiling curve. . . .”

Our guiding idea, however, contradicts somewhat toWestwater statement regarding the distribution of pore siWe try to tailor a heating surface not with a distributionpore sizes, but with amono-pin structure pattern formed bidentical elements. These elements communicate with eaother through the liquid, which is not necessarily the cwith cavities formed in the heating wall. In other wordan efficient surface shouldnot be provided with cavities buwith protrusions of the same shape homogeneously disuted over the surface.

The elements of the micro-structure can possessshape. Fig. 14 illustrates an arbitrary shape of thements arranged on the heating surface in a staggeredtern. The cross-section of each element should besame, but there is not a specific requirement regardinshape. However, as we are interested in a possiblyTLP, the border line of the cross-section of the elem

l

-

Fig. 14. Mono-element pattern of a surface structure; A represent a cformed by neighbouring surface elements.

Fig. 15. The von Koch fractal curve as border of the cross-sectional ara structure element.

should not be smooth but composed of small pieces reing in a zig–zag fashion of the envelope. In other worthis line should be afractal like the coast line of an island [62]. Suitable for this purpose could be, for instanthe well-known von Koch curve giving islands of varioshapes, Fig. 15.

The von Koch curve is one of the classical fractal objeIt is constructed from a line of length c. The central thirdthis line is replaced by two lines of the lengthc/3 in a trian-gle form. This process is continued by replacing the centhird of any line segment at each fractal step by two linethe lengthc/3. The protrusion of the replacement is alwaon the same side of the curve. At each step the total leof the curve is increased tending to infinity as the numbesteps goes to infinity, but the surface areaA enveloped bythe curve is finite,A = (2/5)c2

√3, if the basic line forms a

triangle, Fig. 15.The circumference of the structure element designe

the von Koch curve would provide a long TLP and, in adition, give rise to capillary action also along each elemthus assisting in boiling kinetics.


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5. Limits of the model

The above considerations rest on the assumption thinterface of aconcavecurvature already exists. However, dpending on the cavity shape and the interaction liquid-wthe vapour–liquid interface could principally beconvexthusaffecting both the equilibrium conditions and the drivitemperature difference, Eq. (7). Also an attractive actionthe wall on the liquid would alter the equilibrium condtions [37]. Furthermore, inert gases dissolved in the liquidadsorbed on the heater surface could affect both the equrium state and the surface tension at the TPL. As discuby Uhlig [63], the surface tension of liquids decreases wincreasing fraction of gas dissolved in the liquid. In additithe model gives no information about the wall superheathe boiling incipience.

A further effect that should be mentioned in this contis the nonisothermality of the system. The model postulthe equilibrium at the vertex of the bubble of a constantterface curvature. Actually, micro-relief of the heater surfcan affect the interface curvature in the region of the TFurthermore, during the bubble generation the temperaof the interface is not constant so that a part of the free enchange of the system is bounded as latent heat requirkeep the temperature of the interface constant when itsis increased, and the total interface energyσ − T (dσ/dT )

would have to be considered when dealing with the equrium conditions and bubble growth.

6. Conclusions

The mechanisms of bubble generation in liquids havetracted the attention of manynatural philosophersin 18thand 19th centuries. At the end of 19th century the knowlein this area was at such a high level, that the ideas largelyvived to the present time.

On the basis of these old ideas and a criterion byand Graham [6,43] the possibilities of creation of efficisurfaces regarding the nucleate boiling are discussed. Itfound that surface structure must adjust itself when opeing ideally. In other words the surface structure must hsuch properties that the heat transfer resistance decrwith rising heat flux. A structure consisting of appropately arranged micro pins shows such a boiling behavin the region of fully developed nucleate boiling. Thesential outcoming of the considerations is that the boisurface should be provided not with cavities (holes), ausually recommended in the literature, but with identiprotrusions.

References

[1] J.W. Westwater, Boiling of liquids, Advances in Chemical Engineing 1 (1956) 1–76.

s

[2] E.I. Nesis, Boiling of liquids, Soviet Physics Uspekhi 8 (1966) 88907.

[3] P.V. Carey, Liquid–Vapour Phase-Change Phenomena, TaylorFrancis, New York, 1992.

[4] J.G. Collier, J.R. Thome, Convective Boiling and CondensatClarendon Press, Oxford, 1994.

[5] J.R. Thome, Enhanced Boiling Heat Transfer, Hemisphere, Washton, DC, 1990.

[6] Y.-Y. Hsu, R.W. Graham, Transport Processes in Boiling and TPhase Systems, Hemisphere, Washington, DC, 1976.

[7] Anonymous, Evangelista Torricelli, Engineering 8 (1909) 136.[8] Th. Birch, A History of the Royal Society of London, Millar, London

1756–1757.[9] G.S. Kell, Early observations of negative pressures in liquid, Ame

Phys. 51 (1983) 1038–1041.[10] Aristotele, Meteorologica (English translation by H.D.P. Lee), Harv

University Press, London, 1978.[11] T. Fairley, Notes on the history of distilled spirits, especially whis

and brandy, The Analyst 30 (1905) 293–306.[12] E. Halley, An Account of the Circulation of the watry vapours of t

sea, and of cause of springs, Philosophical Transactions of the RSociety of London 17 (1690/1691) 468–473.

[13] H. Cavendish, in: E. Thorpe (Ed.), The Scientific Papers, CambrUniversity Press, Cambridge, 1921 (particularly vol. II, UnpublishPapers, Theory of Boiling).

[14] H. Cavendish, et al., The Report of the committee appointed byRoyal Society to consider of the best Method of adjusting the fiPoint of Thermometers; and the precautions necessary to be usmaking Experiments with those Instruments, Philosophical Trantions of the Royal Society of London 67 (1777) 816–857.

[15] J.A. De Luc, On evaporation, Philosophical Transactions of the RSociety of London 82 (1792) 400–424.

[16] J.A. De Luc, Introduction a la Physique terrestre par les Fluids exsibles, Nyow, Paris, 1803.

[17] S.A. Dyment, Some eighteenth century ideas concerning aquvapour and evaporation, Annals of Science 2 (1937) 465–473.

[18] S. Emeis, Der Meteorologe und Geologe J.A. Deluc (1727–1817)der Wandel naturwissenschaftlicher Sicht- und Denkweisen wähseiner Schaffenszeit, Freiberger Forschungshefte (Montan- und Tnikgeschichte) D 207 (2002) 27–37.

[19] F.C. Achard, Nouveaux Mémoires de l’Académie Royale de Berlin1784–1785.

[20] J.L. Gay-Lussac, D’un Mémoire sur la déliquescence des corps,nales de Chemie 82 (1812) 171–177.

[21] J.L. Gay-Lussac, Note sur la Fixité du degré d’ébullition des liquidAnnales de Chemie et de Physique 7 (1817) 307–313.

[22] F. Marcet, Untersuchungen über gewisse Umstände, welche auTemperatur des Siedepunktes der Flüssigkeit vom Einfluss sindnalen der Physik und Chemie 57 (1842) 218–241.

[23] F. Rudberg, Über die Construction des Thermometers, AnnalenPhysik und Chemie 116 (1837) 39–62.

[24] M. Berthelot, Über einige Phänomene der gezwungenen Ausdehder Flüssigkeiten, Annalen der Physik und Chemie 158 (1851) 3335; Annales de Chemie et de Physique 30 (1850) 232–237.

[25] L. Dufour, Über das Sieden des Wassers und über eine wahrscliche Ursache des Explodierens der Dampfkessel, Annalen der Pund Chemie 200 (1865) 295–328.

[26] G. Krebs, Versuche über Siedeverzüge, Annalen der PhysikChemie 133 (1868) 673–677; Annalen der Physik und Chemie(1869) 144–151; Annalen der Physik und Chemie 138 (1896).

[27] C. Tomlinson, On the action of solid nuclei in liberating vapour froboiling liquids, Proceedings of the Royal Society 17 (1869) 240–2

[28] J. Aitken, On boiling, condensing, freezing, and melting, Transactof the Royal Scottish Society of Arts Edinburgh 9 (1878) 240–287

[29] I. Newton, Opticks, second ed., Innys, London, 1718.


Ed-

e ofans-

ng-IT

edical

rans-878)

stry,

von

er-

ders. 20

ingeat

nce,

ng,) 435

En-

ting

at-

oil-

liq-r 44

tion

ingand

eate0.ool

E

sur-g. 2

ss

ool7.oil-nt,

boil-92,

rch,

inerng

sfer. J.

u-

, in:sfer,

lf-

ys.

[30] A. Lavoisier, Elements of Chemistry, Translated by Kerr, Creech,inbourgh, 1790.

[31] J.T. Desaquliers, An attempt to solve the phenomenon of the risvapours, formation of clouds and descent of rain, Philosophical Tractions 36 (1729) 6–22.

[32] R.J. Boscovich, Theoria Philosophiae Naturalis, Venetiis, 1763; Elish translation by J.M. Child: A Theory of Natural Philosophy, MPress, 1921.

[33] W. Thomson (Lord Kelvin), On the equilibrium of vapour at a curvsurface of liquid, The London, Edinburgh, and Dublin PhilosophMagazine and Journal of Science Series IV 42 (1871) 448–453.

[34] J.W. Gibbs, On the equilibrium of heterogeneous substances, Tactions Connecticut Academy of Arts and Sciences 3 (1874–1108–248.

[35] J.J. Thomson, Applications of Dynamics to Physics and ChemiMacmillan, London, 1886.

[36] J.W. Gibbs, Thermodynamische Studien (Deutsche ÜbersetzungW. Ostwald), Engelmann, Leipzig, 1982.

[37] J. Mitrovic, On the equilibrium conditions of curved interfaces, Intnat. J. Heat Transfer 47 (2004) 809–818.

[38] J.D. van der Waals, The thermodynamic theory of capillarity unthe hypothesis of a continuous variation of density, J. Statist. Phy(1979) 197–224 (Translation by J.S. Rowlinson).

[39] J. Mitrovic, On the profile of the liquid wedge underneath a growvapour bubble and the reversal of the wall heat flux, Internat. J. HMass Transfer 45 (2002) 409–415.

[40] R.L. Webb, Principles of Enhanced Heat Transfer, Wiley–InterscieNew York, 1994.

[41] M. Jakob, W. Fritz, Versuche über den VerdampfungsvorgaForschungsarbeiten auf den Gebiet des Ingenieurwesens 2 (1931447.

[42] C. Corty, A.S. Foust, Surface variables in nucleate boiling, Chem.grg. Progress Sym. Ser. 51 (17) (1955) 1–12a.

[43] Y.Y. Hsu, On the size range of active nucleation cavities on a heasurface, ASME J. Heat Transfer C 84 (1962) 207–216.

[44] B. Yu, P. Cheng, A fractal model for nucleate pool boiling hetransfer, ASME J. Heat Transfer 124 (2002) 1117–1124.

[45] P. Griffith, J.D. Wallis, The role of surface conditions in nucleate bing, Chem. Engrg. Progress, Sym. Ser. 56 (30) (1960) 49–63.

[46] J. Mitrovic, Survival conditions of a vapour bubble in saturateduid flowing inside a micro-channel, Internat. J. Heat Mass Transfe(2001) 2177–2181.

–

[47] W.M. Rohsenow, Status of and problems in boiling and condensaheat transfer, Progr. Heat Mass Transfer 6 (1972) 1–44.

[48] J.R. Howell, R. Siegel, Activation, growth, and detachment of boilbubbles in water from artificial nucleation sites of know geometrysize, NASA TN-D 4101, 1967.

[49] H.B. Clark, P.S. Strenge, J.W. Westwater, Active sites for nuclboiling, Chem. Engrg. Progress Sym. Ser. 55 (29) (1959) 103–11

[50] C.-Y. Han, P. Griffith, The mechanism of heat transfer in nucleate pboiling, Internat. J. Heat Mass Transfer 8 (1956) 887–913.

[51] A. Singh, B.B. Mikic, W.M. Rohsenow, Active sites in boiling, ASMJ. Heat Transfer 99 (1976) 401–406.

[52] K. Bier, D. Gorenflo, M. Salem, Y. Tanes, Effect of pressure andface roughness on pool boiling of refrigerants, Internat. J. Refri(1979) 211–219.

[53] K. Cornwell, Naturally formed boiling site cavities, Lett. Heat MaTransfer 4 (1977) 63–72.

[54] Y. Fujita, The state of the art—nucleate boiling mechanism, in: Pand External Flow Boiling, ASME, Santa Barbara, 1992, pp. 83–9

[55] S.M. You, T.W. Simon, A. Bar-Cohen, A technique for enhancing bing heat transfer with application to cooling of electronic equipmeProceedings IEEE/ASME ITHERM 3 (1992) 66–73.

[56] A. Bar-Cohen, Hysteresis phenomena at the onset of nucleateing, in: Pool and External Flow Boiling, ASME, Santa Barbara, 19pp. 1–14.

[57] A.D. Messina, E.L. Park Jr, A new tool for nucleate boiling reseaChem. Engrg. Comm. 4 (1980) 69–76.

[58] J. Mitrovic, Wärmeübergang bei der Verdampfung von R11 an eebenen Heizfläche mit künstlichen Vertiefungen, GVC – VDI Sitzu“Wärme- und Stoffübertragung” Bad Dürkhein 28/29 April 1988.

[59] J.J. Wei, H. Honda, Effects of fin geometry on boiling heat tranfrom silicon chips with micro-pin-fins immersed in FC-72, InternatHeat Mass Transfer 46 (2003) 4059–4070.

[60] J. Mitrovic, F. Hartmann, A new microstructure for pool boiling, Sperlattices Microstruct. 35 (2004) 617–628.

[61] J.W. Westwater, Things we don’t know about boiling heat transferJ.A. Clark (Ed.), Theory and Fundamental Research in Heat TranPergamon Press, Oxford, 1963, pp. 61–73.

[62] B.B. Mandelbrot, How long is the coast of Britain? Statistical sesimilarity and fractal dimension, Science 155 (1967) 636–638.

[63] H.H. Uhlig, The solubility of gases and surface tension, J. PhChem. 41 (1937) 1215–1225.

how to create an efficient surface for nucleate boiling?

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