Mourad André Bontemps

come

Enhanced heat transfer in shell-side condensation

INTRODUCTION

Enhanced Heat Transfer in

Shell-Side Condensation

Andre Bontemps* and Mourad Belghazi

Universite Joseph Fourier

LEGUGRETh CEA Grenoble, France

The typical example of a non-compact heat exchanger is the shell-and-tube type.

However, many attempts have been made to increase the compactness of such heat exchangers. Among these are the use of enhanced surface tubes in order to replace the smooth tubes still used. This paper describes the evolution of experimental observations and reviews the main models available in the literature for predicting the shell-side heat transfer coefficients for single tubes and tube bundles for pure fluids and azeotropic mix tures and for non-azeotropic mixtures.

ln the case of condensation of pure fluids, heat transfer is controlled by the thermal resistance of the condensate fil.m. The augmentation of condensation heat transfer can be achieved through thinning the condensate film. This can be obtained by draining the con densate via gravity, surface tension or, more rarely, electrical or other mechanical forces.

Another way is to augment turbulent mixing of the condensate. In the case of mixtures, a supplementary resistance appears which is produced by the accumulation near the liquid vapour interface of a layer of the more volatile vapour whose condensation rate is lower than those of the other vapours. This resistance controls condensation heat transfer in most cases and the ways to augment heat transfer should be different.

A large number of specifically designed enhanced surface tubes have been tested to find tlhe best surface geometry for condensing either pure fluid or vapour mixture. These surfaces can be classified in three types: one-dimensional ( 1-D) surfaces (smooth tubes), two-dimensional (2-D) surfaces (with transverse plain fins) and three-dimensional (3-0)

surfaces (with interrupted fins, spines, wires, etc ... ). The 2-D and 3-D surfaces allow the surface tension effects to be enhanced. Moreover, other enhancement techniques can be employed by using promoting systems attached to the tubes such as drainage strips or external systems such as electric fields.

In this paper, main results concerning condensation heat transfer at the outside of smooth tubes are recalled to serve as a reference. Then, main experimental results and theoretical methods of performance prediction are presented and discussed for 2-D sur face tubes. Finally. some resuhs and theoretical models are presented for 3-D surface tubes and comparison is made with 2-D surfaces. Several relevant reviews have already been presented by many authors. One can cite Marto ( 1984) for smooth tubes and heat transfer augmentation techniques and Marto ( 1988) for smooth or integral-fin and enhanced surface tubes, Webb ( 1988), [START_REF] Sukhatme | Condensation on enhanced surface horizontal tubes[END_REF] and more recently, Browne and Bansal ( 1999). The role of surface tension was emphasised by [START_REF] Shah | The role of surface tension in film condensation in ,extended surface passages[END_REF] and Yang ( 1999) .. A statistical review was carried out by Rifert ( 1998) in which are included the basic principles of models as well as the dynamic of the published works from 1947 to 1997. Whilst the effects of the vapour velocity will not 1Ģ considered here it is useful to mention the paper of Cavallini et al. (1996) which is, to our knowledge. the only work which looks at the effects of vapour velocity on condensation on integral-fin tubes.

However, these reviews concerned essentially condensation of pure vapours. For this rea son, special attention will be paid to vapour mixtures of which few results have been pub lished in the literature.

PURE FLUIDS 1.1 Single horizontal smooth tubes

The early film condensation analysis for a horizontal smooth tube was carried out by [START_REF] Nusselt | Die Oberflachen Kondensation der Wa sserdampfes[END_REF], with the following hypotheses: heat transfer in the liquid film restricted to conduction, pure vapour at saturation temperature 1ûtat' wall temperature Tw uniform and no shear at liquid-vapour interface. Neglecting momentum effects, a balance of the shear, gravity and pressure forces leads to the classical expression of the average heat transfer coefficient: (1)

where p1 and p,, are the liquid and vapour density respectively, }1 1 the liquid dynamic vis cosity, 11 the liquid thermal conductivity and &11v the latent heat of condensation.

Defining the Nusselt number Nu by: a D Nu=-

(2)
1t, formula (I) can be written by using dimensionless numbers, as ( )t j-1

Ga Pr1

Nu Nu = 0. 1Y8 Ph

where Ga is a Galileo number defined by

Pr 1 the liquid Prandtl number and Ph the phase change number:

Ga = 8 (P I -P1• ) p,i D3 2 Pt v, (3)
(4)

(5) (6)
The other way is to define a Nusselt number independently of geometry (also called condensation number) by writing or by u. ing the above defined dimensionless numbers:

[ I ) . ]' / -1 •� - ,,
Nu -0. 72 8 1/ i Ga • Ph (9) (I 0)

Numerous studies followed the pioneering work of Nusselt accounting for condensate subcooling [START_REF] Rohsenow | Heat transfer and temperature distribution in laminar film condensation[END_REF], vapour superheating, inertial forces (Span-ow & Gregg, 1959) and shear stress. Nevertheless, the Nussclt formula remains a� a standard to calcu late the heat transfer coefficie nt when the vapour is stagnant. Note that this formula was established by assuming the fluid thermophysical properties to be constant and taken at the saturation temperature. It is accepted now that the nuid properties are to be taken at a characteristic temperature which is often chosen as the arithmetic average T1 between the wall temperature Tw and the saturation temperature 1úw r (I I)

A diffe rence up to I 0% may be observed when using different characteristic temperatures Other characteristic temperatures can be used, in particular if condensate subcooling is taken into account.

(Figure I). 2300 2100 e � 1900 - �1700 1500 •• • ., I "• , ...• •• ••• •• ">, • ... .. ... . . .. . 1--. Nusse'\T 1.r J ....... Nusselt (T 1 .. r:, • measurements • .. •-•-• 1300 +-----------------+---------------��---------------4-----------------+---------------

I .2 Smooth tube bundle

With the same assumptions as in the case of a single tube, Nusselt analysed conden sation on horizontal banks of smooth tubes. He assumed all the condensate dropping from any tube fa lls on the next lower tube. He found that the heat transfer coefficient averaged over all n tubes in a vertical bank is given by: or a, = 0. 728 a1 being the heat transfer coefficient of the top tube. The experimental data for banks of tubes falling above the values of the equation ( 13), Collier and Thome ( 1994). [START_REF] Kern | Process Heat Tr an� fe r[END_REF] proposed to adapt this formula by modifying the 1/4 exponent to take into account the dif ference between actual phenomena (ripples, etc ... ) and ideal model of Nusselt. This kt.l to a family of correlations of the form: a,, = , -r a , ( 14) y= I /6 being the value proposed by Kern. For the jl11 tube, one obtain. the following rela tion:

a j _ -t -r ( ' I J ' •r --} -j- a , ( 15
)
This modification does not account for the dependence of aj on the heat nux or on the temperature difference T.wt -T," . Chen ( 1961) suggested that since the condensate is subcooled, further condensatiolil can occur on the liquid falling from one tube to the other. Assuming all the cooling energy is removed and considering the additional effect of the momentum gain. he found the following result:

Single integral-fin tubes (2-D)

The basic surface extension is the low-fin 2-D geometry. These fins are either rectan gular or trapezoidlal and the fin density can vary from 433 fins per meter (fpm) or 11 fins per inch (fpi) to 1640 fpm. (42 fpi). Other 2-D geometries were used whose most com mon are given in fig ure 3. The effect of the fins is to drain the condensate either by gravity or by surface tension effects, improving the heat transfer coefficient. However surface tension effects are also responsible for condensate retention or flooding between the fins in the lower part of tubes which deteriorate the heat transfer coefficient (Figure 4). The resulting coefficient is a compromise between these two effects.

Gravity drainage models

The fi rst model to analyse the condensation on rectangular fi ns was developed by [START_REF] Beatty | Condensation of vapors on outside of finned tubes[END_REF]. These authors neglected surface tension forces and considered a Nusselt-type condensation on a vertical plate ( fin flanks) and on horizontal tubes (fin tips and space between fins). The heat transfer coefficient can be written as

I [ A r 1 7 JA! l an K = --a"+ a,. TJ A A (I 7)
where a H and a P are the heat transfer coeffLcients given by Nusselt for horizontal tube and vertical plate respectively and where A1 and Ar are the surfaces of the fin flanks and of the tube parts between the fins respectively. The total surface is A=A,.+Ar 11 is the surface efticiency (taken as I by Beatty and Katz) and n1 the fin efficiency.

This heat transfer coefficient can be written under the classical form:

-,;.8 9 (C o Pt; )1 /.f ( f) l t / .f I a a K -O.IJ - ---.!... - -

Ph l>eq TJ

where the equivalent diameter is defined as

( ;,'! r = I J 1 1 1 (A� )[ .f' H � r /);. / , l
and where e"q is an equivalent tin height

(20)

In tine above formulae, De and Dr are the diameters at the tin tip and at the fin root respec tively (Figure 5).

The Beatty and Katz formula was improved by Smirnov and Lukanov ( L 972) to account for fin tips. the formula is unchanged if using the new equivalent diameter:

( l l / .f ( l ( l ( I J ( J ( J

I A f I A, I Ar I -- =1.317[ ---+---+--- D ('( ,
A ,lf f' :.(,.f A ct t {) : / .J A eq D :./-1 1.3.2. Surface tension ef f ects a -Retention angle Several authors ( see for instance [START_REF] Rudy | An analytical model to pred ict condensate retention on horizontal integral-fin tubes[END_REF], [START_REF] Masuda | Static configuration of liquid films with low radial fins: impl ications for condensation heat transfer[END_REF]) have calculated and/or measured the angle e1> 1 of the liquid rise height between the fins. The widely accepted value is that calculated by [START_REF] Honda | Augmentation of condensation on horizontal finned tubes by attaching a porous drainage plate[END_REF] who developed an approximate expression for tlhe unflooded angle C!>: Moreover, [START_REF] Masuda | Static configuration of liquid films with low radial fins: impl ications for condensation heat transfer[END_REF], by observing static liquid retention have shown that the liquid can be retained on the upper part of the tube (unflooded region) at the bound ary of the fm flank and of the tube surface. b -Heat trans f er coe f ficient The most simplest method to account for condensate retention by surface tension fo rces is to use the Beatty and Katz theory by substracting the submerged part of a tube.

In their model, Beatty and Katz do not take into account explicitly the flooding of the lower part of the finned tube. However, the coefficient 0.689 in place to 0.728 has been obtained by fitting experimental results for condensation of 6 fluids on a low fin density tube. Butrymowicz and Trela (1997) consider that such a modification is the consequence of condensate retention allowing the flooding angle to be determined as (/> -0.689

f -0.728
Such a constant value is not in agreement with the theoretical results. A first attempt to account for the variable flooded region was made by Rudy and Webb (1981) in as.suming that only the unflooded region is active. They wrote a =anK ; =anK (I � <1> : ) =anK ( I � Cv)

(24)
where C b is the fraction of the tube which retains the condensate. The authors fo und that this equation underpredictetl their experimental results and po. tulated that other mecha nisms occurred to drain the condensate. Another approach is to account for the retention effect by doing a weighted average of the heat transfer coefficients for the flooded and the unflooded region. Sardesai et al. ( 1982) and Owen et al. ( 1983} proposed an extension to the Beatty and Katz model and expressed the average heat transfer coefficient as: or under the form:

( P ) 1 / -1 * , . , Nu =0.728 I /� Gtl • Ph (25) _ e _ {1-C b ) + _ e Cb l( {) J l / -1 ( /) ) 1 / -1 '1 [)til I), . (26)
where a h is the heat transfer coefficient in the flooded zone calculated from usual corre lations for single phase flow. However, these authors fo und al o that this method under predicted the experimental results.

We bb et al. ( 11985) developed a theoretical model which assumes that (i) equation ( 17) applied only for the unflooded fraction and (ii) the heat transfer coeffi cient on the fin flanks a1 is established by assuming that surface tension is the dominant force in conden sate dramage from the fin surface. They proposed the equation:

( A . Ar +A, ) a 11 = ( I -Cb ) a H -t + 11 f a 1 • A + Cb ab (27)
where aH is the heat transfer CQefficient on the unflooded root surface of the tube between tins. The determination of a r is made by using the method of [START_REF] Adamek | Bestimmung der Kondensation-grossen auf Feigewellten Obertlachen zur Auslegun Optimaler Wandpro file. Wiirm e-1111d Stoffii bertJ[END_REF] who describes the curvature of the• surface condensate with a function depending on an expo nent t; who e exact value i difficult to know. They fou nd that their model predicted their experimental data for R-1 I to within ± 20 %and Wan niarachchi et al. ( 1986) fo und that their experimental data for steam were predicted within about ± 20 % except fo r com pletely flooded tubes.

The most complete but complex method was developed by Honda and Nozu ( 1987) to predict the average heat transfer coefficient for film condensation on horizontal tubes with trapezoidal fins. In their model, the tl!lbe is divided in flooded and unflooded region (Figure 6). On the fin surface, the authors assume that the condensate is drained by sur face tension and gravity and that in the interfin space the condensate is drained only by gravity. They solve numerically the equation for the condensate film thickness and, based on their numerical results, they give an approximate expression for the Nusselt numbers in both the unflooded (Nud,) and flooded (Nud f ) regions. They finally give the average heat transfer coefficient under the form: ... where 11 is the tin efficiency, T wu and T 11'( are the dimensionless wall temperatures in the unflooded and flooded zones respectively. In the model are included the wall temperature variations determined by an iterative procedure. The model predicts the experimental results of various investigators within ± 20 %. A further extension of this analysis by [START_REF] Honda | A generalised pred iction method for heat transfer during film condensation on a horizontal low ti nned tube[END_REF] reduced the prediction to within ± I 0 %. Another model was presented by [START_REF] Adamek | Pred iction of tilm condensation on horizontal integral finned tubes[END_REF] for predicting the heat transfer coefficient for condensation on tubes with trapezoidal or rectangular fins. In their model, the tube surface is divided in 3 regions: unflooded, flooded and drop-off zones. This last zone, where a condensate drop is formed, insulates the fin tips. The heat trans fer in this zone, estimated to represent I 0 % of the tube circumference, was neglected. The average heat transfer coefficient is given by:

4 N f Leclr 1Èht" ( .
. )

a A w = A L1 T '<"wr J 1oo ded + m floodtd (29)
where N 1 is the number of fins per meter, Lel'll the tube length and A the heat exchange sur face area. The mass flow rate 1iz1111f1o o ded is determined by adding the contributions of the different parts of a tin in the unflo. oded region. The mass flow rate ,;,flooded is given by the condensate formed on the fin tip which is considered as the only active part in the flood ed region. This model is rather easily usable since it does not need a iterative procedure. It was tested with 7 fluids and 80 different tube geometries and predicted the experimen tal results to within± 15 % for most of them.

More recently, [START_REF] Sreepathi | Heat transfer during film condensation of R-123 vapour on horizontal integral-fin tubes[END_REF] have developed a generalised correlation from a theoretical model in which the fin tube surface has also been divided in two region: flooded and unflooded. The fin surface was divided into three parts (i) the fin tip and the upper corner of the fin where the condensate flow is assumed to be smface tension driv en (ii) the fin flank where the condensate flows by gravity (iii) the valley part for which an empirical relation was used. Using the different heat transfer correlations for each part, they obtained the correlation:

Nu = Ph " 1 ( D; } C1r (2 • C b )C�8 Su "2 'I' 1 12 + C • I f. Cb JC'f:,:'Ga "3 I (Deb,)
+co. cb J ---,;-8

(30)
where 8 is the condensate thickness in the valley region, Su is the surface tension number, n1, 1r2, n3, n4, C 1 , C , . and Care constants which have been determined by comparison with experimental data for fluids as different as R-123, R-I I, water and ethylene glycol with different fin geometries. They obtained:

n 1 = 0./8, n 2 =0.25, n3 = 0.2/, n4 = 0.51 c, = 1.14, c,. = 2.40, c = 0.97.
This. corre lation predicts the heat transfer performance to within ± 30 % or better depend ing on the fluid.

A different appro<:.eh was employed by [START_REF] Rose | An approx imate equation for the vapour-side heat transfer coefficient for con densation on low-tinned tubes[END_REF] by using approximate relations and dimensional analysis arguments to obtain an algebraic expression of a condensation enhancement ratio £defined as the rat io of the heat transfer coefficient of a tinned tube based on the surface area of a plain tube with diameter equal to the fin root diameter, divided by that of a plain tube with diameter equal to the fin root diameter at the same vapour-side temperature diff erence. At given t1T, this enhancement ratio is:

where

De t, $ (1 -fr)(f)i-D, 2) T 1Īt.r = --0+- r+ D,. p rr cosO 2/J,. p • f.1l 2a tan(cP/2) • J p p, Dee <P f ::: 4 a Wll( 1Ĭ/2) . s p g /)(' b,. cP 1ù = (!!.L. . + 0.51 (J 0,. 3 /) e ( pI -p ,. ) !!. t , )1 /.J T f = 2.82 D,. + 0.51 a 0,. ( ) 1 /.J e m.
( Pt-p,. )g e3 (31)

(32) (33) (34) (35) ( 36
)
and em is a effect�ve mean vertical fin height given by: eC/J e =--for C/J �TC I 2

111 sin cP eC/J e111 = for C/J � 1C I 2 (2 -sin 1ī)
and �(fP) a function whose a polynomial approximation is:

�( (/>) = 0. 874 + 0.199110'2 (/>-0.2642 10'1 cP2 +0.553oio•3 C/J3 -0. 1363 w•2 <1> 4 (37) (38) (39)
Some of the terms of this equation depend on constants determined by fitting existing experimental data. In particular the 8 1 constant is taken as 8 1 = 2.96. Briggs and Rose ( 1994) improved the model by accounting for fin efficiency.

The last two methods can be easily used without iterative procedures . Moreover, the Rose method shows a correct variation of the heat transfer coefficient as a function of fin pitch. Briggs and Rose ( 1999) give a detailed comparison of the results of many of the pre viously described models, with a large data base of experimental results.

Optimisation principles

Despite the considerable number of theoretical models proposed in the literature, the prediction of the optimal fin parameters (geometry, fin spacing, fin height and fin thick ness) is still not accurate. As a result, interest was focused on experimental studies in order to investigate the effects of various fin parameters on the vapour-side heat transfer coeffi cient. In this section some investigations related to the optimal fin parameters will be pre sented.

a -Fin height An increase in the fin height results in a surface exchange augmenta tion, which enhances the heat transfer coefficient. On the other hand an increase in the fin height increases the flooded fraction and also reduces the conduction heat transfer through the fin, which deteriorates the heat transfer coefficient. These two antagonistic tendencies yield to an optimum fin height. [START_REF] Wanniarachchi | Film condensation of steam on horimntal lin ned tubes: effect of fin spacing. thickness and height[END_REF] provided experimental data for steam condensation outside a horizontal copper tube with rectangularly-shaped fins. The tubes have a fin spacing of 1.5 mm, a fin thickness of I mm and four different fin height (0.5 mm, I mm, J .5 mm and 2 mm). They found that the enhancement ratio increases with increasing fin height, but the percentage increase in the enhancement ratio is less than the percentage increase in area ratio. A fin height of 2 mm gave the best heat transfer performance. [START_REF] Das | Effects of fin height and thermal conductivity on the performance of integral-fi n tubes for steam condensation[END_REF] conducted experiments during condensation of steam on integral finned tubes. Four different material tubes (Copper, Aluminium,

Copper-Nickel and Stainless Steel) were tes.ted, with diameters at the fin base of about 14 mm, and fin heights ranging from 0.4 to 1.5 mm. They found that when increasing the fin height the enhancement ratio increased for higher conductivity tubes (Cu. Cu-Ni and AI), and decreased with lower conductivity tubes (Stainless Steel). The Stainless Steel tube behaviour was explained by the fact that the effect of conduction through the fins is stronger for lower conductivity materials. They indicated! that the optimum tin height lies beyond 1.5 mm for high conductivity tubes and may lie below 0.5 mm for Stainless Steel tube.

b -Fin thickness [START_REF] Wanniarachchi | Film condensation of steam on horimntal lin ned tubes: effect of fin spacing. thickness and height[END_REF] conducted experiments on the conden sation of steam on horizontal copper tubes with diameters at the fin root of 19 mm, a fin spacing of I mm and a tin height of I mm. They found a best fin thickness in the range of 0.75 mm to lmm. When the fin thickness was increased (> I mm) the surface area decreased and resulted in a decrease in the HTC. When the fin thickness was decreased below 0.75 mm, the amount of condensate retained in the intertin spaces was more impor tant, which lead in an increased thermal resistance and a decrease in the heat transfer coef ficient. [START_REF] Briggs | An experimental investigation of condensation on integral fin tubes: effect of ti lm thickness, height and thermal conductivity[END_REF] experimentally investigated the fin thickness influence on the con densation heat transfer coefficient during condensation ofCFC 113 and steam outside hor izontal finned tubes. They tested three tubes made of different materials (copper, brass and bronze) with rectangular-section fins, having fin spaci ng of I mm, two different fin heights (0.9 m111 and 1.6 111 111 ), and fin thickness in the range 0.25 to 0.75 111 111 . The other geometric parameters were the same for all tubes. For CFC I 13 the enhancement ratio shows a minimum for a fin th ickness of 0.5 mm. This minimum was the same for all three tube materials and for both fin heights. For steam they found that there is slight increase in enhancement ratio when the fin thickness increases. They explained this by the fact that a lin thickness increase resulted in conductance of the thicker fins, which outweighs the decrease in surface area.

c -lnrer-j in space The two antagonistic phenomena (the condensate drainage on the fin sides and the condensate retention) due to the surface tension forces suggests the exis tence of an optimal inter-fin spacing and this optimum depends on the fluid nature. [START_REF] Marto | Film condensation of steam on hor izontal tinned tubes: Effect of tin shape[END_REF] experimentally studied the steam condensation on copper tubes having a diameter at the fin root of 19 111m, a fin thickness and a fin height of I mm. They found that the optimal inter-fin space is about 1.5 mm.

Sreepa thi et al. ( 1996) conducted condensation experiments outside a horizontal cop per ttUbe with HCFC 123 as the working fluid. They noted that for a tube with a fin spac ing of 0.85 mm and a fin thickness of 0.15 mm the optimum fin base spacing value is around 0.3 rnm. They pointed out that the heat transfer performance is very sensitive to fin buse spacing around the optimum value.

Belghazi (200 I) condensed HFC 134a outside copper horizontal finned tubes with trapezoidal shaped fins. The diameter at the fin base is about 16 mm and the fin height is 1.4 mm. He fo und the optimal fin spacing to be around 0.6 mm. d-Tube diameter An experimental study conducted by [START_REF] Michael | Filmwise condensation of R-113 on horizontal integral-tin tubes of diffe rent diameters[END_REF] provides CFC I 13 data during condensation on copper tubes having three diffe rent diameters ( 1 2.7 mm, 19.05 mm, and 25 mm). All the tubes have a fin thickness and a fin height of 1 mm and fln spacing of 0.25 mm, 0.5 mm, 1 mm, 1.5 mm, 2 mm and 4 mm. Although it would appear that the tube diameter has negligible effect on the heat transfer enhancement ratio due to the normalisation method, it is found that this ratio increases with tube diameter, probably due to decrease in flooding.

e -Fin shape pro file The fin shape optimisation is of a great importance in the enhancement of integral-fin tube performances. [START_REF] Gregorig | Film condensation on finely rippled surfaces with consideration of surface ten sion[END_REF] performed a theoretical study assuming that the surface tension fo rces are dominant, and proposed an optimal fin profile which drains more easmly the condensate on the fmn flanks, and gives an effective enhancement of the vapour side heat transfer coefficient. [START_REF] Marto | Recent progress in enhancing film condensation heat transfer on horizontal tubes[END_REF] conducted experiments during condensation of steam on horizon tal finned tubes. Data were obtained for copper tubes with fins of rectangular, triangular, trapezoidal, and near-parabol ic cross sections. They concluded that the near-parabolic fin shape providing a gradually decrease in curvature from the fin tip to the fin root results in an increase of I 0 to 15 percent in steam-side heat transfer coefficient compared to the heat transfer coefficient of the three other finned tubes tested. [START_REF] Webb | Row effect for R-11 condensation on enhanced tube[END_REF] compared the performance of the Gewa SC tubes with a "Y" shaped fins to I 024 fin per meter integral-fin tube during condensation of R II, they found that the average condensation coefficient of the Gewa SC tube is 27 percent higher than that of the I 024-fpm tube.

Kedzierski and Webb ( 1990) proposed a fin profi le with a curvature changing monot onically from the tip to the middle part of the fin foanks and having a small fin tip radius. A numerical study of [START_REF] Zhu | Optimisation of fin geometry of a hori.wntal low-finned condenser tube[END_REF] reveals that the optimum fin shape resembles the fnn shape proposed by Kedzierski and Webb ( 1990).

Blane ( 1994) condensed R l34a and R22 outside the Gewa SC and the Gewa K26 (I 024 fpm) tubes. He pointed out that the vapour-side heat transfer coefficient of the Gewa K26 is 15 percent higher than the Gewa SC tube, because the retention of the condensate in the lower part of the tube is greater for the Gewa SC tube than of the Gewa K26 tube. He noted also that the Gewa SC overall heat transfer coeffi cient is 40% higher than the K26 value because the Gewa SC has a finned inner surface. [START_REF] Honda | Effect of circumferential rib on film condensation on a horizontal two-dimensional fin[END_REF] proposed a fin profi le with a circumferential rib on the flank of a two-dimensional fin. They concluded that the circumferential ribbing enhances the film condensation on a hor�zontal two-dimensional fin tube. The enhancement is more significant for a double rib than for a single rib fin.

Lmr integra/finned tube bundle

The models developed for a single enhanced tube are not directly applicable to tube banks, since the heat transfer in the lower rows is affected by condensate inundation and the HTC is lower for these tubes. In the literature there are two approaches to thi prob lem:

The fir t simply consists in applying the Nu. selt approach developed initially for smooth tubes. [START_REF] Katz | Condenstion of six tinned tubes in a vertical row[END_REF] where r is the flow rate of falling condensate per unit length.

(40)

In the column mode case there is an affected (A-region) and an unaffected (U-region) regions, whereas in the sheet mode case there is just one region (A-region) see figure (6). Then, they calculate the heat flux for each region and deduce the average heat flux of the considered• tube as in the single tube case, taking into account the proportion of sum-face area covered with impinging condensate. The comparison of this model to the experimental results of Marta ( 1986) who pro vided data of steam condensation outside a bundle of horizontal finned tubes shows an under-estimation of experimental results ranging from 5% to 20%.

Murata & Hashizume ( 1992) developed a model predicting the HTC of tube bundles having rectangular fins. For this purpose they carried out an analysis of the film conden sate. The inundation is taken into account through the condensate flow rate of the upper tubes which leads to a modification of the condensate thickness in the interfin space. To validate their model they compared it to experimental data during condensation of R II and R 114 in bundles of 8 rows, with rectangular fin tubes of various fin pitches. Theory and experiments differed by about 20%. Belghazi (200 I) provided data of HFC 134a con densation outside five commercial horizontal finned tubes (Ki t, K 19, K26, K32 and K40 tubes having II, 19, 26, 32 and 40 fins per inch respectively). He fou nd that the Katz & Geist ( 1948) correlation gives good results for the tubes having high fin densities (K26, K32 and K40) but underestimates the inundation effect for the K II and K I 9 (Figure 7). He also pointed out that the Honda et al. ( 1989) and Murata & Hashizume ( 1992) models did not give a significant amelioration in comparison to the [START_REF] Katz | Condenstion of six tinned tubes in a vertical row[END_REF] corre lation (Figure 7), despite of their rather complex approache .

• ••••••••• ••• ••••••••• ••••••••• . .
1.5 Spec ial enhanced stuface tubes (3D)

I Sill g le tube

A lot of geometries have already been tested, for example, spine [START_REF] Webb | Investigation of surface tension and gravity effects in film condensation[END_REF], saw-tooth shape (Webb andMurawski, 1990, Cheng andTao, 1994), Gewa C+ (Belghazi, 200 1). To study the surface tension effects in 3-D geometries (spines), experiments were con ducted by [START_REF] Webb | Investigation of surface tension and gravity effects in film condensation[END_REF]. A gravity ba ed model failed to represent experimental re ults whilst a surface tension based model predicted the condensation coefficient with in 10%.

Belghazi (200 I) developed a model to determine the heat transfer coefficient during condensation of HFC 134a on a Gewa C+ tube (Figure 8). He divided the tube into four regions : (a) the fin region upon the notch, (b) the fin region below the notch, (c) the fin f1ank between two notches and finally the circumferential region between the fins. He as umed that the condensate f1ow is surface tension driven in the regions (a) and (c), and is gravity driven in the regions (b) and (d). The heat transfer coefficient is given by : a b and a d are calculated from the Nusselt correlation for a vertical plane plate and for a (4 1) smooth horizontal tube respectively. a a and a c are also calculated from the Nusselt expression for a vertical plane plate, where the gravity force p1g is replaced by an equiv alent in terms of surface tension. He found that this model agrees fai rly (±I 0%) with the experimental results.

Tu be bundle

Webb & Murawski ( 1990) presented experimental results of condensation of R.l l on the shell side of a vertical bank of five horizontal tubes. They compared two kinds of three-dimensional tubes (Turbo C and Tred D) to integral fin tubes (I 024 fpm) and to the Gewa SC tubes. They pointed out that the turbo C tube shows the highest single-tube per formance.

They found that the data for all tubes fo llow similar curves, when plotted in a i versus

Re the condensate Reynolds number, the straight line curve fits yield equations of the form: aj = CRe-w (42)

They found further that w is equal to 0.58, 0.51, 0.22 and almost zero for the Tred D, Turbo C, Gewa SC and the integral-fin tube respectively concluding that the Turbo C and the Tred D have an important inundation effect.

Cheng & Wang ( 1994) tes�ed three three-dimensional tubes and compare its perform ances to low integral fi nned tubes of 26, 32 and 41 fins per inch, during condensation of stationary vapour of HFC 134a on a bundle of three rows. They concluded that the row effect (inundation effect) is more pronounced for three-dimensional-fin tubes than for low-fin tubes.

Honda et al. ( J 991 )( 1992) conducted experiments during condensation of R 113 on staggered and on in-line bundles of three-dimensional tubes and of flat-sided-fin tubes. They found that the inundation is more important in the in-line bundle than in the stag gered bundle, and there is more inundation in the case of three-dimensional-fin tube bun dle compared to the flat-sided-fin tube bundle. The same conclusion was fo und by Belghazi (200 I) for condensation of HFC 134a.

VA POUR MIXTURE

General

The studies of condensation heat transfer of mixtures were first linked to petrochem ical problems and the first theories of mixture condensation were established 65 years ago with the work of Colburn and Hougen (J 934). Their interest has increased again during the last decade with the use of new refrigerant mixtures. Nevertheless, there are very few publications on condensation heat transfer of mixtures on horizontal smooth or finned tubes. We can only cite two previous review papers: the first from Wang and Chato ( 1994) and the second from Thome ( 1994). An interesting review on condensation of mixtures on flat and finned vertical plates must be cited (Hijikata and Himemo, 1990) because the main parameters controlling heat and ma transfer are discussed. A li t of recent the<Oret ical studies of steady laminar film condensation of a vapour mixture on a flat plate is given by Rose et al. ( 1999). In this section we will give an overview of cur rent theories and of the experimental resu lts with underlining the main t7e atures compared to pure fluid condensation. Some new results obtained with the R23/R D4a mixture will serve as a base of discussion.

Current theories

For a mixture of several vapour , two cases have to be considered. First, �hen the mixture fo rms an azeotrope, the behaviour of the fluid is similar to that of a pure fluid. In this case, the temperature profile near the wall is comparable to the one seen fl gure 9 (a). On the contrary, for a zeotropic mixture, the less volatile vapour condenses prefer entially, the more volatile accumulating near the liquid-vapour interface thus creat�ng a layer (called diffusion layer) through which the less volatile component must diffuse (Figure 9 (b)).

As shown in figure 9 (a), the main resistance to heat transfer is located in the con densate film for condensation of a pure fluid. For a zeotropic mixture an additional ther mal resistance due to the vapour diffusion layer affec ts heat and mass transfer towards the interface. In most cases this latter resistance controls the condensation process. To deter mine the heat and mass flow rates, two methods are currently in use:

an equilibrium method caJied the "condensation curve" or "cooling curve" theory, -the film method.

Others methods have been developed which consist to solve the boundary layer equa tions for natural or forced convection of the vapour mixture parallel to a flat plate or per pendi,cular to a smooth tube.

1. Condensation curve methods

In these methods, developed by [START_REF] Silver | Gas cooling with aqueous condensation[END_REF] and [START_REF] Bell | An approximate generalized uesign method for multicomponentlpar tial condensers[END_REF], the fluids ( vapour, gas and condensate ) are assumed to be local ly in equilibrium throughout the condenser. In the Silver method the heat transfer coeffi cient aex, between the bulk gas and the condenser wall is calculated by:

I I Z R ---=--+-- aext 1 a 1 1} ag A , (43)
In this equation, a1 is the heat transfer coefficient for the condensate layer and the heat transfer coefficient a 8 is calculated for the gas phase flowing along the condenser by itself. The Zg coeftic ient is given by

Z X _ dT g = g Cpg dh/11 (44) (45) (46)
where X is the mass flow fraction of the gas, c is the specific heat of the gaseous mix ture anldT/d hm is the inverse slope of the equ{Jfbrium condensation curve hm = f(T ), hm being the specific enthalpy of the fluid. Ty pical condensation curve for a binary mixture is given in figure 10. In the liquid-vapour zone, one can distinguish 3 types of curves: (a) the concentration of the more volatile component is greater than that of the less volatile, (b) the two components have nearly the same concentration, (c) the conce.ntration of the more volatile component is smaller than that of the less volatile.

The main interest of this method is its simplicity, since the mass transfer parameters need not be known (diffusion coefficients in particular ). It is suffic ient to determine the condensation curve and the heat transfer coefficients a1 and a�. If Q is the heat flow rate, the local overall heat transfer coefficient U between the gas and the coolant is defined by:

(47)
where T8 is the bulk gas temperature, Tc the coolant temperature and where U is calculat ed by adding the thermal resistances:

I I I --= + ,.11'(1/1 + ( 48) U 1 arool A ; aext A1
where anwf is the coolant side coefficient, A; the internal heat exchange surface area and r"'1111 the thermal resistance of the tube wall. 2.2.2 Film theory This theory was first developed by Colburn and Hougen ( 1934) for con densation of a vapour in the presence of a non-condensable gas and ex tended by [START_REF] Colburn | The condensation of mixed vapors[END_REF] to condensation of a zeotropic binary mixture. Then, it was improved by [START_REF] Ackermann | WarmeObergang und molekulare Stoffli bertragung im gleichen Feld beigrossen Te mperatur und Partialdruckdifferenzen, (Simultaneous heat and mass transfer with large temperature and partial pressure differences)[END_REF]. The heat transfer coefficient ad between the condensate/gas illler fac e and the coolant is defined by the heat balance equation:

• ,.. Y -Y 1 a,t fT J-Tc )=a� (Tg -Tt)+ L11 1Jv f3o � (49) I-Yv
where T1 is the interface temperature, 1Ê1v the molar latent heat of condensation, r: , and Y� are the mole fraction of the vapour in the bulk gas and at the interface respectively. {30 * is the corrected mass transfer coefficient given by: where * .::

f3o = f3o -;- (50)
e--I

(5 1) fir is the total molar condensed flow rate and {30 is the mass transfer coefficient which can be obtained from the analogy between heat and mass transfer [START_REF] Chilton | Mass transfer coeffi cients prediction from data on heat transfer and fluid friction[END_REF]:

_ at:: ( Pr )213 f3o --1m: -- cPI� Sc ( 52
)
This coeffic ient can be calculated by using standard correlations for a, or by adapting these correlations from spec ific experiments [START_REF] Honda | Experimental measurements for condensation of downward-nowing R 123/R 134a in a staggered bundle of horizontal low-tinned tubes with fo ur geometries[END_REF].

8

On the other hand, the ad coefficient is given by:

I I I --= +r w + -- (53) ad 1 acoot A ; a , A,
The heat transfer coefficient a � is the gas-phase coefficient corrected for mass trans fer effect as:

(54)
The local overall heat transfer coefficient may be defined as:

Q = U 1 ( T8 -Tc )=ad Ao ( Tt -Tc ) (55)
A systematic comparison between the film and the condensation curve methods was conducted by Webb et at. ( 1996) who indicated the limits of the latter method.

2.3 Smooth tubes 2.3. 1 Sin g le horizontal smooth tube Many papers have been published on condensation on horizontal smooth tubes, in the presence of non-condensing gas. To the authors' knowl edge, few studies have been carried out on condensation <Of a vapour mixture on a smooth tube and most of them up to 1990 were listed by Fuji et al. (1990). The first theoretical study seems to be thfé one by Denny and South (I 972). These authors developed the boundary layer equations to investigate the effect of bin ary mixture condensation at the fo rward stagnation point of a horizontal cylinder and gave numerical results for a steam methanol mixture. [START_REF] Kuang | An experimental investigation for condensation of non-azeotropic refrig erant mixtures outside a horizontal tube[END_REF] adapted the Nusselt equation to the case of a zeotropic mixture by replacing the leading constant 0.728 and the exponent 1/4 lby two constants AO and A I respectively. These constants were tilted with the experimental results for 4 mi xtures: RI I/RI2, Rl i/R22, RI I/R502, and RII/RI2/R22. Fujim et al. ( 1990) studied several different pattefÅs of gravity-controlled condensation of hi nary mix tures on a single smooth horizontal tube, and [START_REF] Hijikata | Condensation of azeotropic and non-azeotrop ic binary vapor mix tures[END_REF] studied the per formances of the binary mixture CFC 1 13/CFC 114 on a smooth tube while including the intluence of the vapour tlow direction on the heat transfer performance. [START_REF] Wang | Condensation heat transfer of a non-azeotropic binary mix ture on a horizontal tube[END_REF] solved the boundary layer equations in the case of natural convection neglecting the pres sure gradient in each phase and compared their model to the results of the experiments carried out with the binary mixture HFC 152a/HCFC22 (Figure II). The complete equa tion system for condensation of a binary mixture on a smooth horizontal tube has been given by Belghazi (200 1). [START_REF] Signe | Condensation heat transfer of a pure fluid and bina ry mixture in a bundle of smooth horizontal tubes. Comparison of experimental results and classical models[END_REF] and [START_REF] Belghazi | Condensation heat transfer of a pure tluid and binary mixture outside a bundle of smooth horizontal tubes. Comparison of experi mental results and a classical model[END_REF] presented exper imental results for the R23/R 134a zeotropi,c mixture. The experimental results of these two latter authors are summarised in figure 12 where the heat transfer coefficients as a function of t1T =Th-T11., (Th is the bulk vapour temperature and T, . . the tuhe wall tempera ture), are represented. ...

Sfoth tube

+ 3% R23 • 06% R23 .4.5% R23 68.5% R23 • • 1u11% R23 • • • • • I . . . .... • • •• • • • • ._ e .. e e .. •• • • ! , I i i �\ ��� • ... '• #� .. •1. .. A .. �� • -�t .. ••� . ... � � li �@ �g !�!�� � � � I 600 �------�--------r-------�, .
-------�------� 1 2 7 12 17

T..,rT.,., (K)

, 22 27 These results can be analysed similarly to those of [START_REF] Hijikata | Condensation of azeotropic and non-azeotrop ic binary vapor mix tures[END_REF] for a tlat plate:

(i) The results tend to the Nusselt solution as t1T increases.

(ii) In the small llT region the heat transfer coefficient is rate controlled by the dif fusion layer (iii) The value of the heat transfer coefficient could be explained by considering that the thermal resistances of the liquid film and of the diffusion layer coex ist independently in series.

The use the condensation curve theory allows these results to be qualitatively inter preted. In the small t1T region the a1 value is very high (Nusselt theory) and the corre spondtng thermal resistance is low. Moreover, in the case of the lowest concentrations of the more volatile component, the corresponding condensation curve is the (c) curve in fig ure I 0. In this case, the slof of the condensation curve dh/dT at the dew point Td is high leading to a small value of the l/a factor i-e to a high value of the corresponding thermal resistance. Conversely, for highe/concentrations, the slope of the condensation curve at

Td is low and it can be written:

� � R23 low cvncellfration < �I � R23 llil(h ("IIIICtlllmtion (56)
In accordance with the experimental results, for a given i1T, the condensation heat transfer coefficient for low concentration or the more volatile component (R23) is higher than that for high concentration. For high fyT value, the heat transfer is rate controlled by the condensate film because the reverse mass diffusion becomes negligible.

The theoretical analysis of these re. ults has been made with the conden at ion curve method (Figure 1.3). If the agreement is fa irly good for the very small concentration in the more volatile component ( 1.5 % in R23), it is rapidly becoming worse as this concentra tion increases. The authors proposed, as suggested by [START_REF] Webb | The relationship between tne Colburn and Silver methods of corndenser design. l11[END_REF] to introduce the Lewis number Le in the fo rmula (43):

with I I 1É1C2 Z ---= --+ � a ext Ao a, A , ax A, Le =a/ V (57) (58)
a being the thermal diffusivity and Vthe mass diffusivity of the mixture. In this case the agreement is rather good, even for high concentrations of the more volatile component. in condensation of a vapour mixture in a bundle of tubes is the choice of the vapour tem perature. Indeed, the bulk vapour temperature is strongly dependent on the position in the condenser. Moreover, condensation can occur on the temperature sensor itself leading to an erroneous measurement. A way of avoiding such problems is to u. e only one tempera ture, the dew temperature being generally chosen. Seveml authors on the contrary have placed thermocouples inside the bundle either by shielding the thermocouple under u dummy tube (Signe et al., 1998. Belghazi et al., 200 I) to measure the vapour temperature or by attaching a shield and a gutter just above and below the thermocouple to measure the vapour and the condensate temperature respec tively [START_REF] Honda | Experimental measurements for condensation of downward-nowing R 123/R 134a in a staggered bundle of horizontal low-tinned tubes with fo ur geometries[END_REF]. An example is shown on the figure 14 in which the local vapour temperature is measured for a given composition of the mixture R23/R 134a (Belghazi et at., 2001 ). Contrary to pure fluids, no influence of the inundation effect on the heat transfer coefficient was observed. It can be noticed that theoretical calculations using the modified condensation curve method are in good agreement with the experimental results. Comparison between experimental results and modified condensation curve theory.

Fin ned tubes

2.4.1 Single horizo11tal finned tubes A resume of results for the condensation of zeotrop ic mixtures on the outside of fm ned tubes is shown in table 1. Reference From the experimental studies of [START_REF] Murphy | Condensing !heat transfer for RI I4/R 12 mixtures on horizontal finned tubes[END_REF], [START_REF] Hijikata | Condensation of azeotropic and non-azeotrop ic binary vapor mix tures[END_REF] and Belghazi et at. ( 1998), the first general conclusion is that the higher concentration in the more volatile component and the more degraded the heat transfer coefficient if compared to the less volatile component one. This can be observed in figure 15 from the Hijikata and Himeno studies ( 1990) for condensation of R 113/R I I and R I 13/R 114 and in figure 16 which corresponds to a complete study carried out for condensation of a R23/R 134a mix ture on low finned tubes whose fjn pitches varied from I I to 40 fpi. The fo llowing remarks, some being similar to those for a smooth tube, can be done:

(I) A small amount of the more volatile component is sufficient to create a dif fusion barrier which controls the heat transfer and causes the heat transfer coefficient to be strongly decreased.

(2) As for a smooth tube, in the small DT reg ion the heat transfer coefficient is rate controlled by the diffusion layer

(3) As flT increases, the heat transfer coefficient for a finned tube increases markedly, while it increases only slightly for a smooth tube.

(4) At high flT the heat transfer coefficient tends towards the heat transfer coef ficient of the less volatile fluid.

(5) The more important the mass frac tion of the more volatile component, the greater the decrease in the heat transfer coefficient.

(6) At high concentration of the more volatile fluid the heat transfer coefficient tends to an asymptotic limit.

(7) When the concentration of the more volatile component has a significant value (> 3 % in this case), the order of magnitude of the heat transfer coeffi cient is bare ly dependent on the concentration.

To the above, one can add the results of [START_REF] Hijikata | Condensation of azeotropic and non-azeotrop ic binary vapor mix tures[END_REF] who remark that contrary to the pure fluid case, the best f¡rformances are obtained with high fins when a vapour mixture is condensing. Considering the figure 17, it can be seen that the thickness of the diffusion layer greater or smaller than the fin height. If the thickness is small com pared to the fin height, the wavy heat exchange surface area is greater than the projected area of the tube. Conversely. for a thickness greater than the fin height, the heat exchange surface area is approximately the same as the projected area and the heat transfer coeffi cient diminishes. For small flT, the fins are covered by the diffusion layer and the heat transfer coefficient strongly decreases. As the condensate film thickness increases, the temperature diffe rence between the vapour bulk and the liquid-vapour interface decreases and the diffusion layer in thinned. The fins are no longer covered by the diffusion layer leading to a significant augmentation of the heat transfer coefficient.

As for smooth tubes, a theoretical analysis can lbe carried out by the condensation curve method. In the case of finned tube the formula (57) has been adapted by the simple following way: the orders of magnitude of the heat transfer cffficients a 1 and a 8 are very di fferent (factor I 00 to 200). The choice of an accurate theory to determinea1 is less important than in the case of pure fluids. It is the reason why in this case the Beatty and Katz formula was chosen. On the other hand, the gas heat transfer is efficient on the unflooded part of fins, and the formula (57) becomes: This poor agreement can be explained by remarking that the dependence with the Lewis number is not as simple as it is proposed in the formula (59).

� 6A r-, +�6 +ll •� � •• • • .. � • • •• • o +---�----�--�----.----.----r---� 4
2.4.2. Finned wbe bundle It has been seen that, for pure fluids, the inundation of lower tubes in a bundle has a smaller effect for finned tubes than for smooth tubes. In the case of a mixture, the bulk vapour temperature varying strongly between the condenser inlet and the outlet, this tends to increase the value of the heat transfer The combi nation of these two effects can make the heat transfer coefficient be increased compared to the first row of the bundle. This is observed in figure I 9 for the condensation of R23/R 134a on tubes with I 9 fpi. In this figure, together with experimental results are given the theoretical interpreta tion with the modified condensation curve model. The strong variations of the heat trans fer coefficient cannot be represented by this method. However, the total heat power is cal culated with a good accuracy (± I 0 %, Figure 20

Enhanced surfa ce tu/Jes

The condensation of a vapour mixture on enhanced surface tubes has induced less studies than for pure fluids. Indeed, the first industrial approach is to use the tubes manu factured for pure fluids. As an example, the heat transfer coefficient for condensation of the R23/R 134a mixture Gewa C + tube is given in fi gure 21. It can be observed a drastic fa ll of the heat transfer coefficient even at low concentration of R23. ln this particular case, this can be explained by remarking that the fin height of this tube is slightly smaller than that of the trapezoidal fins previously studied. The tins are completely covered by the diffusion layer.

CONCLUSION

The effects of the different parameters (tube geometries and fluid properties) on shell side condensation heat transfer are presented in th is paper. Low-finned tubes (20 geome tries) are currently in use in shell-and-tube condensers and sp ecial enhanced surfaces (3D geometries) are in development. These two types of tubes are used with pure fluids as well as with vapour mixtures. The main conclusions that can be drawn are:

Low finned tubes. Single tube. Pure fluid.

(i) The heat transfer enhancement factor compared to a smooth tube can vary from 5 to 10.

(ii) The optimal co nfiguration of fins is close to be ing establ ished. The presence of ri bs on the fin flanks add a supplementary enhancement factor.

(iii) The rete ntion of the condensate on the underside of the tubes has a detrimen tal effect on heat transfer. More research is needed to minimise this effect.

(vi) The models of [START_REF] Honda | A generalised pred iction method for heat transfer during film condensation on a horizontal low ti nned tube[END_REF] and Rose ( 1994 ), allow the heat transfer coeffic ient to be predicted with a good accuracy .. However, the Rose model is more easy to use.

Low finned tubes. Tube bundle. Pure fluid.

(i) Low-finned tubes are barely affected by the inundation effect.

(ii) The problem of the tube arrangement in a shell-and-tube heat exchanger is mot completely solved.

(iii) The model of [START_REF] Honda | A generalised pred iction method for heat transfer during film condensation on a horizontal low ti nned tube[END_REF] is the most complete which predicts the heat transfer coefficient of a bundle. However, the inundation effect can be predicted with a correLation of Nusselt type having an exponent varying from 0 to 0.07.

Spedal enhanced surface tubes. Single tube. Pure fluid.

(i) 3D surfaces have been shown to have heat transfer coefficients greater than 2D surfaces.

(ii) No general models exist. Specific geometries have specific models.

Special enhanced surface tubes. Thbe bundle. Pure fluid.

(i) 3D surfaces can be strongly affected by the inundation effect.

Low finned and enhanced surface tubes. Vapour mixtures.

(i) A small amount of the more volatile component produces a strong decrease in the heat transfer coefficient compared to that of the pure less volatile fluid.

(ii) The classical condensation curve method underestimates the experimental results. This method was adapted by introducing the Lewis number. Theoretical results are in good agreement with experimental results espedal ly for low concentrations of the more volatile component.

(iii) The 3D surfaces are not any more effkcient than 2D surfaces since the ther mal resistance of the diffusion layer controls the heat transfer.

NOMENCLATURE Latin Letters

Thermal diffusivity Heat transfer surface area Fin spacing at fin root h,

8

  Pi ( Pi• Pv J1~, llhtv a Nu -0.728 D 1½i ( T s at • T w )

  where ris the lineic condensate mass fiow. With these notations, the Nus eft theory gives:

FIGURE 1 .

 1 FIGURE 1. lnnuencc of fluid characleristic tem p erawres on theoretical values of the heat transfer coefficient (After Belghazi, 200 I).

  .. ;� fl hl l •]' / -1 ( c "i (T_ (ot •Til. J) a , =0.728 , 1+0.2 (n-1)_.:,_ _ __ _ II /) J.. lf (7 .(l/1 -Til. ) L1 ����with the condition that c ' '' ( T.wu -T i l. ) This equation agrees reasonably well with experimental data. It has been shown that using the Chen sugge tion with the Kern exponent allows the two phenomena of ripples and subcooled falling condensate to be taken into account and to obtain a better agreement ( Belghazi et al., 200 I) (Figure 2) 2. Varintion of the ratio hetween the heat transfer coeflicient of the jth row and the heat transfer <:oeftkicnt of the lir�a row as a function of the row numher. (a) Con1rarison experimental rc. ults and Chen ct al. model. (.h) Com p arison experimental resulls nnd modified Chen ct al. model.

  3. Fin profiles in 2-D geometries: (a) Rectangular fin. (b) Trapezoidal fin. (c) Curved profile and rectangular part. (c) Curved profile.

FIGURE 4 .

 4 FIGURE 4. Condensate retention at the lower part of integral-fin tubes.

FIGURE 5 .

 5 FIGURE 5. Definition of geometrical parameters in a tube with trapezoidal tins.

  <l> = COS I -l With e >b,/2 . [( 4 a cos. e ) ] .

  t:,.ll ) (I . c b ) + (I . t;�l ) c b (28)

  proposed a correlation in the form of equation ( 15) with g equal to 0.04 instead of 1/4 as proposed by Nusselt in the smooth tube bundles. The second consists in developing a model, first for a single tube, and then for a bundle, by considering two different situations according to whether the lower tubes are unflooded or flooded by the condensate flowing from the lll pper tubes. Such a model. was proposed by Honda ct at. ( 1989) who extended their model developed initially for a single horizontal finned tube. In this model they calculate . eparatcly the heat flux in the flooded and unflooded regions for the top tube row. For the second and . ubsequent rows they distin guish the flow mode of impinging condensate using the following criteria: with Column mode for K � 0.42 Sheet mode K> 0.42

  -6. Physical motlcl of llonda ct at. (I 989).

  • Experiments --Katz & Gci�t ----Murata & Ha�hizumc -llonda ----"* Nu�-.clt 1:" ------------. . .. ...... .. . .. . ..... •......• --. -.:-:::-.-:.-:-:. -: .. . -:-. . .... .•.. . . ..... . ... f'. :.--. :-.. . ... . . . . 04 I tal I IK 'L ... , 4ToiK 0-2 +-----. ----... ----..--�--.------.

FIGURE 7 .

 7 FIGURE 7. Heat transfer coefficient in a tube bundle during condensation of HFC 134a (Bclghazi, 200 I).

  FIGURE 8. Three-dimensional tube geomelries.

FIGURE 9 .

 9 FIGURE 9. Temperature profiles near the wall: (a) Pure fluid or azeotrope. (b) Zeotropic mixture.

A0

  and A0 are respectively the reference surface area and the actual extef¬al surface area of a tube, A0 being equal to A0 for smooth tubes. The a8 coefficient can be corrected for mass transfer effects by writing[START_REF] Mcnaught | Mass-transfer correction terms in design methods for multi-component/par tial condensers[END_REF] the molar flux of the condensing v af¢ur.

  . 10. Specific enthalpy or a binary mixture as a function of temperature for different concentrations of the �:omponents.

  Condensation hcul tnm�fer cocnicicnt <1S , a function of DT for the R 152a/R22 mixture at differ ent concentrations (After Wang et al.. 1995).

FIGURE 12 .

 12 FIGURE 12. Condensation heat transfer coefficient as a function of .1T for the R23/R 134a mixture at differ ent concentrations.

lT

  Cl � � ��� � �1Ĉ f!' � �� :�o' t1 [ o" ,_ --_J A •�».' •. ,.Tw ( K) FtC.l'RE I J. C<)nden�atiQn of R2J/R 134a mix lUre: Comparison of experimental results with classical 11nd rnm.lilicd condensation curve theories.30 2.3.2 Smooth wbe lnmdle A crucial problem in the heat transfer coefficient measurements

FIGURE 14 .

 14 FIGURE 14. Condensation of R23/R 134a mixture: Heat transfer coeffi cient as a fu nction of the row number.

Fluid

  Low finned tube (Tube bundle) and Takata{ 1999 2

  Heat transfer coefficient of free convective condensation of mixtures on a high-fin tube (after Hij ikata ct al., 1986).

  t.• ' .... .. l' JJ ' ...... o5t,�� &3,. � 'Xi\ �u�

  Condensation heat transfer coefficient for R23/R J34a mixtures with different composition on finned tube�.

  17. Comparison hetwcen diffusion layer thi•ckness and fin height (After Hijikata and llimeno.It can be seen in the figure18that the agreement is fairly good for low concentrations in the more volatile component but this agreement becomes poorer as the concentration

  -------r-------,--------.------: I R. Condensation of R23 /R 134a mixture. Compmison of experimental resulls with condensation curve theory.

FIGURE 19 .

 19 FIGURE 19. Condensation of R23/R 134a mixtures on finned tubes with 19 fins per inch. Ratio of the heat transfer coenicient of the jth row by the heal transfer coefficient of the first row as a fu nction of the row number.

  FIGLIRF. 20. Measured heat flux as a function of the heat flux calculated with the condensation curve method.

Fr<illRE

  --.-----�-----,----.,..• --•----•------, 21. Condcnsntion of R23/R 134a mixtures on Gcwn C+ tubes. Ratio of the heat transfer coefficient of lhc j th row hy the hent trnnsfcr coct'tkicnt of the lirst row as a function of the row numhcr.

TABLE I .

 I Condensation studies on finned tubes with vapour mixtrures.

Pi ( Pt . p,. ) ).; t &,,,.(3) 1 / 4 II D Jlt ('f.mt • Tw ) an -1 / 4 -=n a, (12) (I3)


F Nallet

P Godignon

Dominique Planson

Christophe Raynaud

J P P Chante

Very Low RON measured on 4H-SiC Accu-MOSFET high power device

Keywords: 4H-SiC, MOSFET, Current Limiting Device, Simulation, I-V Characteristics, Low Specific On-Resistance, Forward Current Density, Serial Protection

Very low R/sub ON/ measured on 4H-SiC accu-MOSFET high power device

I. INTRODUCTION

Since april 2001, SiC devices are commercially available. These new devices are Schottky diodes proposed by Microsemi and Infineon Technologies AG. The available grading are 300 V/ 10 A and 600 V/ 4-12 A for PFC applications and DC/AC converter. SiC technologies should be able to produce high quality of power rectifier, but there is no SiC power switches commercially available yet. In the high frequencies field, the current trend seems to be the MESFET which could be placed between the silicon and the GaAs ones [START_REF] Weitzel | Silicon Carbide High Frequency Devices[END_REF].

For power applications, the main researches turn towards the power MOSFET, JFET and the thyristor GTO structures. The main problems encountered in thyristor technologies are the low current gain obtained (b=20) comparing with the silicon ones, du to the low minority carrier lifetime measured (best of 5 µs measured for low injection level and low doping concentration [START_REF] Udal | Measurement of Charge Carrier Lifetime Temperature-Dependence in 4H-SiC Power Diodes[END_REF] [START_REF] Grivickas | Band edge absorption, carrier recombination and transport measurements in 4H-SiC epilayers[END_REF]). Another problem is the low efficiency (30 %) of the peripheral breakdown protection used in thyristor technologies [START_REF] Ryu | 3100 V, Asymmetrical, Gate Turn-Off (GTO) Thyristors in 4H-SiC[END_REF], which leads to an increase of the P-base epi-layer thickness and then, leads to a lower current gain of the NPN bipolar transistor. Some SiC unipolar structures present higher electric characteristics than the last evolution of the silicon power Mosfet (alias CoolMos TM [START_REF] Lorenz | COOLMOS TM -a new milestone in high voltage power MOS[END_REF] or superjunction MOSFET). Nevertheless, in SiC technologies, the SiO2/SiC interface presents a high density of trap and the oxide layer itself owns a large quantity of fixed charge. Those parasitic charges reduce the electron mobility in the inversion layer. This low mobility value would be also the consequence of the crystalline orientation SiC surface chosen for the SiO2 growth. A lot of research team are working on better technological conditions for making SiC power MOSFET with lowest specific on-resistance (surface studies, SiO2 growth conditions, post-implantation annealing process). To avoid insulator/SiC problems, the current trends turn towards JFET or Accu-MOSFET. Such devices, shown in the literature, exhibit the best electrical characteristics obtained in SiC technologies : low specific on-resistance and high current density ability (Accu-MOSFET : 16 mWcm 2 / 1600 V [START_REF] Tan | High-voltage accumulation-layer UMOSFET's in 4H-SiC[END_REF] ; JFET : 10 mWcm 2 / 600 V and 14 mWcm 2 / 1800 V [START_REF] Friedrichs | SiC Power Devices with Low On-Resistance for Fast Switching Applications[END_REF]).

Nevertheless, the technological steps used for the built of these devices require complex (expensive) process (deep implantation, epitaxial growth inside, deep plasma etching and a lot of mask levels) and there is no sign of a next commercially SiC power switch. In this paper, another unipolar device structure is shown and an evaluation of the electrical static characteristics of prototypes is given. The physical properties of SiC allow the development of new devices for applications not covered by the silicon technologies. The function (serial circuit protection) requires to limit a short-circuit overcurrent during a time long enough to allow the opening of the power line (a 230 V / 50 Hz network) by a circuit breaker under reliable conditions. The design of such a device [START_REF] Nallet | Conception, Realisation et Caractérisation d'un composant limiteur de courant en carbure de silicium[END_REF] is proposed here with a special view on its specific on-resistance studied in simulation with the DESSIS ® ISE software [START_REF]ISE integrated System Engineering[END_REF], and in experimental measurements. This device has to work under high junction temperature and the thermal aspect will not be discussed here, but they are given elsewhere [START_REF] Nallet | Electrical and electrothermal 2D simulations of a 4H-SiC high voltage current limiting device for serial protection applications[END_REF]. A current limiting device must have the lowest resistance as possible for the normal use, the End User requirements specify a value close to 10 mWcm 2 , high current saturation density and simple technological process.

II. DEVICE STRUCTURE, SIMULATION AND PROCESS

A. Device structure and specific on-resistance 1) Device structure, IC-MOSFET (Implanted Channel MOSFET) : The design of the current limiting device is based on a Power Mosfet (like a N channel VDMOSFET in silicon technology) in which a N channel is implanted and the source and gate contacts are connected (VGS=0 V) (figure 1).

Channel region (channel length, L CHANNEL )

Intercell region (Intercell Width, 2L INTER )

P + P +

Depleted region

Pinch off region

Current density 100 kAcm -2 5 kAcm -2 1 kAcm -2

As the Power Mosfet structure, the anti-parallel built-in diode doesn't allow a bi-directionnal capability. The current limitation only appears in case of positive drain-to-source bias voltage (figure 2). For low VDS, the device acts as a resistance, RON ; and if VDS increases over VDSSAT, the resistance reaches highest value (ideally ∞) and the current stays equal to the current saturation value. The pinch-off effect is localized at the end of the N channel region.

2) Specific on-resistance : This component has to be ranging for 600 V / 50 A and its on-resistance should be lowest as possible. For a fixed efficiency of the peripheral protection (evaluated by simulation using DESSIS ® ISE), the thickness of the drift-layer can be estimate. In this case, the desired breakdown voltage is 600 V and the peripheral protection efficiency is about 50 %. The protection used is chosen in order to minimize the number of photolithographic mask, and we take a guard rings protection made in the same way that the P + layer. By the way, the peripheral protection used is composed by three P + guard rings of 10 µm width and of 3 µm width between each other's. The N epitaxial layer of 4´10 15 cm -3 / 7 µm is chosen and a breakdown voltage of 720 V is simulated with the guard rings protection. A breakdown voltage of 630 V is experimentally obtained from a pin test-diode protected as well, comparing to the 730 V of the simulated one. The entire on-resistance, RTOTAL, is the addition of the channel resistance, RC, access resistance, RA, and drift resistance, RD (Fig. 3, Fig. 4).

The on-resistance depends on the channel parameter (doping level : NCHANNEL, junction depth : XJCHANNEL, and length : LCHANNEL) and on the drift layer doping level and thickness. The access resistance value, RA, is linked to the intercell width (2´LINTER) through the parasitic JFET effect induced by a smaller intercell width (below 2 µm). On figure 3, the total on-resistance is represented versus the doping level of the channel, NCHANNEL. For XJCHANNEL=0,3 µm and LCHANNEL=4 µm, the channel resistance decreases when the doping level increases. Up to 2´10 15 cm -3 , the channel resistance, RC, (figure 4) become lower than the drift one and contribute for 40 % to the total resistance (in the simulation, we take n=ND. In case of incomplete ionization of the donor, electron density, n, is closed to 0,8´ND at 300 K, that means a change of 20 % up for the total resistance value).

On figure 5, the total specific resistance is plotted versus the channel parameter. The goal, for the total resistance value, is 10 mWcm 2 and it can be achieve with a channel doping level up to 2.5´10 17 cm -2 , a channel length of 4 µm and a channel junction depth of 0.2-0.25 µm. The choice of these technological values leads to a current saturation density of 1000 Acm -2 (this is the upper bound that we take, deducted from simulation results). In this way, the experimental result should be less sensible with the channel variation and a value of 12 mWcm 2 could be obtained.

B. Technological data

The 4H-SiC wafer used for the fabrication was purchased from CREE Research. It is composed by a N ++ grown substrate (r=20 mWcm / 430 µm) and a N type epitaxial layer (4.1´10 15 cm -3 / 7 µm). The process used requires 5+1 mask levels (The first level only used for placing the devices on the wafer, with the alignment crosses). The P + buried layers are made by ionic implantation of aluminum. The channel region is implanted over the P + buried layer (nitrogen). A dry oxide of 50 nm is grown after a post-implantation annealing stage at 1700 °C / 30 mn [START_REF] Lazar | High Electrical Activation of Aluminium and Nitrogen Implanted in 6H-SiC at Room Temperature by RF Annealing[END_REF]. The source contact is ensured by a high dose nitrogen implantation and a nickel layer. A plasma etching step is used to allow a connection with the buried P + layer and the source contact (bulk-to-source short-circuit in microelectronic technologies).

The table 1 summarizes the technological data used for the current limiting device.

Table . 1

Process steps

Technological data P + implantation (Al) Nchannel implantation (N) Ncontact implantation (N) Epilayer (N) Substrate (N + ) 500 keV / 10 14 cm -2 30-180 keV / 1.1´10 13 cm -2 30-100 keV / 10 15 cm -2 4´10 15 cm -3 / 7 µm r=20 mWcm

The values given on table 1 lead to a N channel with a doping level of 2-2.5´10 17 cm -3 and a junction depth of 0.2-0.25 µm.

For the mask design, a multicell structure is defined with a hexagonal perimeter that allow to optimize the conduction perimeter versus the active area and simplify the geometrical adaptation with a circular periphery (figure 6). Different devices with different channel length (4,5 and 6 µm) and intercell length (4,6 and 8 µm) were realized. the conduction perimeter is kept constant and equal to 2880 µm. When using the implantation simulator developed by E. Morvan [START_REF] Morvan | Modelisation de l'implantation ionique dans alpha-SiC et application a la conception de composants de puissance[END_REF] for describing the doping profiles and using the finite element simulator DESSIS Ò ISE, the projected electrical behavior shows an onresistance of 12 mWcm 2 , a current saturation density of 1050 Acm -2 and a saturation voltage close to 15 V. III. I-V CHARACTERISTICS.

The electrical characterization are made with a curve tracer tektronix 370. The devices are tested with probe on the entire wafer. The results are shown on figure 7 and figure 8. The simulated I-V characteristic (using technological projected data) is pointed on the graph for comparing with the real I-V curve. We find a good match between the simulation curve and the real curve in the case of a step-by-step measurement. It supposes that the projected technological data have been done and that the SiO2/SiC charge density (interface+inside SiO2) is low, may be ten time smaller than the channel dose (»5´10 12 cm -2 ) and close to »10 11 cm -2 . A saturation current density of 900 Acm -2 and a specific on-resistance of 13 mWcm 2 are measured. This value are closed to the simulated one : 1050 Acm -2 and 12 mWcm 2 that means the good electrical conductivity of the compensated channel comparing with the simulation (µnchannel-simul=450 cm 2 V -1 s -1 ).

By comparing the measurement using the step-by-step method and the screen caption method, an illustration of the self-heating in the device is given. The step-by-step measurement means that the couple (I,V) is kept during the applied voltage rises. With the step-by-step method, each point is taken at a constant junction temperature and this temperature increases with the losses (and voltage) in the device. In the case of the screen caption curves, the ended voltage is applied and, after the I-V curve is saved. With the screen caption method, the junction temperature inside the device is roughly the same for each point of the curve. The effect of the channel length is remarkable : the saturation current decreases as the channel length increases. Using a MOSFET like or JFET like analytical model, the saturation current should vary as 1/LCHANNEL but there is not enough LCHANNEL values (two values) to fit correctly the experimental curve. The intercell width has to be lower as possible to optimize the active area. Nevertheless, its bottom value is closed to 4 µm, below that the resistance rises a lot. With DESSIS Ò ISE simulations, the critical value for the intercell length is found to be 3 µm, below it the parasitic vertical JFET effect increases drastically the on-resistance. On the fig. 9, the specific on-resistance is plotted versus the intercell width for two channel length values (4 and 5 µm). When the intercell width changes, only the access resistance change and this variation can be estimated roughly using a linear interpolation with a slope of 0.5 mWcm 2 /µm. While keeping constant the intercell width, it is possible to evaluate the resistance shift (linear approximation) versus the channel length value (only two points). We obtained 7 mWcm 2 /µm for .

This variation (7 mWcm 2 /µm) is not only due to the channel resistance variation. In fact, the source contact area decreases with an increase of the channel length : the add up LCHANNEL with LSOURCE is kept constant in the layout. For a constant specific contact resistance value, the contact resistance (W) increases with the channel length as . The variation of the specific on-resistance versus the channel length obtained on figure 9 is due mainly to the reduction of the active contact area and not only to the channel resistance increase. This one should vary less than 7 mWcm 2 /µm, as is it observed in simulation because the total on-resistance is low and the channel electron mobility seems to be as predicted in the simulated devices.

For the device with a channel length of 6 µm, the on-resistance rises to 100 mWcm 2 due to the smallest source contact area. IV. CONCLUSION With comparing to the other devices (figure 10), already published, it seems that the IC-MOSFET belongs to the best unipolar devices built in SiC technologies. The technological steps used are common in silicon technologies (until post-implantation annealing) and only 5+1 mask levels are needed (adding a gate control should only require two levels more). The electrical characteristics experimentally obtained show a specific on-resistance of 13 mWcm 2 and a current saturation density of 900 Acm -2 . The I-V curves obtained are very closed to the simulated ones (DESSIS Ò ISE software) and are very uniform over the wafer : more than 90 % of the device are working with a spreading of electrical characteristics of 20 %.

Fig. 1 :Fig. 2 :

 12 Fig.1: Structure of the current limiting device ( a peripheral cell). The IC-MOSFET is shown with its guard rings protection, the implanted N channel and the P + implanted layer. The channel and intercell regions are noted on the schema.

Fig. 3 :Fig. 4 :

 34 Fig. 3 : Simulation of the variation of the partial specifics on-resistances of the device versus the channel doping level (NCHANNEL). The channel length is 4 µm and its junction depth (NCHANNEL/P + ) is 0.3 µm

Fig. 5 :

 5 Fig. 5 : Simulation mapping of specific on-resistance versus the channel technological parameters.

Fig. 6 :

 6 Fig.6: Photography (optical microscope) of a current limiting device. The guard ring protection is shown. The dark hexagons are the source contact part that reach the SiC N ++ surface, the white parts (between the dark hexagons) are the source contact that overlay the oxide layer.

Fig. 7 :

 7 Fig. 7 : Experimental and simulated I-V characteristics of current limiting device with 4 µm for the channel length value. The saturation voltage is 15 V. The current density is calculated considering the entire source contact area.

Fig. 8 :

 8 Fig. 8 : Experimental and simulated I-V characteristics of current limiting device with 5 µm for the channel length value. The saturation voltage is 15 V. The current density is calculated considering the entire source contact area.

Fig. 9 :

 9 Fig. 9 : Specific on-resistances measured plotted versus the intercell width (extracted at VDS=1 V) for several current limiting prototypes with different technological characteristics (channel length, LCHANNEL and intercell width, 2´LINTER).

Fig. 10 :

 10 Fig.10: State of the art of the unipolar SiC devices (power switches) ordered by specific on-resistance versus breakdown voltage (year 2001). Only few 4H-SiC devices reach the 6H-SiC theoretical limit. The highest breakdown voltage obtained is 6.1 kV (4H-SiC SIAFET from Kansai[START_REF] Takayama | Static and Dynamic Characteristics of 4-6 kV 4H-SiC SIAFETs[END_REF]) and the best trade VBR/RON is obtained with a 3.5 kV / 25 mWcm 2 (4H-SiC JFET from SiCED[START_REF] Friedrichs | Application Oriented Unipolar SiC Switching Devices[END_REF])

ACKNOWLEDGMENTS

We acknowledge Schneider Electric S.A. for his financial and technical support, CNM of Barcelona who manufactured the prototypes and Mihai LAZAR for the post-implantation annealing process.


Bruno Aoostini

I,Z Andre Bontemps

Barbara Watel

Bernard Thonon

BOILING HEAT TRANSFER IN MINI-CHANNELS: INFLUENCE OF THE HYDRAULIC DIAMETER

The present experimental study shows how the reduction of the hydraulic diameter affects the heat transfer coefficient for a boiling flow in mini-channels. Flat aluminium multipart extruded tubes composed of parallel rectangular channels with hydraulic diameters 0.77 and 2.01 mm were used with refrigerant Rl34a. It was shown that the reduction of the hydraulic diameter increased the heat tra nsfer coefficient and favored dry-out, probably because of the thinning of the liquid layer due to the bubble confinement. However it was found that the quality averaged heat transfer coefficient was still greater than what would be obtained in macro-tubes.

INTRODUCTI ON

New environmental policies on global warming require that emissions of gases with significant greenhouse effect should be decreased. The use of mini-channel heat exchangers (hydraulic diameter about 1 mm) contributes to achieve this pwpose thanks to higher heat transfer coefficients, thermal effi ciency and a lower required fluid mass. They are widely used in condensers for automobile air-conditioni ng and will be used in evaporators and domestic air conditioning. However, more general use requires a better understanding of boi ling heat transfer in confined spaces. In pa rticular it is necessary to o utline the effects of the confinement on heat transfer in mini-channels.

In spite of numerous publications on the experimental study of heat transfer in boiling flows, still few concern the specifi c study of the inftuence of the hydraulic diameter on the boiling heat transfer coefficient. Consequently classical correlations of boiling heat transfer coefficient in macro-tubes take into account the effects of the hydraulic diameter rather poorly. The Steiner and Taborek (1992) correlation includes a Dt;0.4 term based on some experimental results for hydraulic diameters as low as l mm. Ishibashi and Nishikawa (1969) experimental results within a confined annular space showed that when the bubbles were confined, the heat transfer coefficient was proportion al to D t; 0 67. [START_REF] Aritomi | Thermohydraulics of boiling two-phase flow in high conversion light water reactors (thel:}ohydrau lics at low velociti es)[END_REF] obtained Dt; 0 • 75 for boiling flows in annular spaces with Dh < 4 mm. [START_REF] Tran | A correlation for nucleate flow boiling in small channels[END_REF] proposed a correlation for flow boiling heat transfer in mini-cham1els with a Dt;1 for the confinement effect. Finally, [START_REF] Kew | Confined bubble flow and boiling in narrow spaces[END_REF] argued that the confinement should have a sizable influence on the heat transfer coefficient when a new dimensionless number, the confinement number defined as Co = ( cr / (D; • g • (p1 -Pv)) )0•5, is greater than 0.5.

EXPERIMENTAL APPARATUS

The test loop and test section

The test loop includes a liqui d pump (10-100 Uh) and a glycol-water mixture circuit for heat evacuation. Subcooled liquid enters the inlet manifold, then is vaporised in the test section and condensed in a heat exchanger by the water glycol flow. The test section, shown in fi gure 1, consists of two different flat tubes. The inlet and outlet manifolds are 10 Lmn diameter tubes in aU pattern at 90 degrees. The manifold diameter is five to thirteen times higher than the channel hydraulic diameter to limit fluid distribution effects. The whole test section is thermally insulated with 40 mm thick wrapping foam. For heat transfer measurements the length Lj of the tube (zone @) was heated thanks to Joule effect by passing an electric current (up to 2 800 A) from two brazed electrodes through the tube w all . Experimental conditions are summarized in table 1.

Figure 1 shows the test section and instrumentation. Wall temperatures Twj (0 < j < 9) on the tube external surface were measured with 0.5 mm diameter calibrated type E thermocouples. Fluid inlet and outl et temperatures (re spectively Tfl,i and TR,o) were measured with 1 mm diameter calibrated type K thermocouples. Calibration was carried out every 5 K between 268 and 333 K witb a Rosemount 162-CE platinum thermometer. The thermocouples used for wall temperature measurements were equally spaced and fixed with aluminium adhesive on the tube surface. Thanks to the aluminium high thermal conductivity and the tube walls low thickness (0.35 rrun) the measured temperature is equal to the wall temperature in contact with the fluid (the difference was estimated less than 0.01 K).

The channel geometry

The determination of the channel dimensions has been carried out using scanning electron microscopy. The dimensions of several channels were measured and the average and standard deviation were calculated. The uncertainty was estimated as twice the standard deviation (95 % of the measurements in this interval). The hydraulic diameter was calculated with the total flow area (S11) and wet perimeter (PJL) measured from electron microscopy imaging in order to take into account the effect of the first and last channels, and the corners which are rounded, yielding Dh = 4 S 11/ P11. Steady state values were monitored thanks to the Hewlett Packard 3421A multiplexer with a 30 minutes time lapse between each change in mass flow rate or heat flux. An averaging occurred after every 20 values and uncertainties were calculated according to [START_REF] Kline | Describing uncertainties in single-sample experiments[END_REF] and [START_REF] Moffat | Contributions to the theory of single-sample uncertainty analysis[END_REF][START_REF] Moffat | Using uncertainty analysis in the planning of an experiment[END_REF] methods, with twice the standard deviation. For every fixed mass flow rate, the heat flux was adjusted in order to obtain series of outlet vapor qualities between 0.2 and 1 with a step of 0.05 approximati vely. At the same time the pressure was kept constant by adjusting the quantity of fluid in the test loop for each heat flux and mass flow rate variation. The total electrical power P dissipated in the test section was calculated as the product of voltage and current. The variations of Rl34a thermopbysical properties with temperature were calculated with the REFPROP 6.01 software. Uncertainties are reported in table l.

DATA REDUCTION

The heat flux and power dissipated between 0 and z are calculated respectively by

u .] . z q=-and Q(z)=U•l•-. S Lj (1)
The temperature of the subcooled fluid absorbing the power Q(z) is calculated with a heat balance:

() ( ) Q(<J) _ c,,,t(O)+c1,,t(z) Tjt z = TJt 0 + M . _ with CpJ = 2. . •C p,J (2)
This equation is implicit with Tfl (z) because cp,1(z) is a function of T11(z) so that it must be solved iteratively. The tube coordinate Zboil where bulk boiling starts is the position along the tube where the fluid bulk temperature is equal to the saturation temperature at the local pressure, since liquid pressure losses cannot be neglected in mini-channels.

Therefore both the temperature and the pressure values must be iterated to determine Zboil because the single-phase pressure loss is a function of Zboil•

In order to calculate the vapor quality, the local pressure and the fluid temperature, a beat balance was used over the length dz giving

oQ= M. [x•cp,v(Tsar) •dTsm + (1-x) •Cp,i(T.r at) dTsat +hiv(Tsat + dTsar ) • dx].
(3)

The measured total pressure drop through the test section includes the pressure drop of the single-phase liquid flow (6.p10), since subcooled fluid enters the tube, and the two-phase flow pressure drop. Figure 2 shows the average pressure drop gradient ( 6.Pmes -6.pt0) I Lrp, with LTP = Lzwu, as a function of the outlet quality Xo-�10 300 The homogeneous model was chosen to model the local pressure because this model predicts that (6.Pmes -6.p10) I LTP is linear with x0 when the gravity and acceleration pressure losses are negligible. This is shown on figure 2 where the lines represent the predictions of the homogeneous model.

The two-phase pressure drop and the saturation temperature depend on the vapor quality so that the local pres sure, fluid temperature and quality must be calculated simultaneously with an iterative method. The details of these calculations are given by [START_REF] Agostini | Etude experimentale de !'ebullition en convection forcee de fluide refrigerant dans des mini canaux[END_REF].

Finally the heat transfer coefficient is calculated by

(j a(z) = ( ) ( ) ' 7;,, Z -G•m :Z (4)

EXPERIMENTAL RESULTS

Figures 3 and4 show the local heat transfer coefficient as a function of the local quality for one given mass flow rate and several heat fluxes. The trends are the same for the other tested mass flow rates. The heat transfer coefficient does not depend on the heat flux given the uncertainties. For both tubes there exists a critical quality beyond which the heat transfer coefficient decreases sharply with increasing vapor quality and this critical quality is smaller for the smallest hydraulic diameter. This critical quality was defined as the intersection of lines fitted by linear regressions when the heat transfer coefficient is plotted as a function of the local quality. This method Jed to Xcr = 0.43 ± 14% for tube 1 and Xcr = 0. 19 ± 26% for tube 2. The critical quality was found to be independent of the heat flux and mass flow rate in the tested range. It doesn't mean that there i s no such dependence but rather that if Xcr depends on q and 1h, this variation does not appear because of the uncertainties.

The physical interpretation of this critical quality is easier when studying the local wall temperatures and their statistical uncertai nties as a function of the local quality. The trends are the same for both tubes. In the case of tube 1 for example, for qualities lesser than the critical quality both the local wall temperatures and their uncertainties are constant as expected. Furthermore 6.Tw is about 0.2-0.3 K which is an acceptable uncertainty for temperature measurements with a boiling flow. On the contrary beyond Xcr. Tw and 6.Tw increase steadily with x to the point that the uncertainty is multiplied by 10 at high qualities.

These phenomena are consistent with a partial dry-out of the liquid layer at the internal wall. The following interpretation is proposed. As the vapor quality increases for a given heat flux, the thickness of the liquid layer decreases so that dry-out occurs more easily. Below a critical thickness, corresponding to a critical quality, a periodic dry-out alternates with a regeneration of the liquid layer. Since the wall is periodically in contact with liquid or gas, the heat transfer undergoes important fluctuations, because of the bad heat transfer with gas. These fluctuations are all the more important that the vapor quality is high, because a high quality means more frequent dry-outs. Finally these heat transfer coefficient fluctuations cause the time averaged wall teml:xra ture to increase and fluctuate with quality, so that 6.Tw increases with x. Cornwell andKew (1992, 1995) proposed that a new flow configuration, the confined bubble regime, is dominant in mini-channels where the bubbles are confined between the channels walls. In such a regime, these confined bubbles thin the liquid layer, all the more that the confinement is important. Furthermore the liquid layer should be regenerated between two successive passing bubbles. This model could explain why the critical quality decreases with the hydraulic diameter because of the liquid Layer breakdown \mder the confined bubbles.

In order to compare the heat transfer coefficients in tubes 1 and 2, data points must be carefully selected. For a proper comparison, measurements with very close heat fluxes, mass flow rates, vapor qualit1es and boiling regimes for both tubes must be used. Ideally the working pressure should also be the same, but pressure has no significant influence on the heat transfer coefficient in the convective boiling regime and the pressure difference between tube 1 and 2 is not that important (±12% of the average pressure). Furthermore [START_REF] Agostini | Ascendant flow boiling of refrigerant Rl34a in small channels[END_REF] measurements on tube 1 showed that between 417 and 604 kPa the pressure had no sizable influence on the heat transfer coefficient, even in the nucleate boiling regime. Among about 750 data points available for each tube, only 8 had such characteristics.

As illustrated on figures 5 and 6 the heat transfer coefficient is higher in tube 2 before any dry-out occurs. The enhancement ratio is constant for the 8 data points given the uncertainties. The average enhancement ratio is o:n/an = 1.74±0.31, that is (Dh;rz/ Dh,T J )-0.6± 0• 1 which is, given the uncertainties, close to the values proposed by Ishibashi and Nishikawa (1969) and [START_REF] Aritomi | Thermohydraulics of boiling two-phase flow in high conversion light water reactors (thel:}ohydrau lics at low velociti es)[END_REF] Ql Although the confinement increases the heat transfer coefficient, it was shown that dry-out had the opposite effect and was dominant in mini-channels. Thus it is possible that the average heat transfer coefficient over the boiling length is not increased compared to what would be measured in a macro-tube. In order to answer this question this average e)(perimental heat transfer coefficient divided by that predicted by [START_REF] Shah | Chart correlation for saturated boiling heat transfer: equations and further study[END_REF] in a 10 rom diameter tube was represented as a function of the tested heat fluxes on figures 7 and 8. The conclusion is that even at high heat fluxes, that is high vapor qualities and important dry-out, the average heat transfer coefficient in mini-channels remains higher than what would be obtained in a macro-tube. Thus the dominant dry-out observed in mini-channels does not completely compensate for the enhancement ef f ect due to the confinement.

:"� l+• •• • • • . . • • •n-•• • • � • • • 1HJnr lfl

CONCLUSIONS

The influence of the hydraulic diameter on the heat transfer coefficient in mini-channels was experimentally stud ied. It was found that partial dry-out occurred in mini-channels at lower vapor qualities than in macro-tubes. When the hydraulic diameter decreases from 2.01 to 0.77 rom, the critical quality decreases from 0.43 to 0.19. It was all: experimentally shown that when the hydraulic diameter decreases fr om 2.01 to 0.77 rnrn, the heat transfer coefficient coefficient is multiplied by 1.74 approximatly. However this enhancement is somehow balanced by the early occurence of dry-out. Nevertheless the heat transfer coefficient averaged on the whole boiling length remains higher than what would be obtained in a macro-tube. As a conclusion the decrease of the hydraulic diameter is an effective means of q (kW I m2)

Figure 1 :Figure 2 :

 12 Figure 1: The test section.

Figure 3 :Figure 4 :

 34 Figure 3: Local heat transfer coefficient versus local qual ity, l>), = 2.01 mm

  It i s not clear how Tran et at. (1997) established the termDt; 1 because the range of tested hydraulic diameters, 2.4-2.92 mm, is too small to build a correlation. It is probable from their articles that it comes from an analogy with single-phase flow classical theory and has no e)(perimental ba sis. On the contrary the Dh"0 • 4 term proposed by the Steiner and Taborek (1992) is based on some e)(perimental data.Nevertheless the data concerning refrigerant fluids (R11 and R113) were pettormed for hydraulic diameters from 7 to 20 mm only. The lowest hydraulic diameters (from 1 to 5 l:b) were tested with Helium I only so that this Dt;0.4 factor is difficult to compare with the present results. I 0000 ,--,--,--.-....-n.--rr-..--r-r• • • • • • • n•• • • n• • •llhtl � I 000 l:¡l:¢l:£l:¤l:¥l:¦l: §l:¨l:©l:ªl:«

Figure 5 :Figure 6 :

 56 Figure 5: Influence of the confinement on the heat trans fer coefficient, th = 239 kg/ m2 s Figure 6: Influence of the confinement on the heat trans fer coefficient, rh = 288 kg/ m2 s

Figure 7 :Figure 8 :

 78 Figure 7: Comparison of the average heat transfer coef ficient and that predicted by the Shah (1982) correlation, Db =2.01 nun

  The ftuid measured with a calibrated Ro semount type II absolute pressure sensor. Three differential pressure sensors calibrated from 0 to 7 .6, 40.5 and 182 kPa measure the pressure loss through the test section. A Rosemount Micro-motion coriolis flowmeter was used to measure the mass flux of Rl34a downstream of the pump.

	Table 1: Operating conditions and uncertainties
			tube 1	tube2
	m (kg/m2 s)	90-295	± 1.7-8.6% 214-469	± 3.3-8.6%
	q (kW/m2)	6-31.6	±2�. 1%	2.8-19.5	±3 %
	Tw, T11 (K)	276-308	±0.2-3 K	281-307	± 0.2-2 K
	� 'fsub,i ( K )	1-17	±0.1 K	1-8	±0.1 K
	p; (kPa)	405	± 3.4%	517	±2.7%
	�P (kPa)	9.5-37.5	± 1.2-17%	153-1570 ± 0.3-3.7%
	a(kWjm2 K) 0.8-10.3	±6 -30%	0.6-32.5	± 5-30%
	Xo	0.26-1	± 1-7%	0. 23-0. 9	±2-9%
	Co	0 .4 6		1.15
	flow	ascendant		ascendant
	inlet pressure was

The heating voltage U and current I were measured directly through a HP 3421A multiplexer.