Paper No. 63-HT-3

J. H. UENHARD Associate Professor,

Deportment of Mechanical Engineering.

Assoc. Mem. ASME

P. T. Y. WONG Teaching Assistant, Deportment

of Mechanical Engineering.

Washington State University, Pullman, Wash.

Introduction T

The Dominant Unstable Wavelength and Minimum Heat Flux During Film Boiling on a Horizontal Cylinder

Predictions of tire dominant unstable 'WGl'etength and the minimum heat flux during film boiling abot'e a fia.t plate are found to be inapplicable in the case of boihng 011 small ·wires. Ne'/i) expressions are developed for the case of a horizontal cylinder, by ac[Ollnting for the eft'eet of surface tension in Ihe transverse direction upon the Taylor instabdity of fhe interface.

Original measurements of 'WGl'elengths and l1zinimum h.eal fluxes on small 'Wires are also prm>ided. These data support the predictions.

HE film boiling regime is eharaderized by the steady formation and release of bubbles at the liquid-over-vapor interface over a heating element. Zuber and Trihus [1,2]' proposed in 19,5R, that th is behavior result.ed from the Taylor inst.abili ty of the liquid-vapor interface. They argued that, as long as more vapor was being generated than was required to sllstain the nat,uralrute of growth of unstable disturhances, the disturbanees would collapse and release hubbi es periodieaJJy. It also foJJowed that the spacing between bubbles would be a c()n~lant value equal to the wavelength of the disturbance most susceptible to eollapse.

Earlier studies of plane unstable interfaees by Kelvin [:1 I, and by BeJJman a.nd Penningtoll [4], provided Zuber and 1'ribus wit·h expressions for the wavelength, An of the shortest unstable dist.urbance, acnd t.he wavelength, Ad, of the most, dangerous Ilnstable disturbance. Kelvin showed that aJJ disturbacnces with wavelengths less th~lI1 A" where:

(1)

would be st.able. BeJJman and Pennington showud that. distllrbaIwes would grow most rapidly when:

(2)

Tfle term IJ ill equations (l) and (2) designates the surfaGe ten

, Numbers in braekets designat.e l{ efcrcllcc~ at the end of paper. Contributed by the Heat Tran;;fer Divi,ion of THE ..b'ER1CA" So

C IETY OF' MECHANI C.\!. ENGINEEHS for prespntation at t.he AS:VIEArC hE Heat Transfer Conference and Exhibit. Bo~t.on,:\Ias!i., Augu;;t .11 - 14, 1963. :Vlallllseript. rece ived at A8ME Headquarters, Ylarch 12, 1963. Paper No. 63- .JlT-3.

sion between a liquid and its vapm; Pi and Po arc the liquid and vapor densities, respeet.ively;

Fig. I The assumed geometry of film boiling on a horizontal cylindrical heater

x

The Contribution of Surface Tension Considered as a Sinusoidally Varying Pressure Contri bution

Fig. 2 Two-dimensional model for film boiling on a horizontal cylindrlcol heater

length, X, should be equal to the cri t iea l or the lllost da ngerous wavelength will be deferred nntillater.

The eflec t of surface tension along the curvature in the transverse direetion is the sallle as an a.ddit.ioNa l component of pressure, P" acting t.o push the interface in toward the wire, where:

(J' p , = - -.- (4)

radIUS

t.his "pressurc" ranges between (J' I R in the va lleys and (J' I( N + 0.) at the peaks of the wave ; it has an average value of (J'/ ( R + ~) and an ampli t ude of (J'a.j2( R' + aR ). The amplitude can be approximated us (J'a /2 R' since R » ao, This pressure cont ributi on will act in phase with the collapsing wave and will serve t.o shorten the dominant wavelength.

A simplified two-dimensiona l analyt ical model will be estahlished to des(,ribe this three-dimensional physical model. Fig. 2 shows an equivalent t wo-dimensional wave in a liquid-overvap or interface. The cont.ribution of curvature in the t ransverse direction will be included in the form of an addi t ional pressure difference component, D.p" across the interface. This c.omponent will be numerically equul to t he oscillating component. of P"

The analy tical descript ion of this model is huil t upon t.he work of Rayleigh a nd Kelvin (us described by Lamb [3 [) as foll ows:

The interface is assumed to be disturbed by waves of the form:

.,., = a. eos kx cos wt (5)

which, when w is real, is t.o be construed as t he real part of :

.,., = ae - iwt cos kx (6)

where w is the angular frequency of t he wave and the wave number, k, is :

(7 )

The liquid and vapor are assumed t.o be incompressible and inviscid, and the perturbation is assumed to be 8Jllall in comparison wi th t he dep th of bot.h fluid byerR. Bern oulli's equation for the system is then:

The pressure difference ( Po - Pf), which balances the inertia. terms on the right-hand side of equation (il ) is composed of two parts:

(9)

where D.p" being in phase with the disturbance, is :

(J'D.p = - a cos k:c cos wt ( 10)

I 2R'

and l1R" the inverse radius of curva ture in the x -y pla ne, is:

1 0' .,.,>. = ~ = - ak' cos b; cos wt (11)J1 1 ux

Subst.itution of equations ( 10) and ( Il ) into equ ation (!)), a nd of the resul t into equation (8) gives:

(J' (12 )

2R'

or :

(J'i.: (1J )

The nature of w governs the stability of t he disturbance (as Taylor [61 has shown ). If w is real, the stabilizing effeet of surfa(:e tension in the axial directi on will smooth out the disturbanee. If w is imagi nary, the forces of gravity and surface tension in the transverse direction will domina te and t he disturbance will in(:reuse exponentia lly, in accordance wi th equation ( 6).

In t he present (:ase, w pusses from real to imaginary as the right-hand side of equati on (13) passes t.hrough zero. The eritieal wave number, "'e, is then obt.ained by equating the right-hnnd side to zero:

(14 )

and t he critieal wavelengt h :

The most dangerous wave number, kd' is " bt ained by maximi zing ( - iw ):

d(iW)] [ dk k ~ k"

o ( 16)

whence :

( 17)

and:

( 1~)

2R2

Equations ( 15) and ( 18) show t hat as R is decreased , surface tension in the transverse direction acts t o shorten the wavelength. The wav elengt h will, in fact, diminish in direct proptlrtion to the radius whell:

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Prediction of the Minimum Heat Flux A minimum heat. flux prediet.ion for t he present configurat ion

can now be formed with t he help of an energy balanee at the surface of t he heater :

qm i" [

latent heat] [bUbbles ] tTlt nsport per wave per hubble I oS l' ill atioli

[

minin;um. illllllber] [Wfl.ves per] of oSI·Il lat.lOns umt area per uni t ti me of heater

(19)

or :

where, wi t h aid of equation (6):

dr, (21)

ell

Equation (20 ) is a direct adaptation of Zuber 's '/min derivfltion. Three of his assumptions a re also being employed tentatively in t he case of " cylindrical heater. T hese assumptions are tested in t he subsequent sections of t his paper :

The dominant wa velellgt.h is Ad. 2 The depa rture rudius of a bubble is Ad/4. :1 Lewis' experiment al determin"tion of the range in which

t he wave grows exponent ially applies in t he present configumtion.

Substi tut.ion of equations (21 ), (1:3 ), and ( 18) into equation (20) yields the desired prediction for qmin:

v~ Pohjo [ZfJ PI - Po R PI + p,

a ]'h[ Y( P! - Po) 1 ]-'i' (22) + (PI + P )fl2 - a + 2WoExperimental Determination of the Dominant Wavelength and q,n i n

A program of experimental evaluat ions of A a nd qmin Oil slender horizontal wires has been made in order t o test the preceding predietions. itesis tan('e wires of N ichrome V (0.0025 ~ R in. ~ 0.0254) and Tungsten (0.001 ~ R in. ~ 0.002) were mounted ,. in It horizont.al pyrex tube at atmospheric pressure and used t o boil isopropanol and benzene of reagent grade. The apparat us, shown in F ig. 3, embodied the following features:

~~~I~:nser Variac crcJ Glass-metal seal

Cold Heater Wire . PowerU"\ Thermometer (Test Specimen) = Trans-

Py rex Tube II tarmer Nylon Fittingl r

H=~~~~~ A

Preheater Battery Motion- Picture 50V or Still Camera 20 A (In Fron t at Tube )

Fig. 3 Schematic representatlan af experimental apparatus

Journal of Heat Transfer

The t ubula r tes t section was provided wi t h a t hermometer to confirm that the liquid was sat.urated during runs, a nd was equipped with a llOV-3A, a-c resistance preheater. A Niehrome rectangle one in. wide was mounted ill the same perpendicular plane as the wire to facili tate measurement from photographs. The lighter wires used (0.001 ~ R in. ~ 0.010) were provided with battery-supplied direet current, while the heavier wi res (0.0159 ~ R in. ~ 0.0254) were, fo r eonvenience, supplied with a lternat.ing current. Si nce experimental results were similar for wi res of 0.007!J-in . mdius, upon which observati ons were made wit h both a -c and d-c power supplies, t he effec t of current alternat,ion in t he la rger wires was judged t.o be negligible.

Both still a nd motion pictures were made of t.he wave action. High-speed (2500 frames per sec ) motion pietures were made fo r benzene boilillg on a O.07g-in . radius wire a nd for isopropanol boiling on wires of 0.0254, 0.0079, and 0.0032 ill. radii. Most of t he visual da ta, however, were obt ained from a large 111llllber of still photographs. Both kinds of vislla l resul ts consisted strictly of elevation views of the wire durillg film boil illg at heat fluxes in excess of qmin.

The test wires were e1eaned wit.h soap and hot water, a nd were rillsed with both hot water and acet one, prior to their installation in t he t ube. During the experiment,a l runs care was exercised to keep t he wires from becoming red hot. T his precau t ion protected both t he wire surface and t he liquid from deterioration. The preheater was turned off immediately before observations for t wo reasons. The first was to clear the Held uf vision of bubbles . The second was to a void the effeet of an electric field ( reported by Bonjour et a!. Iii I in 1( 62 ) upon boiling. The field created by the p reheater in the present experiment.s was foul1d to inereftSe qmi. on t he smaller wires by a faetor of as much as fOllf.

Hent flu xes were computed direetly from measurement-s of voltage and amperage lind the dimensions of the wire. Wa velengt.hs were measured from still photographs or from projections of the 16 mm high-speed motiol1 picture film onto a microfi lm-reader screen. The probable error ill heat fluxes due to measurements was not over 3 percent in any instance. The probable error in measurements of the wavelengths ranged between 1 percent for the largest one to 20 percen t· for tbe sma llest.

·While t he experi mentH I errors were relatively low, somewhat larger errors of judgment iLrose in observing t he minimum heat fluxes and wavelengths. The observation of qm in was made difficult by heat conducti on into the eleetroeles which held t he wires. This caused fil m boiling to collapse at the ends at heat fluxes in excess of qmin-a difficulty whieh was over('.ome by watc hing for evidence of local eollapse n.way from the ends. The range of uncertainty of interpretation of this observation was about ± 20 percent on t he average!

The observation of the dominant wavelengt h was rela.tively st.raightforwa rd for wires for which R ~ 0.010 in. The bubble release patterns were genera lly good although both isolated deformi t ies, 3.nel drift in t he phase angle of oseillation along the length of the wires, acted to upset t.he uni formity of t he patterns. Fig. 4( a ) shows a typical uuiform release pattern , ILnd Fig. 4( b ) shows typical deformities. The uneertainty of in terpretation of wavelengt h observations in this range was usua lly about ± 20 percent.

In the ease of wires with radii for which 0.001 0 ~ R in. ~ 0.010, the phel1omenon of bubble merger entered to obscure t he wave pattern. Bubbles generated during the first half of a eyd e tarried on t.he wire long enough to come int.o cont act. with neighboring bubbles from the second ha lf of a cycle. A merger would occur between the two, which made ident ificati on of the 10('.3.1 wave pat tern impossible. A single instance of this beha vior is shown in F ig. 4(c) for It compa ra,t ively la rge wire. Fig. 4(e), on the other hand, shows a small diameter wire on which the wave ad·ion ran only be observed in u few isolated locati ons. The average

, The specific uncerta in t ies of each of the present data are displayed in the graphieal presentations of these data .

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0) GOOD BUBBLE DEPARTURE. BUB9LES VERY NEARLY IN PHASE WITI-! ONE ANOTHER. (R= 0 .0 254 IN . , q: 16,00 0 BTU/FTZ I-1 R, ISOPROPANOL)

.----- - ~.'---· ·0 D-C

Q9 Q Q Q g ,.nQ A 9 Q

'c) GO OD BU BBLE DEPART URE PATTE RN . WIT H ONE CLEAR CASE OF to4E RG ER.

(R-= 0.0079 IN . , q = 56 ,000 a TV/FT Z HR , BENZENE )

b ) TYP ICAL iMPERFECT WAv E PATT ERN. (R :0.C2!l 4 IN . ,

q = 16,000 BTU/H! HR, ISOPROPANOL)

d } RELAT IVE LY CON TI NUOUS PHASE SH IFT ALONG THE I.. ENGTH OF THE WIRE .

( R: 0 0079 rN ., q: 54 ,000 BTU/HZ HR, ISOPROPANCL!

e) EXT ENSIVE MERGI NG OF NEIGHBORING BUBBLES. DOMINANT wAVE LENGTHS ARE IDE NTIFIED IN TWO PLA CES.

( R =0 .00 32 IN. , . q = 118 ,50 0 BTU/n i: HR , ISOPR OPANOLl

f) WAVE BEHAVIOR COMPLETELY 0 8OCUREO 8 Y 8UBBLE ,..ERGINGS. {R= 0.0005 IN.,

q =450,000 BTUIFT2 HR, ISOPROPANOL I

Fig. 4 Various pallerns of bubble doparture from horizontal wires (black objet! below wire is I-in . reference scale)

Table 1 Measured dominant wavelengths and heat fluxes, for various wire siz.es and fluids

Liquid

heater radius

dominant wave length hes t flux

i n. in. Bt u/ft"hr

Isopropanol 0 .0010 0.02 1 144. 000 0.0015 0 . 029 61 . 000 0 . 0020 0 . 0 36 4 5 . 000 0 . 00 25 0 .048 52 . 000 0 . 00 32 0. 06 0 60 . 000 0 . 0050 0 .112 31.000 0 . 0063 0.126 36.000 0. 0079 0.155 17.200 0 .0100 0.200 14.300 0 .0159 0.288 12.000 0. 0201 0.341 16.70 0 0. 0254 0 .450 16.40 0

Benzene 0.001 5 0 . 0 33 112 .900 0 . 00 20 0 .048 5 0 . 000 0 . 0025 0 .066 45. 600 0 . 0040 '0 . 068 54. 000 0 . 0050 0 .1l8 19. 100 0 . 0079 0 .173 19 . 700 0.0100 0 .193 17 .400

uncert ainty of wavelength observations in this range rose t o ahout ± 40 pen·ent.

Xo wave action could be ident.ified on wires for whi(·h R < 0.001 in. Fig 4(f) illllstra.tes thi s.

Observed wavelengths for t.he mnge of radii , and for th e two liq uids, are presented in T :tble J . The hent flux es at whieh these observations were made are induded llS well. Since these heat flu xes are in eXC'eSll of qm ; .• , an additiona l set of measurements of q a nd A for given wires W HS made to ('onfirm the independence of A ll nd q. These da ta are given ill T ahle 2. Table:3 shows the minimulll hea t Hux as It fundion of mdiu8.

T\\'o addit.ional observa tions were made to ('heck the sec·ond and t.hird assumptiolls listed ai>ove equation (22). Bubble depa rtnre radii, R,,, were obtained from the photographs and the ra.tio A/ H,. was fOrlllPd (see Table 4 ). The observations of R

"

Table 2 Measured dominant wavelengths for various heat fluxes for isopropanol

heat er radius heat f l ux

d om i nant wav e length

i n . Btu/f t 2 hr i n.

C . 0025 47 . 500 0 . 052 52 . 000 0 . 048 66 . 000 0 . 048 7 6 . 500 0.046 82.000 0.04 9 89.500 0 .050

I 93, 60 0

103.000 0 .048 0 .04 9

131. 000 0 .051 171 . 000 0 . 050

0 . 0100 14. 300 0 . 200 15 . 500 0 .194 20 . 100 0 . 197

I 22.500 0. 209 26 .100 0 . 203 30 . 200 0 . 207 39. 800 0 . 209 50 . 000 0 . 218

-

Table 3 Measured minimum heat flux for various wire sizes for isopropanol

heat e r (Bt.u/ ft 2hr )qm i n radius (in. )

0 . 0025 21.500 0.0032 22 .500 0 . 0050 16 1 600 0.0063 15 . ; 00 0 . :))00 12 . 500 0 . 0159 8 . 200

6,6000 . 0254

Table 4 Measured bubble radii and the ratio of A/RI, for various wire siz.es for isopropanol

hea t e r radi us

bubble r adius A/Rb

na tur e o f wav e pat terr.

in. in .

0.0063 (0 . 040) 0 · 3) serious me rging 0 . 0079 (0.04 5) 0· 5 ) s ome merging 0.0100 0.0159 0 . 0201 0 .0254

0 . 055 0 . 0700 0.0900 0 .1000

3 .6 4. i 3 ·8 4 · 5

11.ttl e or no

merging

Table 5 Range of amplitude during which interfate grows exponentially

Liquid

hea t flux

Btu/ ft 2 hr

heater rad ius

in .

range of exponential growth, and uncerta in t y o f observa.t ion

Be nzene 56 . 000 0 . 0080 O .!> ?J.!> 0 · 53 . ( ~10%

Iso ;> ro pa.nol. 16 . 000 0 . 0254 o .!>?'J.!> 0 .36 ( 115%)

were quit.e reproducible, so the uncertainty of A/ Ri• is rough I.\' the same as t.hat of A. The range of exponential !\rowth of waves was ohtained frum measurements of a few waves in ea('h of two mo t.ioJ] pictures as well (see T able Ii ).

F or a much more detailed des(' ription of the present. experiments and of da ta. redu(·t ion t.eehniques. the reader can ('onsult reference 19 J.

Comparison of Theory WHh Experiment Figs. 5 and 6 displ a.y the observed waveleng ths for isopropanol

and benzene, respedively. Equations (15) and (18)- the theoretical predictions for A,. and A"-'[lre included in these presentat.ions. The data indica te t ha t the dominant. wavelength is genenllly only about 25 percen t higher t han t.he predieted Ad' Furtherm ore, no dominatlt w,\veleng th as sm all as A, was ob-

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1.00

c

-< .c c> c.. 0.10 b Measured Value of the-I .. Dominant Wave Length > I Range of Uncertainty

of measured value ~ "

f Predicted A. for a Harizontal Cylinder

t Ad for a Horizontal Cylinder 0.01

0.001 0.01 0 .1 0

Heater Radius, R (in.)

Fig. 5 The effect 01 heater radius upon the critical and most dangerous ' wavelengths for i.opropanol

I. 00 ~---'--'--T'""'"O--'-""""TT""--'---'---'-""T""r-r,.,.,--'"

Ad for a Flat Plate ~ --- - - Ac for 0 Flat Plate

r:::

-< .c '" c 0 .10.. oMea,ured Value of the-I .. Dominant Wave Lon Qth > I RanQo of Uncertainty

of m.asured valu,~ " Predicted Ac for a Harizontal

Cylinder

Ad for a Horizontal Cylinder 0.01 LL_-L_L-~~~LL__L--L~~~~~_~'

0.001 0.01 0.10

Heater Radius, R (in.)

Fig. 6 The effect of heater radiu. upon the critical and most dangerous wavelength, for benzene

served. This suggests that the first. assumpt.ion in the derivat.ion of equation (2:2) was corred, and that the present theory is successful. Fig. 7 is included to show that X can be evaluated

( at lilly reasonably low heat flux in excess oJ qmi". The figure shows t.hat there is no identifiable variat ion of X with q.

( Fig. 8 compares the present {f,nin data with predieted values given by equation (22). Equation (22) predicts that qmin will decrease in inverse proportion with H, as H becomes large, sinee the single row of bubbles will subtend au increasingly large area. Actually, when R becomes large, additional rows of bubbles will be accommodated 3 along the top and the present descript.ion will cease to apply.

While Zuber's flat. plate prediction does not represent t.he lilllit. to which equation (22) tends, nor docs it describe the physical circumsta.nces of boiling on a large cylinder, it. is nevertheless instructive to consider it in Fig. 8. It has therefore been included and with it, is shown Berenson's [Ill moditicnt.ion of Zuber's predict.ioll. The latter differs from equation (3) only in

t.hat the constant ;~ (j) '/.(or 0.1 i7) has been adjusted by semiempirical means to 0.09.' Berenson's predict.ion aecordingly

, Breen and Westwater [10] have observed that thi s two-dimensiona lity is pronounced in isopropanol boiling o n a cylinder of radius. R = 0.:3:36 in.

• Zuber himself [2] gave an alternate evaluation of the bubble release frequency which indieated that the constant should lie between 0.194 and 0.255.

Journal of Heat Transfer

-., 0.08 R=0.0025 in.c

-< 0.06 .c-

Ol 0.04 c CI)

-.J 0.02 CI)

> c 0.00 ~ a 4 8 12 16

Heat Flux, q(10·Btu/ft2 hr)

C Q3 R= 0.010 in.

-< .c 0.2 J f~ ~ ~ i ~ 01

~ 0.1 -.J ~ 0.0 L-____L-____L-____L-____L-____L-__--I

c02 3 4 5 6

~ Heat Flux, q(IO·Btu/ft'hr) Fig. 7 Measured dominant wavelengths versus heat flux for isopropanol

The Presenf Theory for Small Cylinders (Eqn.(22))

Zuber's Flat Plate ~

Theory (Eqn.(3))

:> "CD '0 10

" Present Data c

.. Data of LienhardE CT Iand Schrock

I Uncertainty of Berenson's Semi- Empirical Observation Modificofion of Zuber's

Flot Plate Theory 2 L--L-L~~~L___~__~~~~~____~~~~

a.002 0.01 0.10 0.50 Heater Radius, R (in.)

Fig. 8 The effect of heater radius upon qmin

fit. his experimental data quite closely. Equation (22) ( which is a Zuber-like prediction ) would also fit the present data closely if the rcult.iplying constant. were arbitrarily reduced from 7!" - V3 (or 0. 216) to!l. value of 0.057. 60

I t t hen rem ains to question the appropriateness of the second and third assumptions used in deriving equation (22). Table 4 shows tha t the use of Xj4 as the departure radius is entirely reasonable in the range for whicb these dttta can be obtainecl and Table 5 provides two approximate veritications of t.he assumed range of exponential growt.h.

Conclusions Equation (18) preclicts dominant wavelengths during film

boiling on a horizontal wire that are 25 percent. or less in excess of measured values. It reveals a hit.herto unreported decrease in w~welength with heat.er mdius, resulting from t he cont ribution of t.ransverse surface tension.

Zuber 's predict ion of the minimum heat flux on a flat plate is adapted to the present geometry and the assumpt.ions used in this derivation a re supported wi t h experiment.al data. The resulting predict ion is high by a eonstant factor, as was Zuber's flat plate prediction, although t.he form of bot h predictions is apparently correct.

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References N. Zuber and M. Trihus, "FUJ·ther Remarks on the Stabilitv

of Boiling Heat Transfer," UCLA Rept. No. 58-5, Univ. of Calif. ;t Los Angeles , J anuary, 1958.

2 N. Zuber, " Hydrodynamic Aspects of Boiling Heat Transfer, " Atomic Energy Commiss ion Report No. AECU-4439, Physics Rnd Mathematics, June, 1959.

3 H. Lamb," H ydrodynamics," 6th edition, Dover Publications, New York, N. Y., 1945, p. 455, et. seq.

4 H. Bellman and R . H . Pennington, "Effects of Surface T ension and Viscosity on Taylor Instability ," Quar. Appl. Math., vol. 12, 1954, p. 15!.

5 D. J. Lewis," The Instability of Liquid Surfaces When Accelerated in a Direction Perpendicular to Their Planes, II ," Proe. Roy. Soc. (London), Series A-202 , 1950, p. 81.

6 G. I. Taylor , " The Instability of Liquid Surfaces When Accelerat.ed in a Direction Perpendicular to Their Planes, I," Proc. Roy. Soc. (London), Series A-20 I, 1950, p. 192.

7 J. H. Lienhard and V. E. Schrock, "The Effect of Pressure, Geometry, and t he Equation of State Upon the Peak and Minimum Boiling Heat Flux," ASME Paper No. (J2- - HT-3, AIChE-ASME, 5th Nat'1. Heat Transfer Conference, Houston, T exas (August 5 to 8, 1962).

8 E. Bonjour, .1. Verdier, and L. Weil," Improvement of Heat Exchanges in Boiling Liquids Lnder the Influence of an Electric Field," AIChE Preprint 7, AIChE-AS},1E, 5th Nat'[ Heat Tra.nsfer Conference, Houston, Texas (August 5 to 8, 1962).

9 P . T . Y. Wong," Effects of H eate r Geometry Upon the LiqllidVapor Configuration in Film Boiling," Wash. State rniv., In~t . of Tech., Bull. No. 26i, Fehruary, 1963.

10 B. P. Breen and .1. W. Westwater, "Effect of Diameter of Horizontal Tubes on Film Boiling Heat Transfer ," Chem. Enol'. PTOg., vol. 58, no. 7, July 1962, p. 67.

11 P. J. Berenson , "Transition Boiling Heat Transfer From a Horizontal Surface," M.I.T., Heat Transfer Laboratory T echnical Rept. No. 17, 1960.

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