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Pergamon Heat Recovery Sys tems & CH P Vol. 15, No, 5, pp. 389-423, 1995Copyright 1995. ElsevierScience Ltd0890-4332(94)00055-7 Printed in G reat Britain. All rights reserved0890-4332/95 $9.50 + .00

R E V I E W P A P E RE L E C T R O H Y D R O D Y N A M I C E N H A N C E M E N T O F H E A T

T R A N S F E R A N D F L U I D F L O WP. H . G . ALLEN* and T. G. K A R A Y I A N N I S t ~

*Therm o-Flu ids Engineer ing Research Centre , Ci ty Universi ty , Lond on, EC IV O HB, UK ; andtSchool of Engineer ing Systems and Design, South Bank Un iversi ty , Lond on, SEI 0AA, U K( R e c e i v e d 1 J u l y 1994)

Ab st rac t - -T he e lec t rohydrodynamic (EHD ) enhan cement mechanism is fi rs t ou t l ined in th is paper . Acomprehensive review of past w ork on E H D single and two-phase heat transfer, as well as past work inthe related area of EHD-induced flow, is then presented. Correlation attempts are also reviewed. Recentexper imenta l resu lts for EH D boi l ing and condensa t ion in s ingle - and m ul t i - tube heat exchangers a rediscussed. A description of the possible practical EHD electrode systems for applications in powerproduction cycles and refrigeration is also presented. The research work needed to clarify outstandingquestions in EHD and encourage its use in practical systems is discussed.

N O T A T I O NABCA,CB, CcC,dDocEE lE l"f , , f~frbrdFDFEr:gGhii~gA i"JKLITN eNN uN u "A N uPeoP rQq

dimensionless gro up (see equ ation (33))d imensionless group (see equa t ion (50))empirical constantsspecific heat (J/kg K )vapour fi lm thickness (m)diameter (m) total differential operatorcharge diffusion coet~cient (mS/s)electric field strength (V/m)electric influence number (defined in equation (31))electric influence number (defined in equation (34))defined in equ ation s (47) and (49) (FV2/m2)frequency (Hz)buoyan cy force (N)dielectrophoretic force on bu bbles defined in equa tion (22) (N)body force compris ing second and th i rd te rm of equa t ion ( I ) (N/m 3)e lec t rohydrodynamic body force def ined in equ a t ion ( I ) (N/m 3)equiva lent EH D force (defined in equa tion (39)) (N/m 3)acceleration due to gravity (m/s2)d imensionless group (see equ a t ion (50))surface height (m)current (A)entha lpy o f evapora t ion (J /kg)therma l energy term (defined in equa tion (4 0)) (J/kg)current densi ty (A/m 2)dimensionless group (defined in equation (42))characteristic leng th (m)length (m)empirical exponentdimen sionless grou p (defined in equation (35))dimensionless group (defined in equation (52))Nusse l t number ( N u = a l l 2 )modified Nusselt number (defined in equation (37))change in N upressure (N/m 2)electric power input (W)Pra n d t l n u m b e r ( P r = ~ % / 2 )the rmal throughput (W)electric charge density (C/m ~)

++Author to w hom correspo ndence s hould be addressed.38 9

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390 P . H . G . ALLEN and T. G. KARAYIANN1SAQ4R . rfR a 'R eR e 'Re oRe'elTA TFVVRG r e e k l e t t e r sC (,f~NFt022 *

7 I0f i e"C4)S u p e r s c r i p t s

change in Q (W)thermal flux density (W/m ~-)radius (m)unit radial vectormodified Rayleigh number (defined in equation (38))Reynolds number ( R e = r / / v )dimensionless grou p (defined in equation (44))dimensionless group (defined in equation (53))dimensionless grou p (defined in equation (45))time (s)temperature (C)temperature difference, wall-saturated vapou r, wall-bulk fluid (K)fluid velocity (m/s)volume flowrate (m~/s)reactor power (kW)

heat transfer c oefficient (W/m 2K)corrected (cond ensation) heat transfer coefficient (W/m -'K)fluid coefficient of cubic expansion (I/K )fluid permittivity (F/m)thermal diffusivity (m-'/s)dynamic viscosity (Ns/m)contact angle (rad)thermal conductivity (W/InK)per turbation wavelength (m)ion mobility (m-'/Vs)kinematic viscosity (m2/s)dimensionless grou p (defined in equation (43))density (kg/m 3)surface tension (N/m)electrical conductivity (S/m)charge relaxation time (s)velocity (V)

mean, indicates vector quantityS u b s c r i p t sc corona, criticalD dielectrophoretic plus electrostrictiveE due to electric fieldg saturated vapou rgw vap our to solidi inner1 liquidlg liquid to vap ourIn logarithmic meanmax maximummin minimumo outer0 of free space (permittivity), at zero electric fieldw solid surfacewl solid to liquid

1. I N T R O D U C T I O NA c h i e v i n g h ig h e r h e a t t ra n s f e r r a te s t h r o u g h v a r i o u s e n h a n c e m e n t t e c h n i q u e s c a n r e s u lt i ns u b s t a n t ia l e n e r g y s a v in g s , d u e b o t h t o t h e in c r e a se d p e r f o r m a n c e o f e q u i p m e n t a n d t h e d e si g n o fs m a l l e r sy s t e m s t o m e e t r e q u i r e d l o a d s . A r e c e n t i n v e s t i g a t i o n i n t o h e a t t r a n s f e r e n h a n c e m e n ti n i t i a t e d b y t h e U K E n e r g y E f f ic i e nc y Of fi ce e n u m e r a t e d 2 0 d i f f e re n t e n h a n c e m e n t t e c h n i q u e s [1 ].

I n g e n e ra l , h e a t t r a n s fe r e n h a n c e m e n t m e t h o d s a r e c a te g o r i z e d a s " p a s s i v e " o r " a c t i v e " , s e eB e r g l e s [ 2, 3 ]. T h e f i rs t c a t e g o r y i n c l u d e s th e h i g h h e a t - t r e a t e d , r o u g h o r e x t e n d e d s u r f a c e s ,d i s p l a c e d e n h a n c e m e n t d e v i c e s, a d d i t i v e s , e t c. T h e u s e o f e x t e n d e d s u r f a c e s w a s t h e p r e f e r r e dt e c h n i q u e i n h e a t t r a n s f e r e n h a n c e m e n t i n t h e p a s t , b o t h i n s i n g le a n d i n t w o - p h a s e s y s t e m s . I nt w o - p h a s e a p p l i c a t i o n s , m a n u f a c t u r e r s h a v e r e c e n t l y i n t r o d u c e d h i g h h e a t f lu x s u r fa c e s . I n b o i l i n ga p p l i c a t i o n s m a n u f a c t u r i n g t e c h n i q u e s a r e e m p l o y e d t o (a ) d e f o r m t h e su r f a c e so as t o c r e a t e

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Electrohydrodynamic enhancement of heat transfer and fluid flow 391re-ent rant type cavi t ies or (b) to depo si t a matr ix o f metal l ic par t ic les on the sur face . Ei ther g ivesa po rous l aye r wh ich enhances bo i l ing by p rov id ing s i t e s ( t he po res ) f o r bub b le genera t ion . Berg les[2, 3] and Yilmaz e t a l . [4] prov ide exper ime ntal resul ts on the p er form ance of these h igh hea t f luxsur faces in boi l ing . In condensat ion appl icat ions, in addi t ion to low f in tubes, tubes wi th sharpsaw - too th - type f in s and t r apezo ida l - shaped ex tend ing f in s a r e examples o f enhanced tubesin t roduced mo re r ecen tly . The second ca t egory o f enhanced me thods inc ludes techn iques such assur face v ibrat ion , f lu id v ibrat ion , vapour suct ion and a .c . or d .c . e lect rosta t ic f ie lds .The e nha nce me nt o f s ingle pha se hea t t ransfer processes, especia l ly in gase ous systems, is an are awhere r e sea r che r s and des igners a r e spend ing a g r ea t dea l o f e f fo r t. The need to improve the hea tt r ans f e r r a t e s was made impera t ive by the eve r i nc r eas ing r equ i r emen t f o r sma l l e r , morecost -ef fect ive thermal systems. In single phase hea t transfer , the bo un da ry layers that fo rm on thethermal ly-act ive sur faces of fer a s igni f icant resis tance to the f low of heat which in gaseous systemscan dom ina te t he r e s is t ance o f f e red by the so lid wa ll s. Enhanc ing t echn iques a r e t he r e fo r e employedto a l t e r t he bo und ary l aye r s tr uc tu r e o f the f low and , i n l aminar o r f r ee convec t ive s it ua t ions , t oincrease the f low veloci ty .

The phase change tha t occu r s du r ing a bo i l i ng and a condensa t ion p rocess i s genera l ly a ve rye f fec t ive mo de o f hea t t r ans f e r . H owe ver , t he re i s fu r the r need to d eve lop me thod s o f enhanc ingthe hea t t r ans f e r r a t e s i n bo th evapora to r s and condense r s . A r e f r ige r a t ion /hea t pump sys t emusua l ly ope ra t es wi th hea t s ink and hea t sou rce a t p r ede te rmined o r no t con t ro l l ab l e ( e .g .a tmospher i c ) t empera tu r es . The work ing f lu id ope ra t ing t empera tu r e mus t be s ign i f i can t ly l owerthan the sou rce and h igher t han the s ink in o rde r f o r t he evapora to r and the condense r t o be o fr easonab le , economic s i ze . I n a r e f r ige r a t ion /hea t pump sys t em these t empera tu r e d i f f e r ences ,which con st i tu te externa l therma l i r reversib il i ty , reduce the coef f ic ient of per form anc e (C OP ) of ther e f r ige r a to r o r hea t p ump . S imi la r a rgumen t s ho ld fo r t he powe r p roduc in g cyc les where theef f ic iency of the cycle i s reduced, as the greatest possib le temperature d i f ference i s reduced by theexternal thermal i r reversib i l i ty ment ioned above.

The benef ic ia l resul t of heat t ransfer enhan cem ent , i .e . the increase in the heat t ransfer coef f ic ient ,wou ld be :

(a) the re duc t ion in the s ize of the hea t exchan gers for g iven ra tings.(b ) t he r educ t ion in t he t empera tu r e d i f f e r ence be tween the f lu ids exchang ing hea t and thusgreater the rmal p lant ef f ic iency. (Al ternat ively , the t ransfer of greater ra tes o f energy thro ugh ag iven s i ze o f hea t exchanger wh i l e ma in t a in ing modera t e t empera tu r e d i f f e r ences . )

Reduc ing the t empera tu r e d i f f e r en t i a l s a t evapora to r and condense r becomes pa r t i cu l a r lyimpo r t an t i n t he more r ecen t deve lopm en t o f pow er p rodu c t ion us ing ocean the rmal ene rgyconver s ion (OTEC) p l an t s , geo the rmal ene rgy p l an t s , so l a r pond genera t ion p l an t s and s imi l a rp l an t s u t i li z ing the o rgan ic R ank ine cyc le (ORC ) . I n t hese p l an t s t he ava i l ab l e t empera tu r edi f ference (between source and sink) i s a l ready smal l , e .g . in OTEC plants th is i s the d i f ferencebe tween the t emp era tu r e o f su rf ace (20 -30C) and deep sea wa te r ( 4 -7C) . P l an t s ope ra t ingbetween such smal l temperature d i f ferences must be s igni f icant ly larger than high temperatureplants (nuclear or fossi l fuel p lants) in order to produce s imi lar outputs . In addi t ion , thei rpe r fo rmance i s more sens i t i ve to t he t empera tu r e d i f f e r en t i a l a t t he evapora to r - sou rce and thecondense r - s ink . A ce r ta in deg ree o f superhea t m us t be exceeded in t he evap ora to r f o r nuc lea tebo i l ing to comm ence . S uch p l an t s may , t he r e fo r e , f ace add i t i ona l " s t a r t - up " p rob lem s i f t h is deg reeo f superhea t i s no t ava i lab l e . Th i s p l aces an add i t i ona l l im i t a t ion on the max im um poss ib l eoperat ing f lu id temperature d i f ference and thus reduces the p lant ef f ic iency.

The enhanc ing e f fec t o f a s t r ong e l ec t ri c fi eld on hea t t r ans f e r r a t e s ( e l e c t rohy drod yna mic - -E H D - - e n h a n c e m e n t ) h a s b e e n k n o w n f o r o v e r 7 0 y r. E a r ly w o r k c o n c e n t r a te d o n t h e e n h an c e -men t o f s ing le -phase convec t ive hea t t r ansf e r . I n t he l a s t 30 y r t he g r ea t e r po ten t i a l o f EH D inenhanc ing two-pha se hea t t r ans f e r r a te s has been r ea li zed by more indus t r ia l a nd acad emicresearchers . This h ad led to the s tudy o f coup led e lect r ic field and p ool bo i l ing in the nucleate ,t ransi t ional and f ilm boi l ing regimes. The ef fect of the e lect ric field on the p eak nucleate an d themin imum f ilm bo il i ng cond i t i ons has r ece ived pa r t i cu l a r a t t en t ion . Whi l e work on E H D bo i l ingproceeded s t ead i ly , r e l a t i ve ly l i t t l e was pub l i shed on EHD condensa t ion un t i l t he l a s t decade ,poss ib ly due to t he g r ea t e r p r ac t i ca l po ten t i a l o f f e r ed by EHD bo i l i ng . The p r esen t paper r ev i ews

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392 P .H .G . ALLENand T. G. KARAYIANNISt h e p u b l i s h e d w o r k o n E H D e n h a n c e d s i n g l e - a n d t w o - p h a s e h e a t t r a n s f e r a n d p r e s e n t s t h e r e s u l t so f r ec e n t w o r k o n b o t h . A r e v i ew o f th e p a s t r e s ea r c h o n E H D - i n d u c e d f l o w - p u m p i n g i s a l s o g i v e nf o r c o m p l e t e n e ss .

2. E H D E N H A N C E M E N T M E C H A N I S MThe p hys i c a l ba s i s o f muc h e l e c t r i c a l ly -e nha nc e d he a t t r a ns fe r l ie s i n the E H D fo rc e , F E pe r un i t

vo l um e , ge n e ra t e d by a n e l e ct r ic f i e ld , s t r e ng t h E , i n a f l u i d o f d i e le c t r ic pe rm i t t i v i t y E , de ns i t y Q ,a t t e mpe ra t u re T . Th i s c a n be e xpre s se d a s [5 ]

w he r e q is t he e l e c tr i c c ha rge de ns i t y i n the f l u id ; q /7 , i ts e l e c t rophore t i c c om pon e n t , i s t he C ou l om bforc e e xe r t e d by a n e l e c t r i c f i e l d upon t he f r e e c ha rge i n i t . The t h i rd t e rm c ompr i s e s t hed i e l e c t roph ore t i c a nd e l e c t ros t r i c t i ve fo rc e s on a nd w i t h i n t he f l u id [6 ] , due t o t he na t u re o f a ndE a nd t he i r spa t i a l d i s t r i bu t i on .

E q u a t i o n ( 1) sh o u l d t h e n b e i n c l u d ed i n th e N a v i e r - S t o k e s e q u a t i o n w h i c h , f o r a n i n c o m p r e s s i b l efluid, is

D dp ~ = pC + ~ v _ W ' + # V 2f , (2 )w h e r e D f / D t de no t e s t he subs t a n t i ve a c c e l e ra t i on c ons i s t i ng o f t he loc a l c on t r i bu t i o n ~ # / ~ t a n dt he c onve c t i ve c on t r i bu t i on ( , ? 'V ) f , The ve c t o r pg i s t he g ra v i t a t i ona l fo rc e pe r un i t vo l ume ; P i st he l oc a l f l u i d p re s su re . The t e rm pV 2f re p re se n t s t he v i s c ous t e rms .

F o r a n i n c o m p r e s s i b l e f l ui d , t h e c o n t i n u i ty e q u a t i o n i sV. f = 0 (3)

a nd t he e ne rgy e qua t i on , ne g l e c t ing v i s c ou s d i s s i pa t i on e f fe c ts , i s8 T a ~E 2 (4 )8-7 + e . V T = xV 2T + pC---~

(The l a s t t e rm i n e qua t i on (4 ) i s t he ohmi c d i s s i pa t i on , w h i c h i s u sua l l y ne g l e c t e d . )F o r a n ohm i c d i e l e c t ri c , t he e l e c t ros t a t i c e qua t i o ns [7, 8 ] a re

V ' E E = qV x E = 0

a nd J t he c u r re n t de ns i t y i s

(5 )(6 )

c3qV . o r + ~ - = 0 ( 7 /

o = q f + a / 7+ ( f . V ) (E/7 ) - D ~ V q . (8)E q u a t i o n s ( 2 - 8 ) w i l l t h e n f o r m u l a t e e l e c t r o c o n v e c t i v e p r o b l e m s .

In s i ng l e -pha se c onve c t i ve he a t t r a ns fe r , t he rma l g ra d i e n t s i n t he f l u i d p roduc e non-un i fo rmi t i e si n t he e l e c tr i c a l c ondu c t i v i t y ( a ) a nd t he d i e l e c tr i c pe rm i t t i v i t y (E) . I f t he re i s a c ha nge o f a ~ a ndE i n t he f l u id t he n f re e c ha rge c a n bu i l d up , w h i c h c a n be a c t e d up on by t he e l e c t r ic f i el de l e c t r o p h o r e t i c c o m p o n e n t o f E H D f o r ce . T h e d e p e n d e n c e o f t h e fr e e c h a r g e g e n e r a t i o n o n t h ee l e c t r i c a l c onduc t i v i t y a nd pe rmi t t i v i t y i s g i ve n a s fo l l ow s .

N e g l e c t i n g t h e m o v e m e n t o f q, e q u a t i o n ( 8 ) b e c o m e sJ = a~/7, (9)w h i l e i n t he s t e a dy s t a t e e qua t i on (7 ) be c ome s

v . J = 0 . ( 1 0 )

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Electrohydrodynarnicenhancement of heat transfer and fluid flow 393T h e n

v . J = v . ( . o g ) = g .v ,7 ~ + , 7 o r- E .w hich , fo r equa t ion (10 ) , g ives

w h i l e , f r o m e q u a t i o n ( 5 ) ,

D iv id ing equa t ion (13 ) by (12 )

R e a r r a n g i n g e q u a t i o n ( 1 4 ) g i v e s

(Yabe [9] g ives

,~ V " E = - / 7 . V a e ,

E V . E = q - E . V E .

E q - E . V E

q = R . V E - E g . V a o .O"

Eq = - - - ~ - ' V t T e ,o"w h i c h n e g l e c t s th e v a r i a t i o n o f t h e p e r m i t t i v i t y . )

A s s u m i n g t h a t e a n d a ~ a r e f u n c t i o n s o f t e m p e r a t u r e o n l y , e q u a t i o n ( 15 ) g iv e s~V . V T & E - d a e

= d r - e . v r ~O"

( l l )

(12)

(13)

(14)

(15)

(16)

(17)in a the rmal f i e ld .

I n t h e c a s e o f a . c . f ie l ds o f f r e q u e n c y f , t h e m a g n i t u d e o f t h e f lu i d c h a r g e r e l a x a t i o n t i m e z , w h e r e= E / tr e, de te rm ines w h e the r f r ee e l ec t r ic cha rge c an b u i ld up in the f lu id , w h ic h can th en be ac te du p o n b y t h e e l e c tr i c f ie l d. I n c o n v e c t i v e f l ow s w i t h f r e e c h a r g e p r e s e n t , t h e E H D e f fe c t b e c o m e s

i m p o r t a n t w h e n z is o f th e s a m e o r d e r a s , o r l es s t h a n , t h e t i m e n e e d e d f o r t h e f l u i d t o t r a v e r s ethe e lectr ic f ie ld [10] .

I f th e r e i s a s p a t i a l c h a n g e o f E t h e n t h e s e c o n d t e r m o f e q u a t i o n ( l ) b e c o m e s i m p o r t a n t . T h ed i r e c t i o n o f t h i s c o m p o n e n t d e p e n d s o n t h e d i r e c t i o n o f i nc r e a s e o f E. T h i s t e r m c a n b e e x p a n d e das fo l low s :

- E : V E = - 1 e T ~ + V p . ( 1 8 )TF o r n o n - p o l a r f l u id s t h e f ir s t t e r m i n t h e b r a c k e t s i s z e r o a n d t h e e q u a t i o n a b o v e r e d u c e s t o

1 E 2 V E = 1 2 E 2 F ( 0 EL ~ 0 p ) T VP 1, (19)w h i c h i n d i c a t e s t h a t t h e r e s u l t a n t c o m p o n e n t f o r c e i s t o w a r d s t h e h e a t e d s u r f a c e . T h e s a m e c a nb e s a i d in t h e c a s e o f p o l a r l i q u id s , a l t h o u g h t h e r e s u l t i n g e q u a t i o n i s m o r e c o m p l i c a t e d . F o rn o n - p o l a r f l u i d s t h e C l a u s i u s - M o s s o t t i r e l a ti o n s h i p :

I - O ~ ] ( E - E0)(E--2E0)p = (20)T 3 'c a n b e u s e d t o s i m p l i f y t h e t h i r d t e r m o f e q u a t i o n ( 1) t o

V [ E 2 [ ~ p ] T p ] = V [ E : ( E -o ) ( ; - 2 E o ) .] ( 2 1 )(s ee Y a b e [ 9 ]) . ( A s i m i l a r e q u a t i o n c a n b e d e r i v e d f o r p o l a r f l u i d s. ) T h i s t e r m o f t h e E H D f o r c ei s a g r a d i e n t a n d t h u s c a n n o t c a u s e a n y v o r t i c i t y i n t h e f lu i d a n d w a s u s u a l l y n e g le c t e d , p o ss i b ly

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394 P .H .G . ALLENand T. G. KARAYIANNISf o r t h i s r e a s o n . I t h a s , h o w e v e r , a s i g n i fi c a n t e f fe c t a t t h e i n t e r f a c e a n d i n t w o - p h a s e h e a t t r a n s f e r[9].I n t w o p h a s e h e a t t r a n s f e r , n a m e l y b o i l i n g a n d c o n d e n s a t i o n , E H D e n h a n c e m e n t c a n b ea t t r i b u t e d t o t h e f o l l o w i n g f a c t o rs w h i c h c a n a c t i n d i v i d u a l l y o r in c o m b i n a t i o n :(a) A c t i o n a t l i q u i d / v a p o u r i n t e r f a c e

T h e E H D f o r c e a c t s to d e s t a b i li z e t h e la y e r o f c o n d e n s a t e o r v a p o u r f o r m i n g d u r i n gc o n d e n s a t i o n a n d p e a k n u c l e a t e a n d f il m b o i l in g , r e s p e c t iv e l y [7 , 1 1, 1 2 ]. F i l m c o n d e n s a t i o n c a nr e v e r s e t o p s e u d o d r o p w i s e c o n d e n s a t i o n a n d f i l m b o i l i n g t o n u c l e a t e b o i l i n g . I n g e n e r a l , t h ed e s t a b i l i z a t i o n c a u s e d b y t h e e l e c t ri c f ie ld r e su l t s i n t h e r e d u c t i o n o f t h e t h e r m a l r e s is t a n c e a t t h eh e a t t r a n s f e r s u r f a c e .(b ) A c t i o n o n v a p o u r b u b b l e s

P o h l [ 6 ] s u g g e s t e d t h a t t h e d i e l e c t r o p h o r e t i c f o r c e c a n a c t o n a n i n s u l a t i n g s p h e r e o f r a d i u s Ra n d p e r m i t t i v i t y c2 i n a s u r r o u n d i n g m e d i u m o f p e r m i t t i v i t y E, p r o d u c i n g a f o r c e F g i v e n b y

F d = 2~ R 3q [(E2 - q ) /(E 2 + 2E , ) ]V E 2 . (22)I f q < E~, wh ich i s th e ca se o f a v ap o u r b u b b le i n a l i q u id , i .e . i n b o i l i n g , t h e b u b b le i s a t t r ac t edto r eg io n s o f l o wer e l ec t r ic f ie ld s t r en g th . ( I f E > E, t h e sp h e r e i s a t t r ac t ed to r eg io n s o f h ig h e re l e ct r ic f ie l d s t r e n g t h . ) A c o m m o n g e o m e t r y s t u d i e d i s o n e o f a c o a x i a l c y l i n d r ic a l e l e c t r o d e s y s t e m .T h e h e a t t r a n s f e r s u r f a c e is a n i n n e r c y l i n d e r a t r a d i u s r j a n d a t e a r t h p o t e n t i a l ( ~ , = 0 ), s e e F i g . 1 .T h e o u t e r c y l i n d e r , ra d i u s r 2 , is a t h i g h v o l t a g e 4 2 . A s s u m i n g t h a t s u c h a s y s t e m i s t w o - d i m e n s i o n a l ,i . e . a l o n g cy l in d r i ca l sy s t em , t h e e l ec t r i c f i e ld E , a t an y r ad iu s r , i s g iv en b y

~2E = - - ?, (23)r ln ( r2~\ r , /

w h e r e f i s t h e u n i t r a d i a l v e c t o r ( p o s i t i v e a w a y f r o m t h e a x i s ) a n d

r . ' - - r , l l n ( 5 1 . ( 2 4 )L \ r , / J

T h e n2

L \ r , / lT h e r e f o r e , t h e fo r c e o n t h e sp h e r e ( o r a b u b b l e a s s u m e d t o r e m a i n s p h e r i c a l) i s

/ / / iL \ r , / jI n e x p e r i m e n t s w i t h r e f r ig e r a n t s t h e r e s u l ti n g e l e c t r o d y n a m i c f o r c e o n t h e b u b b l e s c o u l d b ec o m p a r a b l e o r s i g n i f ic a n t l y h i g h e r t h a n t h e g r a v i t a t i o n a l f o rc e . I n t h e e x p e r im e n t s o f K a r a y i a n n i s

Electrode a t h ighv o l ta g e (# 2 )E a r th e d h e a t e d . , . . . . . . - .

tu b e [ I z = o ) , ~ C "~ ~ ' ~ * ' ~ r ~ '., Vapourbubble

. . . 7 u 0u ,0" - . . . . . - -

Fig. I. He ated tube concentric with a cylindrical electrode.

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E l e c t r o h y d r o d y n a m i c e n h a n c e m e n t o f h e a t t r a n s f e r a n d f l ui d f l o w 3 95

et a l . [13 ] w i th R 114 , t he ou t e r cy l inde r had a d i ame te r o f 38 mm and the i nne r, ea r thed hea tt rans fe r cy l inde r 19 .1 mm . Fo r 20 kV app l i ed a t t he ou t e r cy l inde r and d i e l ec tr i c cons t an t s o f l iqu idand vap our re f r ige ran t o f 2 .17 and 1 .0 re spec tive ly , t he re su lt i ng magn i tude o f t he e l ec t rodynamicfo rce on a bubb le l oca t ed a t t he hea t t rans fe r su r face i s

F d = 5.13 104R3.The buoyancy fo rce i s g iven as

F b = 4 7 z R 3 ( p , _ P 2 ) . ( 2 7 )Fo r a l iqu id and vap our dens i ty o f 1441 and 7 .74 kg /m 3 re spec tive ly , t he fo rce m agn i tude i s

F b = 5.89 x 1 0 4 R 3 ,which i s comparab le t o t he EHD fo rce . In hea t t rans fe r f rom smal l e r d i amete r cy l inde rs (o r i n t heex t reme , f rom wi res ) t he E H D fo rce can p redom ina t e , s i nce i t i s p ropo r t i ona l t o 1/r 3 .In t he exper im en t s o f Winer [14 ], aga in wi th R114 , t he ra t i o r2/r~ was 50.8 x 10-3/5.5 X 1 0 - 3 .Fo r 20 kV the re su lt i ng d i e l ec t rophore t i c fo rce on the bub b le i s

F d = 19.7 x 1 0 4 R 3 ;t h is i s app ro x ima te ly 3 .3 times h igher t han the buo yan cy fo rce .

The acce l e ra t i on o f t he bubb le can cause ag i t a ti on o f t he ne ighbour ing b oun dary l aye r li qu idand thus imp rove the hea t t rans fe r ra t e s . How ever , t he hea t t rans fe r ra te s can be g rea t ly enhancedi f t he bubb les a re made to adhere a nd mo ve a long the hea t t rans fe r su r face . In cases where t hetube ou ter su rface i s m ade of f ins ( low fin tubes) , the local varia t io n of the e lectr ic field and thusthe l oca l d i e l ec t rophore t i c fo rce can be d i f fe ren t bo th i n mag n i tude a nd d i rec t ion than the fo rceon a sm oo th su r face. In t he case o f a l ow f in t ube , t he f i eld is p rog ressive ly weak er f rom the t i pto t he ro o t o f the f in . The d i e l ec t rophore t i c fo rce can then mov e the genera t ed bub b les t o t hespac ing be tween the f in s. Co lum ns o f vapo ur can subse quen t ly fo rm which g row un t il t he buoya ncyf o r c e s o v e r c o m e t h e E H D f o r c e [ 1 5 ] .

I f the cha rge re l axa t ion t ime i s fa r g rea t e r t han the bu bb le de t achm en t pe r iod , t he bu bb les a renot affected by the e lect r ic f ie ld [16]. Differences in the charge re laxat ion t ime of R123 and R11(0 .89 x l 0 -3 and 1 .3 s [16 ]) re spec tive ly cou ld acco un t , a mo ng o the rs , fo r t he h ighe r e nhancem en tra t i o ob t a ined fo r R123 in t he exper imen t s o f Ohad i et a l . [17]. I t i s there fore e vident that the charg ere l axa t ion t ime o f f l uids can be a ve ry imp or t an t pa ram ete r b o th i n s ing le and two-p hase hea tt rans fe r enhancemen t .(c ) C h a n g e i n c o n ta c t a n g l e a n d s u r f a c e t e n s i o n

In t he case o f nuc l ea te bo i l ing , R ohs eno w [18 ] has show n tha t t he deg ree o f superhea t neededfo r bubb le g rowth a t a g iven bubb le s i ze depends d i rec t l y on the su r face t ens ion o f t hel iqu id -vapour i n t e r face . A l so , t he con tac t ang le , 0 , i s re l a t ed t o t he su r face t ens ion by

COS 0 = O'wl -- O'gw- - , (28)~Ttgwh ere trw~, a~w and t rig are , respect ively , the su rface tensions a t so l id-l iquid , va po ur- so l id andl iqu id -vap our i n t e rfaces [19 ]. Bo th 0 and su r face t ens ion have been obs e rved to v a ry wi th e l ec t r icf ie ld s t reng th [12, 20] and th is woul d expla in the in i t ia t ion of ebul l i t ion by an e lect r ic field a t red ucedsuperhea t .

3. S I N G L E P H A S E H E A T T R A N S F E RThe th ree ma jo r ways in wh ich E H D can enhance s ing le phase convec t ive hea t t rans fe r a re :(a ) by f l ow o f " co rona (o r e l ec t r i c ) w ind" ,(b ) by e l ec t rophores is , w i th o r w i tho u t cha rge i n jec t ion ,(c) by d ie lect r ic phoret ic forces ,

bu t (d ) EH D-in duc ed f l ow can be used to impro ve no rm al convec t ive e ffec ts .

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396 P .H .G . ALLENand T. G. KARAYIANNIS(a ) C o r o n a w i n d

A c c o u n t s o f t h i s h a v e v a r i e d f r o m n o t e s i n te c h n i c a l j o u r n a l s , s u c h a s " d e v e l o p m e n t s t o w a t c h :a no i s e le s s f an , w i th n o m ov in g pa r t s " [21 ] to a fu l l -s ca le des ign s tud y fo r i ts app l i ca t ion to a pow ers ta t ion d ry coo l ing s ys tem [22 ] .

G e n e r a l l y , a n a r r a y o f s h a r p p o i n t s o r f i n e w i r e s a t h i g h p o t e n t i a l f a c e s t h e s u r f a c e t o b e c o o l e d ,a t e a r t h p o t e n t i a l . T a b l e 1 l is ts d e s c r ip t i o n s o f a r r a n g e m e n t s f o r w h i c h n u m e r i c a l v a l u e s o f h e a tt r a n s f e r e n h a n c e m e n t a r e g i v e n a n d / o r a p r a c t i c a l a p p l i c a t i o n s p e c i f i e d a l l o w i n g f o r t h e f a c t t h a ti t is n o t a l w a y s e a s y to d i s t i n g u i s h b e t w e e n c o r o n a w i n d i n t u b u l a r s y s t e m s a n d s i m i l a r g e o m e t r i e su t i l i z ing e l ec t rophores i s w i th cha rge in jec t ion .

C o m p a r e d w i t h o t h e r E H D e n h a n c e m e n t p h e n o m e n a , c o r o n a w i n d h a s r el a ti v el y l a rg e e n e rg yc o n s u m p t i o n . F o r e x a m p l e , H o l m e s a n d B a s h a m [ 22 ] s h o w o p t i m u m p e r f o r m a n c e f o r a 2 5 b y2 5 m m n e e d l e a r r a y a t 5 1 m m f r o m t h e h e a t t ra n s f e r s u r fa c e w h e n c o r o n a p o w e r i n p u t i s 3 0 % o ft h e r m a l t h r o u g h p u t . F i g u r e 2 , f r o m M o s s a n d G r e y [ 2 4 ] , s h o w s h o w a n i n c r e a se i n t h e l a tt e r isr e l a t e d t o t h e f o r m e r . T h e " u n i t g r a d i e n t " l i n e s i n d i c a t e " b r e a k e v e n " t o w h i c h t h e e f f ec t t e n d sw i t h i n c r e a s i n g R e y n o l d s n u m b e r , R e .(b ) E l e c t r o p h o r e s i s

E l e c t r o p h o r e s i s w o u l d a p p e a r t o g i v e t h e b e s t r e s u l ts b u t i t s e ff e c t d e p e n d s c r i ti c a l ly u p o n t h ep u r i t y o r o t h e r w i s e o f th e h e a t t r a n s f e r f l u i d , o n w h e t h e r i t i s p o l a r o r n o n - p o l a r a n d u p o n w h e t h e ro r n o t c h a r g e i s i n j ec t e d in t o i t . T a b l e 2 s u m m a r i z e s e x p e r i m e n t a l w o r k , m o s t o f i t o n a n n u l a ra r r a n g e m e n t s , f r o m f in e w i r e s t o n a r r o w d u c t s , s o m e w i t h , a n d s o m e w i t h o u t , d e l i b e r a t e c h a r g ei n j e c ti o n . R e l a t i v e l y l a rg e v a l u e s o f q E " i n e q u a t i o n ( 1) c a n b e a t t a i n e d w i t h m o d e s t e n e r g ye x p e n d i t u r e . A n i o n i z a t i o n c u r r e n t i ( A ) f r o m a s o u r c e i n a v o l u m e f l o w ra t e V ( m 3/s ) g iv e s

iq = ~ (C /m 3) (29)a n d e l e c t r o p h o r e t i c f o r c e

EiqE = --~ (N/m 3); (30)th i s can g ive r i s e to r e l a t ive ly l a rge fo r ces fo r l i t t l e cu r r en t cons umpt ion . F o r example , a gas f lowof 670 10 -6 m3 /s ove r an ion iz ing e l ec t rode f ed w i th 50 /~ A g ives a ch a rge dens i ty o f 0 .075 C /m 3w h i c h , a c t e d o n b y a n e l e c tr i c f ie l d o f s t r e n g t h 1 M V / m c a u s e s a f o r c e o f 7 5 k N / m 3 w h i c h i s a t l e a s tc o m p a r a b l e w i t h t h e p r e s s u re g r a d i e n t c a u s i n g f l o w ( w h i c h d e p e n d s o n t h e n a t u r e o f th e d u c tc r o s s- s e ct i o n ). T h e g e n e r a t i o n o f e l e c tr i c c h a rg e , w h i c h o c c u r s w h e n t h e e l e c t ri c a l c o n d u c t i v i t ya n d / o r p e r m i t t i v i t y h a v e a s p a t i a l d i s t r i b u t i o n , i s d e s c r i b e d b y e q u a t i o n ( 15 ).

S p e c ia l m e n t i o n s h o u l d b e m a d e o f t w o R u s s i a n c o n t r i b u t i o n s o f t h e m i d- 1 9 6 0s , b y B a b o i e t a l .[59 ] and S emenov e t a l . [ 6 0] w h i c h p r o v i d e a l i n k b e t w e e n e l e c t r o p h o r e t i c a n d d i e l e c t r o p h o r e t i ce f f ec ts a s w e l l a s , in r e f . [59 ] , w i th co ron a w ind an d b e tw e en s ing le - and tw o-ph as e h ea t t r an s f e re f f e c t s . T h e y r e v i e w e d e a r l i e r w o r k a n d r e p o r t e d t h e i r o w n n a t u r a l c o n v e c t i o n e x p e r i m e n t s w i t ha i r (7 0 # m d i a . w i r e a l o n g a x is o f 1 7 m m d i a . t u b e ) a n d w i t h t r a n s f o r m e r a n d c a s t o r o i l s (7 0 / ~ mdia . w i r e 10 m m be low a nd pa ra l l e l t o 4 mm d ia . cy l ind r i ca l e lec t rode ) . I n thes e , w i th a i r , a . c . s t re s sg a v e ~ E/0 t0 i n c r e a s in g w i t h E t o a m a x i m u m ( 3.2 w i t h w i r e t e m p e r a t u r e 5 2 C a t 3 .5 M V / m ) t h e nd e c r e a s e d , e v e n c a u s i n g i n h i b i t io n , t h e m a x i m a i n c r e a s i n g a n d s h i f ti n g to h i g h e r E w i t h i n c r e a s in gt e m p e r a t u r e . B y c o n t r a s t , t h e o i ls g a v e u n e q u i v o c a l i m p r o v e m e n t b u t , w h e r e a s trE/tr o f o r c a s t o r o i li n c r e a s e d c o n t i n u o u s l y w i t h w i r e te m p e r a t u r e , f o r t r a n s f o r m e r o i l i t p e a k e d a n d , b e t w e e n 2 08 a n d375C , dec reas ed f rom 5 .8 to 1 .9 a t E = 39 M V /m . B e low 98C , the cu rves a r e concave up w a rds ,w hereas w i th d .c . s t r e s s they t end to s a tu r a te , i n t e r s ec t ing a t ~ E/0 t0 = 3 .4 and E = 28 .5 M V / m ,c l e a r l y s h o w i n g t h a t d i e l e c t r o p h o r e s i s c a n g i v e g r e a t e r e n h a n c e m e n t t h a n e l e c t r o p h o r e s i s .(c ) D i e l e c t r o p h o r e s i s

D i e l e c t r o p h o r e t i c e n h a n c e m e n t w a s t h e f i rs t to b e r e p o r t e d ( e. g . b y S e n f t le b e n [ 6 1 ], S e n f t l e b e nand Bra un [62 ]) and , a l tho ug h l e ss e ff ec t ive tha n ( a ) o r ( b ) , is the s imp les t to com pu te [63 ] andc o r r e la t e . I t c a n a s s is t t h e c o o l i n g o f h i g h v o l t a g e a p p a r a t u s [ 6 4 ]. T a b l e 3 r e v ie w s r e p o r t e de x p e r i m e n t a l w o r k t h a t c a n b e c l a s s i f i e d u n d e r t h i s h e a d i n g .

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Electrohydrodynamic enhancement of heat transfer and fluid flow 397(d ) E H D - i n d u e e d f l o w

Elec t rophore t i c pum ps can be c l a ss i fi ed a s " induc t io n" o r " ion d rag " . Th e opera t i on o f t hefo rmer depend s o n the e l ect r ica l conduc t iv i t y o f t he w ork ing f l u id p rov id ing d i ssoc i a t ed pos i ti veand negat ive ions, which are acted upon by the t ravel l ing e lect rosta t ic f ie ld . This f ie ld i s se t up byin t e rl eaved e l ec t rodes fed i n pa i rs f ro m a h igh vo l t age t h ree -phase supp ly . I f t he f ree cha rges fo l l owthe appare n t mo t ion o f th i s fi eld, impar t i ng the ir mo t ion to t he ad j acen t f l uid , the pum p i s sa idto be an " a t t rac t i on" one . I t s ac t ion i s ana logous t o m agne t i c l inea r mo t ion in tha t t he f lu id ve loc i tycanno t exceed tha t o f t he t ravel li ng f i eld. The s imp les t wa y o f c rea t ing the f ree cha rges i s by mean so f a t empera tu re - - -and hence e l ec t ri ca l cond uc t iv i t y - -g rad i en t [ see equa t ion (16 )] pe rpend icu l a r t othe pumping di rect ion . When heat i s t ransferred from the f lu id to the duct wal ls , the resul t ingd i s t r i bu t ion o f conduc t iv i t y , and hence o f cha rges , favours t he a t t rac t i on mod e , bu t i f t he hea tt ransfer i s in the opp osi te d i rect ion , the charg e d is t r ibut io n g ives flow against the f ie ld and the mod eof ope rat io n i s " rep uls io n" [71]. In e i ther case , the net e lect rical charge in the f lu id i s zero , wh ereasin the ion drag pump charge i s in jected and then propel led by the e lect r ic f ie ld between in jectorand col lector e lect rodes [72].

A l l EH D pum ps a re cha rac t e r i zed b y low ef fi ci enc ies; t he h ighes t repo r t ed i n t he wor k rev i ewedhere i s 10%. However , l ow e f f i c i ency i s cons ide red o f fse t by f reedom f rom mov ing pa r t s .

As has been shown , mos t recen t ly by Sa to e t a l . [73 ], d i e l ec t rophore t i c pum ping ac t ion in ani so the rmal l i qu id can a l so p rov ide convec t ive f l ow to improve hea t t rans fe r conven ien t ly andeff ic ient ly . Ho wev er , t he work o f Say ed-Y agoob i and co l l abo ra to rs [71 , 72 , 74-79] has concen t ra t edon induc t ion ion d rag pumps and the re fo re depends on e l ec t rophores i s . Never the l ess , t o s t a t e , a sdoes re f. [77 ] , t ha t " the d i e lec t r ic f lu id be ing pum ped mu s t con ta in f ree cha rges" canno t beaccep ted . Whe the r e l ec t rophore t i c o r d ie l ec t rophore t ic , E H D pum ping i s poss ib l e and recen texper imen ta l work i s summar i zed in Tab le 4 .

4. T WO -P H A S E H E A T T R A N S F E R

(a ) C o n d e n s a t i o nP u b l i c at i o n s o n t h e E H D e n h a n c e m e n t o f c o n d e n s a t i o n b e g a n a p p e a r i n g i n 1 9 6 5 w i t h th e w o r kof Ve lko f f and Mi l l e r [80 ] and Cho i and Rey no lds [81 ] u s ing R113 . Th i s l i te ra tu re i s rev iewed in

Tab le 5 . Severa l t hemes can be d i sce rned . F i r s t , condensa t ion has been s tud i ed on su r faces t ha ta re f l a t o r cu rved , ho r i zon ta l o r ve r t i cal . In a l l cases , t he d i sposa l o f t he condensa t e , o nce fo rm ed ,can be a problem. On a vert ica l surface , as the condensate f i lm th ickens wi th increasing d is tancedow nw ards , hea t t rans fe r coe f fi c ien t s reduce . In ba nks o f ho r i zon ta l t ubes , t he same e f fec t re su lt sf rom con densa t e d r ipp ing f rom tho se above . Smi rnov and L uka nov [95] repo r t a > 60% red uc t ionin hea t t rans fe r coe f f i c i en t be tween rows numbers one and f i ve fo r R11 condens ing on a bund leof low fin tubes.As shown in F ig . 3 , even the bes t EHD-ass i s t ed pe r fo rmance fa l l s sho r t o f t ha t g iven by us inga s ing le l ow f in p ro f i le t ube . E H D has l i t tl e e ffec t on low f in t ube co ndensa t ion as i t and the Gr igo r ige f fec t ac t i n oppos i t i on . How ever , in add i t i on to des t abi l iz ing the conden sa t e f ilm , EH D can s t r i pconde nsa t e o f f t he su r face and overcom e the e f fect s desc r ibed in t he p rev ious pa rag raph . F igu re4 s h o w s t h a t E H D e n h a n c e m e n t o f R 1 1 4 c o n d e n s in g o n a s m o o t h , 5 06 m m l on g , 1 9 .1 m m o . d.b rass t ub e wi th vapo ur t o t ube -wa l l mean t em pera tu re d i f fe rence o f 25 K i s o f much the samemag n i tude whe the r t he t ub e i s ho r i zon ta l o r ve r t ica l . Va lues o f ~t~ /~0 f rom the measu remen t s o fCo ope r [96 ] a re g iven as a func t ion o f vo l t age app l i ed t o a 38 mm i .d . cy l ind r i ca l co pper gauzeelect rod e surr oun ding the tube. (M easu red me an heat t ransfer coeff ic ients ~tE a t e lect r ic f ie ldst rength E h ave be en corre cted to pr imed values ~t~ taking in to a cco unt the increase due sole ly toreduced AT [89 ]. ) The wo rk desc r ibed ab ove re l ied on th inn ing the condens a t e f ilm . Hea t t rans fe renhancem en t ra t i o s (up to 4 .5 ) were ob t a ined us ing an e l ec trode geomet ry t ha t s t r i p s t he conde nsa t ef rom the su r face [91] , see Sec tion 6 . H igher h ea t t rans fe r enh ancem en t ra t i o s - - -up to 20 - - -were a l sorepo rted in refs [11, 83 , 85] . H eat t ransfer coeff ic ients are co nsider ably red uced in the p resence o fa non-condensab le gas . Bo loga e t a l . [92 ] repo r t ed t ha t t he damag ing e f fect o f t he gas can benul l i f ied by the appl icat ion of an e lect r ic f ie ld .

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3 9 8 P . H . G . A L L E N a n d T . G . K A RA Y IA N NI ST a b l e 1 . R e v i ew o f p u b l i s h e d e x p e r im e n t a l w o r k o n a u g m e n t e d s i n g le p h a s e h e a t t r a n s f e r u s i n g c o r o n a w i n d

H e a t t r a n s f e r ( ~ )A u t h o r ( s ) f l u id ( s ) S y s t e m m ~, N o t e sH o l m e s a n d A i r E l e c t ri c a ll y h e a t e d > 6 C o m p a r e d w i t hB a s h a m [ 2 2] v e r t i c a l c o p p e r p l a t e . ( f o r 2 5 m m e f f e c t o f a i r j e t s

p l a n e o r f i n ne d , f a c i n g b y 7 5 m m n o r m a l a n d p a r a l le la r r a y o f n e e dl e n e e d le t o s u r f a c e ( c o r o n ae l e c tr o d e s, a r r a y a t w i n d i n t e r m e d i a t e

5 1 m m b e t w e e n t h e t w o ) .s p a c i n g ) . B e t t e r r e s u l t s w i t h

V e l k o f f [ 2 3] A i r , o x y g e n ,n i t r o g e n

H o r i z o n t a l i s o t h e r m a lh e a t e d t u b e , 3 1 . 7 5 m m i . d . ,w i t h a x i a l s t a i n l e s s s t ee lc o r o n a w i r e, 1 2 7 / z m d i a . ,s t a r t i n g l e n g t h s 6 , 1 3 a n d2 4 d i a .

M o s s a n d G r e y N i t r o g e n H o r i z o n t a l i s o t h e r m a l[ 24 ] h e a t e d t u b e , 3 0 5 m m l o n g ,

2 5 . 4 m m i . d . N o d e t a i l so f a x i a l w i r e .

2(a t R e =3 0 0 0 w i r e+ ve .

L i t t l ed i f f e r e n c eb e t w e e niv = 0 .5 an d1 .0 m A ) .1.35(a t R e =1200, + vewi re) .

G r o s u a n d A i r , a r g o n , H e a t e d 0 . 2 m m d i a . n i c ke lB o l o g a [ 2 5] c a r b o n d i o x i d e , w i r e i n c o a x i a l h i g hh e l i u m v o l t a g e c y l i n d e r .

3 7 m m d i a .

f i n n e d p l a t e .C o n c e p t u a l d e s i g no f 2 G W s y st e m .I n l a m i n a r r e g im e ,i n c r e a s e d f r i c t i o nf a c t o r e x p r e s s e da s i n c r e a s e o fe f fec t i ve v i scos i t y( d o u b l e d a ti ~ = I m A ,g r e a t e r w i t h - v ewi re) .P a r t o f a m o r eg e n e ra l p r o g r a m m eo f E H D r e se a r ch .N e g a t i v e w i r e g a v ei n h i b i t i o n .D e t a i l e d a n a l y s i sg i v e n f o r t h i sg e o m e t r y . E f f e cti n c r e a s e d w i t hp r e s s u r e a t icc o n s t a n t .

~ 3 ( a ir a tI a t m a n dh e l i u m a t21 a tm) . 2 .5( a r g o n a t1 .4 a tm) . 5( c a r b o n d i o x i d ea t I a t m ) .

R o b i n s o n [ 26 ] A i r H e a t e d p l a t i n u m w i r e , 4 . 25 0 8 u m d i a . , a t h i g h ( w i t h w i r ev o l t a g e , a l o n g a x i s o f 2 6 0 ' C a n dv e r t i c a l s t e el t u b e , n a t u r a l5 3 . 2 m m i . d . , w i t h a n d c o n v e c t i o n ) .w i t h o u t f o r c e dc o n v e c t i v e c o o l i n g .

M c D e r m o t t [ 27 ] A i r V a r i o u s a r r a n g e m e n t s f o r ~ 4z e r o - f i e l d t e m p e r a t u r e s1 3 0 - 5 9 0 ' C . H i g h v o l t a g ea p p l i e d w i t h v a r i o u ss h a r p p r o b e s .

M i z u s h i m a , A i r V e r t i c a l c o p p e r t u b e s , 4 ( a tU e d a , w i t h 4 2 m m i .d . P V C w a t e r R e = 700).M a t s u m o t o j a c k e t , c o o l i n g h o t a i r 2 . 5 ( a ta n d W a g a [ 28 ] p a s s i n g d o w n w a r d s w i t h R e = 2000).

a x i a l n i c k e l w i r e 3 0 0 # mo . d . T u b e s : 6 . 4 m m i . d . ,5 2 0 m m l o n g a n d1 5 m m i .d . , 9 8 0 r a m l o n g .

W i n d i s c h m a n n A i r P o i n t a b o v e p l a n e . 2[29 ] ( l oca l ly )Y a m a g a A i r C o r o n a w i n d f o c us e d b y - -a n d J i d o [ 30 ] s h a p e d i n t e r m e d i a t e

p o t e n t i a l r i n g o n t o( e a r t h e d ) c o o l e d o b j e c t( c u t t i n g t o o l ) .

K i b l e r a n d A i r 1 0 m m d i a . t u b u l a r a s s e m b l yC a r t e r [ 31 ] i n c o r p o r a t i n g p o i n t a t5 k V s p a c e d 5 m m f r o m

( e a r t h e d ) g r i d .Y a b e , M o r i N i t r o g e n a t 4 0 r u m d i a . w i r e , 1 2 0 m m 1 2a n d H i j i k a t a 1 05 P a l o n g , a t 8 . 3 k V , 2 0 r n m b e l o w ( l o c a l ly )[ 32 ] 1 0 0 m m b y 1 0 0 m m , f l a t, h e a t e d

c o p p e r p l a t e .V e l k o f f a n d A i r 1 5 2 , ur n d i a . w i r e s , s p a c e d - 3 . 5G o d f r e y [ 3 4] 1 2 .7 m m p a r a l l e l t o , a n d6 m m f r o m , v e r t i c a le l e c t r i c a ll y h e a t e d ,4 8 3 m m b y 2 51 m m , p l a te .

C o r o n a d i s ch a r g ea t h e a t t r a n s f e rsu r fa ce i ts e lf .

S c h l i e r e no b s e r v a t i o n s h o w sm e c h a n i sm . P o w e rc o n s u m e d 3 Wc o m p a r e d w i t h 1 4 W b y f a n.L i t t l e e f fec t a tR e > 4 0 0 0 .

E f f e c t d e c r e a s e df o r t e m p . > 2 0 0 K .P e r f o r m a n c ea s s e s s e d b y t o o lw e a r r e d u c t i o n .

T o b e u s e d i na r r a y s .

D e t a i l e de x p e r i m e n t a la n d t h e o r e t i c a lana lys i s i n re f . [33 ] .I m p r o v e d h e a tt r a n s f e r i f s t r e a mveloc i ty ~ 10 t imesf r e e c o n v e c t i o nve loc i ty .

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E l e c t r o h y d r o d y n a m i c e n h a n c e m e n t o f h e a t t r a n s f e r a n d f lu i d f l o w 3 9 9Tada , Tak imo to Air Horizo nta l paralle l ( I ) 3 .7 600 < Re < 8000.and Haya shi uniform ly hea ted pla tes , Flow pa tte rns[35] 650 mm long, 225 mm wide, (2) 1.8 visualized ands pac ed 30 m m a pa r t w i th c om pute d .20 0pr o dia . midp lane (3) 2.5ionizing wires, spaced4 0 r a m a t 0 - 1 2 k V a n deither: (I) parallel t of low or (2) transverse to f low.

Also: (3) single ionizingwire followed by mid-planee lectrode (w ith gas-solids us pe ns ions ) .Nelson , Air Ho rizonta l tube , 1590 mm 3.6 Peaks a t 2000 < ReOhad i, Z ia entrance , 1020ram tes t and

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4 0 0 P . H . G . A L LE N a n d T . G . KARAYIANNIST a b l e 2 . R e v i e w o f pub l i she d e xpe r i me n t a l w or k on a u gm e n t e d s i ng l e - pha se he a t t r a ns f e r due t o e l e c t r ophor e s i s

H e a t t r a ns f e r D~,Do, L Em.~ {ctE'~A ut ho r ( s ) f l u id ( s ) ( r a m) ( M V / m) ~ J~ max N ot e sAnnular systemsS c h m i d t a n dL e i de nf r os t[37, 38]

T r a ns f o r m e r 10 , 18 , 500 6 . 9 4 F or c e d c onve c t i ono i l ( ho r i z on t a l ) va l ue s ove r a l l , w a t e rto oi l . (Oi l s ide va luesest imated in [391. )( Re l a t i ve l y sma l l ) p r e s su r ed r o p c h a n g e m e a s u r e d .

T r a ns f o r me r o i l 0 .025 , 22 , - - 8 . 4 ~ 1 .2 S t e a dy d . c . s t r e s st o BS 148 ( ve r t i ca l ) ga ve i nh i b i t i on w h i c hc ha nge d t r a ns i e n t l yt o e n h a n c e m e n t w h e npo l a r i t y r e ve r se d a ndp e r m a n e n t l y w h e n m i x e dwith a .c . Res ul t s of [37, 38]a n a l y z e d a s s u m i n gmixed a .c . /d ,c , s t r ess .F a t t y a c i ds : ( ve r t i c a l ) - - E f fe c t de duc e d f r omstear ic 1.3 hea t in g curves . A.c .ole ic 1.4 mu ch less e f fec t thanpa l m i t i c 1 . 4 d .c . Jou l e a n he a t show nt o be ne g l i g i b l e .Cyc l oh e xa ne 0 .05 , 10 , 20 2 . 2 I nve s t i ga t e s a nd( hor i z on t a l ) e xp l a i ns d . c. i nh i b i t i ondue t o spa c e c ha r ge a tl o w E a n d A T i n g o o di nsu l a t o r s .T r a n s f o r m e r 0 .0 2 5, 2 5 , - - 3 5 - - F o l l o w e d u p [ 3 9 ] b yo i l ( ho r i z on t a l ) i nve s t i ga t i ng :( I ) bounda r i e s be t w e e ni n h i b i ti o n a n de n h a n c e m e n t a t m u c hhigher d.c . E, f i nd i ngosc i l l a t o r y r e g i me ( 2 )t r a ns i e n t due t o po l a r i t yc ha nge a s f unc t i onof p r e - s t r e s s i nga nd r e l a xa t i on t i me s .Tran sform er 1.58, 31.8, 6 .7 1.9 Forc ed conv ec t ion .o i l 2800 N e ga t i ve vo l t a ge ga ve( hor i z on t a l ) g r e a t e r , 50 H z z e r o ,e f fec t . Much grea te rp r e s su r e d r op ne e de df o r s a me he a tt r a ns f e r i nc r e a sewi thout e lec t , f ie ld.T r a ns f o r me r 344 , 364 , 500 2 2 F or c e d c onve c t i on . N oo i l ( ve r t i ca l - c ons i s t e n t d i f f e re nc ei nsu l a t e d a nd be t w e e n pos i t i ve a ndun i nsu l a t e d - ne ga t i ve po l a r i t y bu the a t t r a ns f e r un i nsu l a t e d he a t t r a ns f e rsu r f a c e s ) su r f a c e show s som e w ha tg r e a t e r i m p r o v e m e n t .Av tur , hexan e 3.2/1.6, 12.4, 18.3 ~ 20 Force d conv ec t ion.( i n j e c t i on 600 D e f i ne s i n j e c t i ons t r e ng t h ( ho r i z on t a l ) s t r e ng t h pa r a m e t e r a se s t i ma t e d 0 .7 , q / /~E , a nd c o r r e l a t i on0 . 05) pa r a m e t e r a s ~\ '~p , ' l t.T r a ns f o r me r 1 .59 , 25 .4 , 6 . 8 6 F or c e d c onve c t i on .o i l 1000 G r e a t e r i mpr o ve m e n tus i ng ne ga t i ve po l a r i t y .1.59, 19.1, 7 .6 23 Pressure dro p increased1000 by up t o 66% . Cur r e n t( ho r i z on t a l ) d r a w n : ~ 101~A. Radia l f lowp a t t e r n o b s e r v e d

A l l e n [ 39]

M a s c a r e n h a s ,M a s c a r e n h a s ,F e r r e i r a D eS o u z a a n dRa be l l o [ 40 ]S e nf t l e be na n d S c h n a b e l[41]

C a r e a n dS w a n [ 42 ]

P or t e r a ndP ou l t e r [ 43 ]

N e w t o n a n dA l l e n [ 44]

P o u l t e r a n dMil le r [45]

F e r n a n d e z a n dP ou l t e r [ 46]

Gap between horizontal plates (Heat trans]er downwards)M a s c a r e n h a s O l e ic a c i d[47]

D#'nen$ions2 mm t h i c k 1 .25 1 . 36 U se d s t e a dy s t a t el a ye r , t he r ma l c ondu c t i v i t ya p p a r a t u s . J o u l e a n h e a tshow n t o be ne g l i g i b l e .

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E l e c t r o h y d r o d y n a m i c e n h a n c e m e n t o f h e a t t r a n sf e r a n d f lu i d f lo w 4 01B o r b u l y a , T r a n s f o r m e rK o j u h a r a n d o i lBologa [48]

G r o s s a n d T r a n s f o r m e rP or t e r [ 49] o i l

T ur nb u l l [ 10] Cor n o i lc a s t o r o i l

R e c t a n g u l a r d u c t ( f o r c e d c o n v e c t i o n )P o r t e r a n d T r a n s f o r m e rS mi t h [ 50] o i l

F u j i n o ,Y o k o y a m a a n dMor i [511R I 1 3

I s h i g u r o , " ' F u r o n s o r u b uN a g a t a , Y a b e A E " , ( 9 6 % R 1 13 ,a n d N a r i a i 4 % e t h a n o l )[521

N u c l e a r r e a c t o r a p p l i c a t io n sS t a c h [ 53] A i r

Be r ge r a ndD e r i a n [ 54 ]

Be r ge r a nd D e r i a n [ 55 ]M i s c e l l a n e o u s s y s t e m sC o u l s o n a n dPor te r [56]

( a ) D i sks 70 mmdia . 1 .5 3( b ) Cy l i nde r s , M mm d i a .by 100 mm long(spac ing unspec i f ied) .50 mm d i a . c e l l. 0 . 3 - -

1 0 2 ra m b y 7 6 m m ~ 3a l u m i n i u m p l a t e sse pa r a t e d 25 r a m. ~ 3H or i z on t a l , ~ I180ram b y 1 7 m mse c t i on , 1230 mml ong , uppe rw a l l he a t e d .

S c h n u r m a n na n d L a r d g e[571

C o o p e r a n dA l l e n [ 58]

V e r t i c a l , 120mmb y 2 m m s e c ti o n ,2 0 0 m m h i g h , o n ew a l l he a t e d .H o r i z o n t a l ,15 0 m m b y 2 0 m mse c t i on , t e s ts e c t i on , 600 mmf o l lo w s 1 0 0 0 m m e n t r yw i t h 1 4 o f f 3 0 0 / z m d i a .s t a i n l e s s s t e e l w i r e s ,2 0 m m a p a r t , 5 m m f r o mw a l l , bo t h w a l l s he a t e d .R e a c t o rc o o l i n gc ha nne l : node t a i l s g i ve n .

1.5

( 1 ) ( a ) a i r , A nn u l i 0 . 56( b ) CO 2 ( 120- ( 1 ) 41 mm o . d . ,190"C) a t l ow 28 mm i . d ., 485 mm( up t o 2 a t m) l ong .p r e s su r e s .( 2 ) CO 2 ( 35 - 7 5 'C) a t h i gh ( 2 ) 42 mm o . d . , 5 . 28( up t o 30 a t m) p r e s su r e s . 28 mm i. d. , 500 mm l ong .M o r e e x pe r i me n t a l de t a i ls o f r e f . [ 54 ] a bov e

I0

1.9 atR e = 95 ,= 9 . 1k W / m 2.

8

20 a tR e = 1470,3 a t

R e = 27300,w i r e s a t10 kV.

L i q u i dparaf f in

P e r f l u o r o m e t h y l c y c l o h e x a n e( non- po l a r )

2 0 % i s o p r o p y la l c oho l i nn - he p t a ne ,( po l a r ) pu r en - h e p t a n e( po l a r )T r a n s f o r m e roi l to BS148

1. 2

1.5

H e a t e d t ube s ,3.2, 4.7, 6.4, 9.5 and1 2 . 7 m m d i a . , 1 5 2 m ml ong , p a r a l l e l t o 1 mmdi a . H V e l e c t r ode .1 2 7 / zm d i a . , ~ 6 0260 mm l ong ,h e a t e d p l a t i n u mw i r e pa r a l l e lto, 27.7, 25.4a n d 5 0 .8 m m ~ 4 8f r o m , 2 5 4 m m b y50 . 8 mm p l a t ee l e c t r ode . ~ 60

F a c s i mi l e 3 . 6she l l / t ube he a te x c h a n g e r w i t ha r r a y o f t h r e ee a r t he d , w a t e r -he a t e d t ube s ,12 .6 mm o . d . , spa c e d16 .6 mm ve r t i c a l l y ,be t w e e n e l e c t r ode sw i t h 4 m m c l e ar a n c e .

1. 8

2 . 4 bo t h+ v e a n d- - ve .

8. 7e l e c t r odepos i t i ve .4 .4e l e c t r odene ga t i ve .2. 3

S t u d y o f c o n v e c t i o npa t t e r ns due t o d . c .f ields. No a.c. effect.P a r t o f a n e x t e ns i ves t udy i n t o t he i n s t a b i l i t ydue to an e lec t r ic f ie ld.

( Re l a t i ve l y sma l l )f r i c t ion f a c t o ri nc r e a se s me a su r e d .Ef fec t on hea t t r ansfe rcoeff icient dec reased w i thR e a nd i nc r e a se dwi th hea t f lux.M e c ha n i sm o f e f f e c te x p l o r e d b ys h a d o w g r a p h s .H e a t t r a ns f e r a ndpr e s su r e d r opi nc r e a se f a c t o r sde c r e a se d w i t h R e .H e a t t r a ns f e ri nc r e a se s g r e a t e rt ha n p r e s su r e d r opincreases .

F or a ve r a ge ve l oc i t y( f ) r a nge 4 - 23 m/ s ,r e a c t o r pow e r ( V a )2 0 0 - 2 0 0 0 k W a n dvo l t a ge ( ~b) I - 3 kV , N ui nc r e a se d l i ne a r l y w i t hV R f b / f 2. F l o w o f p a r t i a l l yi on i z e d ga s a na l yz e d( i n t w o d i me ns i ons ) .U p t o 5 0 % e n h a n c e m e n ta n d 8 % i n h i b i t i o nd e p e n d i n g o npr e s su r e , po l a r i t ya n d ( H V p o w e r ) / ( g a svel ocit y) ' .5.

Re su l t s f o r d . c.( po l a r i t y no tspecified), effectsof a .c . " 'much less" .P a r t o f s t u d yi nc l ud i ng bo i l i ng .C l a r i f i e d i mpor t a nc eof e l e c t r i c a lna ture of f luid.a E / a 0 g r a phs suspe c ta s t he y c onve r gea t o r i g i n .

P os i t i ve e l e c t r odehas much less e f fec t .Ef fec t decreases wi thR e , ve r y s e ns i t i ve t oconta_mina tion by a i r andt o A T . C i r c ums t a nc e sg i v i ng i nh i b i t i on f oundb u t t u r n e d t o e n h a n c e m e n tw i t h l ow f r e que nc ya l t e r na t i ng po l a r i t y .

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4 0 2 P . H . G . A L LE N a n d T . G . K A R A Y IA N N IST a b l e 3 . Re v i e w o f pub l i she d e xpe r i me n t a l w or k o n a ugm e n t e d s i ng l e - pha se he a t t r a ns f e r due t o d i e l e c t r opho r e s i s

H e a t t r a ns f e r E ma C t E )A ut hor ( s ) f l u i d ( s ) Di, Do, L M V/m ~oo m~, No tesAnnular systemsS e nf t l e be na nd Br a un [ 62 ] A r gon , oxyg e n 30 o r 50 / a m, 10 .7 1 .5 Cy l i nd e r i n c r yos t a t( n o n - p o l ar ) , ~ 4 5 m m , 7 0 m m , ( e th y l o r o i l b a t h a t t e m p .c a r bon hor i z on t a l , c h l o r i de ) , be t w e e n 90 a nd 400 K .mo nox i d e P r e s su r e 0 . 116- 0 , 986 ba r .

( s l ight ly A.c . and d.c .po l a r ) , u se d , no po l a r i t ye t hy l c h l o r i de e ff ec t. E xpe r i m e n t a l(pola r ) . da t a given in full .A h sm a nn a nd T o l ue ne , 20 / a m , 40 mm , 9 .2 1 .5 Cy l i nd e r i n me l t i ngK r on i g [ 65] n - he p t a ne ( pu r e 70 mm , ( c a r bon i ce . H i gh vo l t a gea nd c om me r c i a l ) ho r i z on t a l , t e t r a - 40 H z squa r e w a ve a ndc a r bo n t e t r a - c h l o r i de ) , d .c .c h l o r i de ,a m m o n i a g a s.D e H a a n [ 6 6 ] n - he p t a ne , 22 , 55 a nd 5 .0 1 .3 Cy l i nd e r i nt o l ue n e . 9 9 . 5 / a m , 4 0 m m , ( n - h ep t a n e ). t h e r m o s t a t , 4 0 - 8 0 C .1 6 0 m m , G r e a t e r v a r i a t i o n o fhor i z on t a l . ~ a nd D t ha n [ 65] .H i gh vo l t a ge a s [ 65 ] .W atso n [67] n-hex ane . 100/am , 30 mm , 24.5 2.6 D.c . s t r ess , no100 mm . pol a r i ty e f fec t.Vertical ductsW e b e r a n d " ' T r an s i l " R o g o w s k iH a l se y [ 68] i n su l a t i ng ( un i f o r m f ie ld )o i l e l e c t r ode s ,25 .4 mm d i a . ,one he a t e d ,spa c e d5 , 1 - 20 .3 r a m.S a vk a r [ 69] L i gh t mi n e r a l D u c t 762 mm 7 .3 2 .2i nsu l a t i ng o i l l ong , 305 mmw i de , up t o12 .7 mm t h i c k( w i t h e qua ll e ng t h e n t r ysec t ion) .

9 . 6 3 .6 60 H z s t r e ss .

60 H z s t r e s s . O ne o rbo t h s i de s he a t e d .L o n g i t u d i n a l r o l lc e l l s p r e d i c te d f r oma na l y t i c a l so l u t i ono f g o v e r n i n g e q u a t i o n s ,i n c l u d i n g E H D f o rc e s ,c onf i r me de xpe r i me n t a l l y . E/~t0 dec rease s wit hRe.N e w t on a nd T r a ns f o r me r F a c s i mi l e 6 1 .25 50 H z s t r e ss .A l l e n [ 44] o i l t o BS I 48 t r a ns f o r m e rw i n d i n g d u c t s ,1 2 . 7 m m b y 5 7 r a mb y 3 3 9 m m l o n g ,6 .3 m m b y 2 8 m mb y 2 6 7 m m l o n g( w i t h e n t r yl e ng t hsec t ions) .Wa ng , Co l l i n s T r a ns f o r me r A s r ef . [ 44] . 6 1 .25 G ov e r n i ng e qua t i onsa nd A l l e n o i l t o BS I 48 so l ve d num e r i c a l l y[ 63] t o i nc l ude E H D f o r c e sc onf i r me d byexper iments of r e f . [44] .Miscellaneous systemO l i ve r [ 70] S u l ph ur - - 8he xa f l uo r i de G a s p r e s su r e l 0 ba r .C o n d u c t o r d i a . 3 3 m m .No ef fec t observed.

E H D el iminates the q decrease betw een E and G and, in addit ion, increases q. These ph enom enahave received very much mo re attent ion than E HD 's other ac t ion, namely the in it iation o f nucleateboi l ing at smaller A T and hence the virtual e l im inat ion of the hysteresis p ort ion (A BC DB 'A) ofthe characteristic, e.g. by apply ing volts at AT value s betwe en b and c. This initiation proc ess hasbeen reported only by Karayiannis e t a l . [13], Jalaluddin and Sinha [101], Basu [10 4] and A llenand Co oper [15] wh o have also m ade a video record o f i t [117] . In this, observat ion is made o fa tube, immersed in R114. Hot water passes a long the tube, los ing heat to the refrigerant . Thus ,near the inlet, the tube surface g ives sufficient superheat for bubb les to evo lve a t a well-defined set

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E l e c t r o h y d r o d y n a m i c e n h a n c e m e n t o f h e a t t r a n s f e r a n d f l u i d f l o wT a b le 4 . Re v ie w of r ec e nt ly pub l i s he d exper im e n ta l work on E H D p um p ing

4 0 3

Auth or ( s ) F lu id ( s ) Sys te m F low rate N o t e sInduction (attraction)Se ye d-Ya goob i , Sun No . 4 o i lCha to , Crowie y wi th a dde dand Kre in [74] She ll ASA -3antis ta t icadditive to

va ry a ~ .

Boh ins ky a ndSe ye d-Ya goob i[75]4 syntheticpe t ro le umfluids, 4pe troleum oils ,I polyol es te r ,I f luorina tedfluid, Ia rom a t ich y d r o c a r b o n ,I siliconefluid, somewi th a dde dove r -ba s e dcalciums u lphona t tov a r y a c.

T o ta l loop le ng th 5 .2 m , 50 m m /s (4 x He a te d s e ct ion o fvertica l l imbs 2.1 m, 16 mm na tura l re turn l imb gavei .d., 3-phase e lectrode convec tio n na tura l convec tions ys te m fo rm e d by r a te ) a t ( fo rwa rd) f low f roma l te rna te m e ta l a nd g la s s op t im um f re que nc y top to bo t tom ofr ings fo rm ing tube ~ I m (~ 5 Hz ) a nd pum p. Som e f lowlong. 30 kV 3-phase oil ~c . de tec ted with outs upp ly , 0 -100 Hz ,revers ible . Natu ra l hea ting or cooling.convec tion generated byhea ting or cooling.Tota l (vert ica l l imb) M axim um High er thanloop le ng th 2 .2 m , 50 m m 385 m m /s s ync hro nousi .d., 430 mm long 3-phase obta in ed ve locit ies observede lectrode sys tem form ed with doped but no t explained.by 18 ga uge c oppe r w i re a rom a t icin g roove s . 12 kV 3-pha s e hydroc a rb onsupp ly, 0-13 Hz , s ine, (n-hex ane)s qua re o r t r i a ngu la r a t 9 Hz .w a v e o r m .

Ion-dragCa sta fleda RI I T o ta l (hor iz on ta l ) loop Ma x im um Cur re n t c ons um pt ionand Seyed- length 2.68 m, 50 mm i .d. , 240 mm /s and ve locity l inearYa goo b i [78] pum ping s e ct ion 360 m m wi th a ll func t ions o f num be rlong. 13 electrode pair s, electrodes of energized8 m m apart , spaced 15 mm , energized e lectrodes .form ed by 20 gauge t in- a t 28.5 kVc oppe r w i re in g roove s ,us ing no s ha rp po in t s .50 kV s upp ly .Bryan and 3 synthe tic Tota l (vert ica l) loop 220 mm /s Eff ic iency ( ;~ 5.5% )Seyed- pe trole um length 1.92 m, 70 mm i.d. , obta in ed increased withYag oobi [77] f luids , 4 pum pin g sec tion 330 mm with charge re laxa tionpe trole um oils, long. 10 e lectrode pa irs , und oped t ime .I f luorina ted 10 mm apart , a lum inium syntheticfluid, I electrodes spaced 5 mm , petr oleu marom atic upp er (emitte r) e lectrode f luidhyd rocarb on, f i tted with 90 s ta inless (dodecyl-1 silicone steel needles, po inti ng benzine)fluid, at collector electrode, at 20 kV.50 kV s upp ly .Bryan and Dodecylbenz ine Tw o pu mp sec tions: 334 mm /s Increas ing Seyed-Y agoobi (a ) as re f. [77] bu t with with reduced f low ra te .[79] tota l loop length 1.86 m. und oped High er e ff ic iency(b) with one e lectrode f luid and and s l ightly higherpa ir only, giving loop 10 e lec trode ve locity with pla inlength 1.33 m and also pai rs collector electrode.hav ing modified collector at 25 kV.electrode (w ith stainlesss tee l wire web extending6 m m radia lly inward) .50 kV s upp ly .Dielectrophoret icSa to , Ya be a nd " Fu ron s oru bu 24 m m s qua re , a bou t 160 m m 143 m m /s E f fe c t o f f low onTaktani [73] A E" (96% R II3 , long, horizon ta l pu mp with convective hea t4% e thanol) , sec tion conta inin g 61 mm toroida l transfe r es t imated.R I 13, R 123. long, 20 mm squa re hollow e lectrode Oth er ( lesshig h volta ge electrode at 20 kV. effective) electrodeadjacent to var iou s a rrang eme nts tested.( toroida l , rod,spherical) earthedelectrodes.

of s i te s . H ow e ve r , t owa r d s t h e ou t l e t , AT i s on ly su f f i c ie n t t o g ive c on ve c t ive h e a t t ran s f e r an d t h u sa we l l d e f in e d " f r on t " i s s e e n b e t we e n b o i l in g an d n on - b o i l in g r e g ion s . O n ap p l i c a t ion o f e l e c t r od ev o l t a g e s g r ea t er t h a n a b o u t 8 k V t h e r e i s i m m e d i a t e - - a n d m o r e v i g o r o u s - - e b u l l i t i o n e v e r y w h e r eon t h e t u b e su r f ac e . In a t l e as t on e c ase ( B ab o i e t a l . [ 111 ] ) , t h e p h e n ome n on was d e l ib e r a t e lyH R S I $ / ~ - - B

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4 0 4 P . H . G . A L LE N a n d T . G . K A RA Y IA N NIST a b l e 5 . R e v i e w o f p u b l i s h e d ex p e r i m e n t a l w o r k o n E H D a u g m e n t e d c o n d e n s a t i o n h e a t t r a n s fe r

A ut ho r ( s ) f l u i d (s ) S ys t e m m~ N ot e sV e l kof f a nd R I 13 V e r t i c a l c oo l e d c oope r 3 , 4 , 5 , 6Mil le r [80] pla te , 152 mm high,

C h o i a n dRe yno l ds [ 81 ]

Choi [821H o l m e s a n dC h a p m a n [ 83 ]

S e t h a ndLee [84]

B o l o g a a n dD i d k o v s k i y[ i l l

D i d k o v s k i ia n d B o l o g a[ 8 5 1

D i d k o v s k y a n dBol oga [ 86 ]S m i r n o va n d L u n e v[871

229 mm w i de , f a c i ng :(1) 102,am dia .ho r i z on t a l w i r e ~ 1 .4( 2 ) M e sh s c r e e ns ~3( 3 ) A l um i n i um p l a t e . ~ 1 .7

R11 3 Ver t ica l s ta inless 2 1, 2 , 3s t e e l t ube , 1346 mmlong, 23.8 mm i .d . ,c o o l e d o n o u t s i d e a n dc o a x i a l w i t h i n n e re lec t rod es 6.3, 12.7and 19.1 mm o.d..A s f o r Cho i a nd Re yn o l ds [81 ].

R114 F l a t s i l ve r - p l a t e d U p t o 6 , 7c o p p e r c o o l e d a n d t i m e se l e c t r ode p l a t e s ( e a c h 101 52 m m - - h o r i z o n t a l - - b y ( o v e ra l l) .3 8 m m - - s l o p i n g )a t d i f f e r e n t a ng l e s t og i v e v a r i a b l e w e d g esha pe d e nc l osu r e .R113 H or i z on t a l c opp e r w a t e r 1 , 6 5 , 8t u b e w i t h c o a x i al o u t e re l e c t r ode .

V e r t i c a l c opp e r p l a t e , 10 ( f o r 22 2 0 m m b y 1 2 0 m m , s p a ce d R I 1 3 &7 mm f r om pa r a l l e l ( p l a i n he xa ne )o r ho r i z on t a l l y s l o t t e d ) 20 ( f o re lec t rode , e ther ) .As for r e f. [11] toge ther wi th As for r e f. [11]. 2 , 5, 6ve r t i c a l a nnu l us ,c o o l e d t u b e 3 0 0 m m h i g h21 mm o . d . , e l e c t r odet ube 35 mm i . d .A s f o r B o l o g a a n d D i d k o v s k i y [1 1 ].

Y a b e , K i k u c h i ,T a k e t a n i , M o r ia n d H i j i k a t a1881

C o o p e r a n dA l l e n [ 89]

T r o m m e l m a n sand Berghmans[ 9 0 1

R113 , he xa ne ,d i e t hy l e t he r

As for ref . [11].

2 , 3 , 7 , 9

R113 , Ver t ica l ann ulus , cooled 3.6 2, 3 , 6 , 7d i e t hy l e t he r ou t e r j a c ke t , 215 mm h i gh30 mm i . d ., a r oun dc e n t r a l e l e c t r ode w i t hsmoot h , s c r e w - t h r e a de dor pe r f o r a t e d su r f a c e ,ga ps 2 . 5 t o 4 r a m.( a ) W a t e r N e e d l e e l e c t r ode a bov e 10l i qu i d su r f a c e .(b) R11 3 Co oled brass pla te , 2 .24 3, 11600 mm h i gh , 100 mm w i dew i t h s h a p e d c o p p e r w i r ee l e c t r ode sys t e ms .R12 a nd R114 S i ng l e c oo l e d ho r i z on t a l 2 . 9 3 , 5 , 7 , 12 , 13t u b e s 5 1 4 m m l o n g w i t hs m o o t h ( 1 9 .1 m m o . d .) a n dlow f in (19.0 mm o.d. )sur faces . E lec t rodesys t e m: ( 1 ) c onc e n t r i cc oppe r ga uz e ( 38 mm i . d . )( a l so ve r t i c a l w i t hR114) (2) Para l le l brassp l a t e s w i t h a ux i l i a r y6 .25 mm o . d . r od ( t os i mul a t e ( I ) ) .R I I , R113 H or i z on t a l smo o t h c oppe r 1 .1 3 , 14a n d R 1 1 4 c o o l e d t u b e 1 1 0 0 r a m l o n g ,18 mm o . d . , c onc e n t r i cw i t h c o p p e r w i r e s p i ra le l e c t r ode , 38 mm i .d .

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Y a b e , T a k e t a n iK i k u c h i , M o r ia n d M a ki [ 91 ]

B o l o g a ,S a v i n a n dD i d k o v s k y [ 9 2]

D a m i a n i d i sCo l l i n s ,K a r a y i a n n i sa n d A l l e n[93]Y a m a s h i t a ,K u m a g a i ,S e k i t a ,Y a b e ,T a k e t a n i ,a n d K i k u c h i[94]

E l e c t r o h y d r o d y n a m i c e n h a n c e m e n t o f h e a t t r a n s fe r an d f lu i d f l ow( a ) S i l i c one T h i n l i qu i d f il m o n a n do i l b e t w e e n e l e c t r i c a l lyc o n d u c t i n g g l a s s s h e e t s .( b ) R l l 3 V e r t ic a l s m o o t h b r a s s 4 .5c o o l e d t u b e 5 4 0 m m h i g h ,18 mm o . d . w i t h c op pe rhe l ica l ( c o n d e n s a t er e m o v a l ) w i r e . 0 . 5 mmo . d . a n d c u r v e d ( s t r e s s

a p p l y i n g ) p l a t ee l e c t r o d e s , 21 .2 mm o . d .R 1 1 3 - h e l i u m F l a t p l a t e 200 mm h i gh 1 .8R l l 3 - a i r 1 2 0 m m w i d e w i t h p a r a ll e l 2 . 6R l l 3 - c a r b o n p l a t e e l e c t r o d e ( h a v i n g 3. 0d i ox i de s l i t s ) o r w i r e e l e c tr o d eH e x a n e - a i r ( 0 .18 mm w i r e s spa c e d 5 mm 5 . 0a p a r t ) .R 1 1 4 H o r i z o n t a l b u n d l e o f n i n e 1.08s m o o t h s u r f a ce t u b e s ,19 .1 mm o . d. + 360m m l o n g .P e r f o r a t e d p l a t e a n dr o d e l e c t r o d e .R114, Ver t ic le b u n d l e o f 102 6n - p e r f l u o r o h e x a n e s m o o t h s u r f a c e s t ai n l e ss 4s tee l tubes , 19 . 05 mmo. d . w i t h c om bi ne dl a t t i c e / he l i c a l w i r ee l e c t r o d e s y s t e m .C o n d e n s i n g t e mp . : 90 C( R I I 4 ) a n d 1 5 0 C( n- pe r f l uo r ohe xa ne ) .

4 0 53 , 5

12

2 , 3 , 4 , 5 , 8

2 , 3 , 5 , 1 5 , 1 6

Notes2( 1 ) A na l ys i s i n t e r m s o f p e r t u r b a t i o n w a v e l e n g th .(2 ) R e s u l t s c o r r e l a t e d .(3) D.c. elec tr ic f ield.( 4 ) C o r o n a d i s c h a r g e g a v e e l e c t r o p h o r e s is .( 5 ) Conde nsa t e f i l m p e r t u r b a t i o n o b s e r v e d .( 6 ) C o n d e n s a t e s p r a y i n g o b s e r v e d .(7) A.c . electr i c f ield.(8 ) I n h i b i t i n g ef f ec t o f n o n - c o n d e n s a b l e g a s p a r t l y n e u t r a l i z e d b y E H D .( 9 ) Conde nsa t e f i l m t h i c k n e s s m e a s u r e d .( 10 ) G a s - l i qu i d i n t e r f a c e s t a b i l i t y s t u d i e d t h e o r e t i c a l l y a n d e x p e r i m e n t a l l y .( I I ) I m p r o v e d h e a t t r a n s f e r d u e t o c o n d e n s a t e r e m o v a l b y e l e c t ro d e s m e a s u r e d .(12) ~E V a l u e s c o r r e c t e d f o r r e d u c e d A T .( 13 ) E H D e f f e c t w i t h l o w f i n t u b e < 1 0 % .(14) E f f e c t o f E H D o n s h a p e o f p e n d a n t c o n d e n s a t e d r o p l e t s d i sc us se d .(15) T u b e l e n g t h e f f e c t s t ud i e d .(16) E l e c t r od e p o w e r c o n s u m p t i o n i n c r e a se d b y o i l c o n t a m i n a t i o n .

a v o i d e d b y r e d u c i n g t h e t h e r m a l l o a d i n g t o t h e e x p e r i m e n t a l v a l u e r e q u i r e d ( i . e . a l o n g E D B ' i nF i g . 5 ) " s o t h a t m o s t o f t h e v a p o u r - f o r m a t i o n c e n t r es w e r e a c t iv e " . A l s o , a s r e m a r k e d b y M a r k e l sa n d D u r f e e [ 2 0 ] , " I t a p p e a r s l i k e l y h o w e v e r t h a t d i f f e r e n c e s e x i s t b e t w e e n v o l t a g e e f f e c t s w h e n ar e l a t i v e l y l a r g e d i a m e t e r h e a t t r a n s f e r s u r f a c e i s u s e d a n d w h e n t h e b o i l i n g t a k e s p l a c e o n a t h i nw i r e " . A f i n e w i r e f ed b y a c o n s t a n t e l e c tr i c c u r r en t c a n n o t i n s t a n t a n e o u s l y p r o v i d e t h e a d d i t i o n a lt h e r m a l e n e r g y d e m a n d e d b y s u d d e n l y p r o m o t e d e b u l l i t i o n . T h e e n e r g y c o u l d o n l y c o m e f r o m ac o n s i d e r a b l e d e c r e a s e i n te m p e r a t u r e , a n d h e n c e i n A T , t h u s s u p p r e s s i n g e b u l l it i o n b e f o r e i t b e c a m ee s t a b l is h e d . B y c o n t r a s t , t h e m o r e u s u a l i n d u s t r ia l c a s e o f a s o u r c e h e a t e d b y f lu i d f lo w m a i n t a i n sa m u c h m o r e n e a r l y c o n s t a n t t e m p e r a t u r e , a s c a n a h i g h t h e r m a l c a p a c i t y s o u r c e ( s e e T a b l e 6n o t e s ) .

E H D b o i l i n g h e a t t r a n s fe r i n v e s t ig a t i o n s i n c l u d e d t e s t s w i th a v a r ie t y o f t u b u l a r s u r f a c e si n c l u d i n g s m o o t h , l o w f in a n d e n h a n c e d s u r f a c e s s u c h a s T h e r m o e x e l . I t w a s f o u n d t h a t t h e n u c l ea t eb o i l i n g h e a t t r a n s f e r e n h a n c e m e n t o b t a i n e d o n a s m o o t h t u b e w a s v e r y m o d e r a t e c o m p a r e d w i t ht h e l o w f i n a n d t h e T h e r m o e x e l t u b e s . T h e m o s t r e c e n t w o r k i n t h i s a r e a ( b a s e d o n d a t a f r o mr e f s [ 13 , 9 6 , 1 1 8] ) i s s u m m a r i z e d i n F i g . 6 o n a " t u b e r a t in g " ( k W p e r m e t r e o f tu b e v s A T ) b a s i sw h i c h , f o r a g i v e n t u b e d i a m e t e r , g o v e r n s h e a t e x c h a n g e r d e s i g n .

A l t h o u g h , a s s h o w n i n T a b l e 6 , a v a ri e ty o f g e o m e t r i c c o n f i g u r a t i o n s w a s e x a m i n e d , o n l y r e c e n t lyh a v e r e s e a r c h e r s c o n c e n t r a t e d t h e i r e f f o r t s o n t u b e b u n d l e s i n h e a t e x c h a n g e r s l i k e t h e s h e l l a n dt u b e . D a m i a n i d i s e t a l . [ ! 1 6] re p o r t e d e x p e r i m e n t s o n n i n e t u b e b u n d l e s c o n s i s t i n g o f e it h e r s m o o t ho r l o w f i n t u b e s . T h e w o r k i n g f l u i d w a s R 1 1 4 . I n t h e c a s e o f t h e l o w f i n t u b e b u n d l e , t h e

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4 0 6 P . H . G . A L LE N a n d T . G . K A R A Y IA N N IST a b l e 6 . R e v i e w o f p u b li s h e d e x p e ri m e n t a l w o r k o n E H D a u g m e n t e d p o o l b o i l i n g h e at t r a n s f er

H e a t t r an s fe r H e a l e d u r f a c e ( q ~ .E ( a te )A a t h o . ) d i a m 0 t e r , m m ) . . . . . .- , . . Notes

C o a x i a l e y l i n dr i e a l y s t e m sBoc h i r o l ,B o n j o u r a n dWei l [981Benzene,hexane , 0 .2t r i c h l o r e t hy l e ne ,t o l ue ne , e t hy l e t he r ,l i qu i d n i t r oge nP ur e w a t e r ,me t hy l e t hy l ke t one , 0 .1a c e t one , me t hy l a l c oho l

Bon jou r ,V e r d i e r a nd We i l [ 99 ]Wa t son [ 67] n - he xa n eCho i [ 100] R113M a r k e l s a n d i s o p r o p a n o l ,D ur f e e [ 20] d i s t i l l e d w a t e rWi ne r [ 14] R114L o v e n g u t h R 2 1 , R 1 1 3 ,a n d c a r b o n t e t ra c h l o r id e ,H a ne s i a n [ 103] c h l o r o f o r mBa su [ 104] Ca r b on t e t r a c h l o r i deJone s a nd R I 13Schaeffer [105]J o n e s a n d R 1 1 3 ,H a n o c k [ 10 6 ] R 1 1 3 / m e t h a n o lZ h e l t u k h i n , A c e t o n e ,S o l o m a t n i k o v , b e n z e n e ,M i k h a y l o v a n d n - d i e t h y lU sm a nov [ 107] e t he rA l l e n a n d R 1 1 4Coope r [ 151K a w a h i r a , R 11K u b o a n dY o k o y a m a [ 1 0 8 ]K a r a y i a n n i s , R 1 1 4Col l i n s a nd A l l e n [ 13 ]O h a d i , R I 2 3 , R 1 2 3 / o i lP a pa r , N g , R I I , R I I / o i lF a a n i a n dR a d e r m a c h e r [ 17 ]Parallel plate systemsO l i n g e r a n d D e i o n i z e dCol ve r [ 12] w a t e rB l a c how i c z , Be nz e neB r o o k s a n dTan [1091K a w a h i r a R I IK u b o a n dY o k o y a m a [ 1 0 8 ]Other systemsJ a l a l u d d i n M e t h a n o l ,a n d S i n h a i s o p r o p a n o l ,[ 101] me t hy l e t hy lke t one , be nz e neA sc h [ 1101 R I I 3

Baboi , Benzene ,B o l o g a a n d t o l u en e ,K l y u k a n o v l i q u i d a r g o n11111

A s f o r Boc h i r o l , Bon j our a nd W e i l [ 98]

2. 7( t r i c h l o r e t hy l e nea n de t hy l e t he r )

6( me t hy l a l c oho l )

3, 6

0.1 2.6 2, 60.254 or 0.508 > 2 1, 4, 6

9.525 6 2, 5, 7> 1 . 45.57 1.6 1,2, 60.51 2.9 I , 2, 6

0.040 2, 3, 6, 80.127 or 0.406 1,4 ,6

0.812, 1 .15 4, 5, 6or 1.835.0 to 6.5 1.82 5, 6( a c e t one )

18 .6 l ow up t o 60 2 , 7 , 8f in o.d.22 .4 4 2 , 3 , 6 , 810,1119.1 4 2,7 ,8

12.7 o.d. 5 .5 (R123 ) I11 . 7 ( RI O

Electrodegap (ram)6 . 35 o r 25 .4 2 , 3 , 6 , 9 , 105.0 to 20.0 2 3, 7, 9

3.0 4.4 2, 3, 6, 10II

System(s)Hea ted sphe re 2, 3 , 6 , 8 , 9a n d p l a n ee l e c t r ode .H e a t e d w i r e( 0 .356 mm d i a . )be t w e e n 25 . 4 mm d i a .d i s c sspa c e d 25 .4 mmor ( a symme t r i c a l l y )12.7 mm a l ia .sphe r e s w i t h60 . 3 mm ga p .H e a t e d w i r e s0.05, 0.070 . 10 a n d 0 . 5 0 r a m d i a .pa r a l l e l t o 6 . 0 mm d i a .c y l i nd r i c a l e l e c t r ode .

2 , 3 , 6 , 1 1

1 , 2 , 3 , 6 , 1 1

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E l e c t r o h y d r o d y n a m i c e n h a n c e m e n t o f h e a t t r a n s fe r a n d f lu i d f l ow 4 0 7Z h o r z h o l i a n ia n dS he kr i l a dz e [ I 12 ]

R u t k o w s k i [ 1 1 3]

Y a b e a n dM a ki [ 114]

S c h n u r m a n na n d L a r d g e[57]

Tube bundlesD a m i a n i d i s ,K a r a y i a n n i s ,A I - D a d a h ,J a m e s ,C o l l i n sa nd A l l e n [ 115]O g a t a ,I w a f u j i ,S h i m a d a a n dY a m a z a k i[16]

D a m i a n i d i s ,K a r a y i a n n i s ,C o l l i n s a n dA l l e n[116]

A c t e o n e , H e a t e d 3be nz e ne ho r i z on t a l ( a c e t one )n - p e n t a n e t u b e s , 6 . 0 a n d8 . 0 mm d i a . , pa r a l l e lt o p l a ne e l e c t r ode .V e r t i c a ls e mi - c y l i nd r i c a lh e a t e d c h a n n e lf a c i ng p l a ne e l e c t r ode .L i q u i d n i t r o g e n H e a t e d h o r i z o n t a lw i r e , 0 . 10 r a m d i a . ,pa r a l l e l t o 3 .0 mmc yl i nd r i c a l e l e c t r ode .R113 / e t ha no l H e a t e d 2 . I( " F u r o n s u b u r u p l a n e b e n e a t hA E ' ) t o ro i d al E H D" 'pump" e l e c t r ode .n - h e p t a n e , H e a t e d2 0 % s o l u t i o n e a r t h e d w i r eo f i s o p r o p y l 0 . 1 27 m m d i a .a l c oho l i n a nd 260 .0 mmn- he p t a n e , l ong e l e c t r odep e r f l u o r o m e t h y l c y c l o h e x a n e b e t w e e nt w o p l a t e s254.0 x 508.0 mmo n e e a r t h e d a n done a t h i gh po t e n t i a l .R114 L ow f i n t ube s ,d i a . 19 .05 mm ,f i n p i t c h 0 . 7 r a m.P e r f o r a t e d p l a t ea n d r o de l e c t r ode .R I 2 3 5 - t ub e s m o o t ht u b e b u n d l e ,22 mm d i a . 0 . 5 ml ong . S t e e lr od e l e c t r ode s6 m m d i a . 3 m mf r om t ube s .

5 0 - tu b e s m o o t ht u b e b u n d l e ,22 mm d i a . 0 . 5 ml ong . 12 e l e c t r odew i r e s 3 mm f r om t ube s .8 0 - tu b e s m o o t ht u b e b u n d l e .22 mm d i a . 2 mlong. Stee lr od e l e c t r ode s6 m m d i a . 3 m mf r om t ube s .

R l l 4 9 l o w f intubes , f inr o o t d ia . 1 7 . 6 m m ,f i n he i gh t0 . 5 mm , f i np i t c h 0 . 88 mm.9 s m o o t h t u b e so.d. 19.1 mm .P e r f o r a t e d b r a s s p l a t ea n d r o d e l e c t r o d e

~ 7~ 7

~ 2

2 . 5

7

7

2 . 5

1 . 3

1,2,3,6,12

3 , 6

2 , 7 , 8 , 1 3

2 , 6 , I I

2 , 7 , 8 , 1 1

2 , 6

2 , 6

2 , 7

2 , 7 , 8

2 , 7 , 8

N o t e s :( I ) D i e l e e t r ophor e s i s a na l yz e d .(2) D.c . e le c t r ic fie ld.(3) A .c. elec tr ic f ield.( 4 ) E ff ec t o f E H D on m i n i m um f i l m bo i l i ng .(5) A.c . e lec t r ic f ie ld f requ ency v ar ied.(6 ) Elect r i ca l l y hea ted source .(7 ) F lu id hea tcd source .( 8 ) E b u l l i t i o n i n i t i a t e d b y E H D .( 9 ) H i g h th e r m a l ca p a c i t y so u r ce .( 1 0 ) F i n e w i r e m e sh o r a r r a y h i g h vo l ta g e e le c t ro d e .( I I ) O b se r va t i o n s o f b u b b l e d yn a m i cs .( 1 2 ) C o r r e l a t i o n su g g e s te d .( 1 3 ) En h a n ce m e n t b y l i q u i d j e t ( b u t b u b b l e d yn a m i cs a l so a f fe c te d ).

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408 P. H. G. ALLENand T. G. KARAYIANNISO~' ( kW/mZK )

I B ' = r c t " ~ ' ~ ' = " ~ z [ i [

L iL

i

1 i1 3 6 10 30

( T , - T o ) KF i g . 3 . EH D e n h a n ce m e n t o f R 1 2 co n d e n sa t i o n w i t h e l e c t r o d e vo l t a g e s 2 0 , 2 5 , a n d 3 0 kV a t o u te r su rfa ceo f s m o o t h h o r i z o n t a l t u b e c o m p a r e d w i t h E N D - f r e e s m o o t h a n d l o w f i n s u rf ac e tu b es ( T s = 30C) [96].

e n h a n c e m e n t w a s s i g n if ic a n t, s ee F ig . 7 . N o e n h a n c e m e n t w a s o b t a i n e d f o r t he s m o o t h t u b e b u n d l ee x c e p t i n t h e c o n v e c t i v e r e g i m e . T h i s w a s a t t r i b u t e d t o t h e e l e c t ri c fi e ld d i s t ri b u t i o n . T h e e l e c t r o d eg e o m e t r y u s e d i n r e f. [ 11 5] r e s u l t e d i n r a d i a l e l e c t r i c f i el d w i t h t h e r e s u l t a n t E H D f o r c e p u s h i n gt h e b u b b l e s a w a y f r o m t h e h e a t e d t u b e s u r f a c e in s t e a d o f o n t o t h e s u r f a c e . T h i s w a s n o t t h e c a s ei n t h e w o r k r e p o r t e d b y O g a t a e t a l . [ 1 6 ] . T h e y t e s t e d t h r e e d i f f e r e n t t u b e b u n d l e s b o i l i n g R1 2 3a n d o b t a i n e d s i g n if i c a n t E H D i m p r o v e m e n t i n th e h e a t t r a n s f e r c o e f f ic i e n t ( s e v en t i m e s a t 1 8 k V ) .O g a t a e t a l . u s e d s te e l r o d s a n d w i r e s p l a c e d c i r c u m f e r e n t i a l l y a n d 3 m m a w a y f r o m t h e t u b e s a st h e e l e c tr o d e s . T h e n o n - u n i f o r m i t y o f t h e r e s u lt i n g e le c t ri c fi el d m o v e d t h e b u b b l e s t o w a r d s t h et u b e s u r f a c e a n d h e n c e e n h a n c e d t h e h e a t t r a n s f e r . T h e b u b b l e m o v e m e n t i n a l o w f i n g e o m e t r y ,w h i c h h a s a b e n e f i c ia l e f f e c t o n t h e h e a t t r a n s f e r s u r f a c e , w a s d i s c u s se d e a r l i er . B o t h r e s e a r c h g r o u p sr e p o r t e d t h a t E H D e n h a n c e m e n t o f b o i l in g h e a t t r a n s f e r i n b u n d l e s i s a s ef f ec t iv e a s o n a s in g let u b e .

E H D b o i li n g in s id e t u b e s w a s s tu d i e d b y Y a b e e t a l . [ 1 1 9 ] u s i n g a 1 0 m m i n s i d e d i a m e t e rc u p r o n i c k e l t u b e a n d a c o a x i a l c y li n d r ic a l p e r f o r a t e d s t e e l e l e c t r o d e o f 5 m m d i a m e t e r . T h e E H Db e h a v i o u r o f t h e n o n - a z e o t r o p i c m i x t u r e o f R 1 2 3 a n d R 1 3 4 a w a s s t u di e d. A n e n h a n c e m e n t o fa l m o s t t h r e e t i m e s w a s o b t a i n e d i n t h e h e a t t r a n s f e r c o e f f i c i e n t . A c h a n g e i n t h e f l o w p a t t e r n f r o ms t r a t i f i e d t o a n n u l a r w a s a l s o o b s e r v e d . T h e e n h a n c e m e n t r a t i o d e c r e a s e d a s t h e m a s s f l u x t h r o u g ht h e t u b e i n c r e a s e d . T h e r e s e a r c h e r s a l s o v e r i f i e d t h a t f o r a g i v e n t h e r m a l d u t y , t h e p r e s s u r e d r o pa c r o s s t h e e v a p o r a t o r i s t h e s a m e , w i t h o r w i t h o u t E H D .

ta g 3 .0a 0

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1 " 0 1 5 2 0 2 5 3 0 3 5 4 0Electrode vol tage (kV )Fig. 4. EHD enhancem ent of R I14 co ndensation at ou ter surfaces of vertical and horizontal tubes(AT = 25 K, TO 90'C) [961.

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