Two-Phase Flow Patterns,

Heat Transfer Engineering , 23:523, 2002Copyright C 2002 Taylor & Francis01457632/02 $12.00 + .00

Two-Phase Flow Patterns,Pressure Drop, and HeatTransfer during Boiling inMinichannel Flow Passagesof Compact Evaporators

SATISH G. KANDLIKARMechanical Engineering Department, Rochester Institute of Technology, Rochester, New York, USA

The small hydraulic diameters employed during ow boiling in compact evaporator passages arebecoming more important in diverse applications including electronics cooling and fuel cellevaporators. The high pressure drop characteristics of these passages are particularly important asthey alter the ow and heat transfer, especially in parallel multichannel congurations. The pressuredrop oscillations often introduce dryout in some passages while their neighboring passages operateunder single-phase mode. This article presents a comprehensive review of literature on evaporationin small-diameter passages along with some results obtained by the author for water evaporating in1-mm-hydraulic-diameter multichannel passages. Critical heat ux is not covered in this article dueto space constraints.

Major progress in compact evaporator developmenthas been made by the automotive, aerospace, and cryo-genic industries over the last 50 years. The thermal dutyand the energy ef ciency increased during this period,while the space constraints became more vital. Thetrend was toward greater heat transfer rates per unitvolume. The hot side of the evaporators in these appli-cations was generally air, gas, or a condensing vapor.The air-side n geometry also saw signi cant improve-ments resulting from increased heat transfer coef cientsas well as greater surface area densities.

As the air-side heat transfer resistance decreased,more aggressive n designswere employed on the evap-orating side, resulting in narrower ow passages. The

Address correspondence to Dr. Satish G. Kandlikar, MechanicalEngineering Department, Rochester Institute of Technology, Rochester, NY14623, USA. E-mail: [email protected]

narrow refrigerant channels with large aspect ratio werebrazed in small cross-ribbed sections to provide a betterrefrigerant distribution along the width of the channel.The major changes in recent evaporator designs involveindividual, small-hydraulic-diamete r ow passages, ar-ranged in multichannel con guration for the evaporat-ing uid.

Figure 1 shows a plate- n evaporator geometry wi-dely used in compact refrigerant evaporators. Therefrigerant-side passages are made from two platesbrazed together, and air-side ns are placed betweentwo refrigerant ow passages. The plates have cross ribsthat are oriented in opposite directions so that the topand bottom plates forming a refrigerant passage havecontact points only at the intersections of these ridges.The two-phase ow of refrigerant is distributed acrossthe width of the ow passage. This feature is important

5

Figure 1 Schematic of refrigerant and air-side ow passages in a compact plate- n type of evaporator.

in that the localized ow oscillations , caused by nucle-ate boiling and expanding vapor bubbles, are dissipatedacross the width and do not affect the upstream ow.

Figure 2 shows two geometries being used morewidely in compact evaporators. The parallel minichan-nel geometry shown in Figure 2a is used extensively incondensation applications , whereas the geometryshown in Figure 2b has received quite a bit of attentionfor boiling applications . The channels are fabricatedby a variety of processes depending on the dimensionsand plate material. Conventional machining and electri-cal discharge machining are two typical options, whilesemiconductor fabrication processes are appropriate formicrochannel fabrication in chip cooling applications .

FLOW PATTERNS IN SMALL-DIAMETERTUBES

Previous Studies

Visualization of boiling phenomena inside owchannels provides insight into the heat transfer mech-anisms. Bubble formation, coalescence, formation ofslugs or plugs, and local dryout conditions are all

Figure 2 Recent developments in multichannel evaporators.

important in understanding the heat transfer phenom-ena. Although some of the heat transfer and pressuredrop equations employed in the design of commercialequipment are derived from ow pattern-based mod-els, the major bene t of ow pattern information lies inunderstanding the causes for premature dryout or criti-cal heat ux (CHF) condition in an evaporator. Anothermajor bene t is in the design of the inlet and the outletmanifolds in multichannel evaporators.

The ow pattern maps available in the literaturewere rst developed for the petrochemical industry(Baker, [1]) for ow of oil and gas in large-diameterpipes. Subsequently, adiabatic ow pattern maps weredeveloped as general ow pattern maps (for example,Hewitt and Roberts [2], and Taitel et al. [3]). In recentyears, a number of ow pattern maps have been de-veloped for speci c conditions such as small-diametertubes, evaporation or condensation, and compact heatexchanger geometries.

Earlier investigator s extensively studied ow pat-terns for gas liquid ows in channels with small hy-draulic diameters. A representative survey of the owpatterns was presented by Fukano et al. [4]. They iden-ti ed bubbly, plug, slug, and annular ow patterns andcompared the ow pattern transitions with the avail-able ow pattern maps. Subsequently, a detailed studyby Wambsganss et al. [5] provided a more compre-hensive summary and representation of gasliquid owpatterns. The role of surface tension becomes more im-portant in smaller-diameter channels. Triplett et al. [6]explain that, due to the dominance of surface tension,strati ed ow is essentially absent, slug (plug)and churn ow patterns occur over extensive ranges of parameters,and the slip velocity under these patterns is small. Strat-i ed ow can exist at very low ow rates, as observed byKasza et al. [7] for a mass ux of 21 kg/m2 s. Hewitt [8]gives a comprehensive summary of ow pattern studiesavailable in the literature. For large-diameter tubes, thegeneralized ow pattern map for an airwater system,developed by Mandhane et al. [9], was quite represen-tative of other ow conditions as well. However, the

6 heat transfer engineering vol. 23 no. 1 2002

theoretically based transition criteria presented by Taiteland Dukler [10] are among the most widely used owpattern maps. Hewitt [8] notes that both evaporation andcondensation processes have a signi cant effect on the ow patterns.

The effect of evaporation on the ow pattern transi-tions was considered to be quite small in large-diametertubes. This is one of the reasons why the ow patternstudies from gasliquid systems, such as air and water,were extended to the case of evaporation. In smaller-diameter tubes, the effect of evaporation could be quitedramatic.

The evaporation of the liquid phase affects the owin two ways. First, it alters the pressure drop charac-teristics by introducing an acceleration pressure dropcomponent that can be quite large at higher heat uxes.Second, the tube dimension is quite small, and the ef-fect of surface tension forces becomes more importantin de ning the two-phase structure.

Table 1 includes the ow pattern studies for circulartubes and narrow rectangular channels with hydraulicdiameters of the order of 3 mm or smaller. Cornwell andKew [12] conducted experiments with R-113 owing in1.2-mm 0.9-mm rectangular channels. The parallelchannels weremachined in aluminumand a 6-mm-thickglass plate was used to observe the ow pattern. In the ow ranges investigated , three ow patterns were ob-served as shown in Figure 3. These authors also ob-served a strong link between the ow pattern and theheat transfer coef cient. In the isolated bubble region,h / q 000:7, indicating the dominance of nucleate boil-ing.When the bubbles occupied the entire channel crosssection in the con ned bubble region, h dependenceon q decreased. The convection effects were dominantin the annular-slug region. In a subsequent study, Linet al. [33] compared the ow region transitions withthose predicted by Barnea et al. [34], developed foran evaporating steamwater system in 4-mm-diametertubes, and Mishima and Hibiki [35], developed one foran adiabatic airwater system in a 2.05-mm-diametertube. The results indicate that the ow pattern mapsdeveloped for airwater ow are in general applicable,but the transition boundaries need to be re ned for owboiling in small-diameter tubes and channels.

Figure 3 Flow patterns observed by Cornwell and Kew [12] in1.2-mm 0.9-mm parrallel rectangular channels.

Moriyama and Inoue [13] conducted experiments insingle narrow rectangular channels with R-113. Theyobserved (1) attened bubbles, con ned by the owchannel (some of them coalescing), (2) liquid strips owing along the wall, and (3) liquid lm ow.

Mertz et al. [18] investigated single- and multichan-nel test sections with water and R-141b owing in rect-angular multichannels , 1, 2, and 3 mm wide. They ob-served the presence of nucleate boiling, con ned bubble ow, and annular ow, and discovered that the bubblegeneration in the channelswas not a continuous process.In addition, the vapor seemed to stay in the channels,blocking the ow and, in some cases, causing a reverse ow to occur in the channels. In both single-channeland multichannel cases, large pressure pulsations werenoticed.

Kasza et al. [7] presented a detailed study on ow vi-sualization of nucleation activity in a rectangular owchannel of 2.5 mm 6 mm cross section. They viewedthe ow using a high-speed video camera with a maxi-mum frame rate of 12,000 frames per second. The mass ux was 21 kg/m2 s. They observed nucleate boiling onthe wall, as the individual bubbles nucleated and grewon the wall. The bubble growth rates were similar tothose in the pool boiling case when the bubbles grewwithout interacting with the wall or any liquidvaporinterface.

Kasza et al. [7] made interesting observations on in-dividual bubbles and their interaction with other bub-bles and vapor slugs. The vapor slugs were separatedfrom the wall by a thin liquid lm with a 0.67-mmaverage thickness. Nucleation was observed in this liq-uid lm. The bubbles growing in this lm did not eas-ily coalesce with the vapor in the slug. Bubbles grow-ing under the liquid slug were attened and covereda larger wall area compared to those growing in theliquid ow. The heat transfer in the thin liquid micro-layer underneath the bubbles improved the heat trans-fer; the bubble frequency and the vapor volume bothincreased for such bubbles. Their ndings clearly in-dicate the occurrence of nucleate boiling in thin liq-uid lms that exist in both slug ow and annular owconditions.

Bonjour and Lallemand [22] report ow patterns ofR-113 boiling in a narrow space between two verti-cal surfaces. The ow patterns observed are similar tothose observed by other investigators : isolated bubbles,coalesced bubbles, and partial dryout. Comparing thebubble dimensions with the channel size is vital in de-termining whether the small channel size in uences thebubble growth and leads to the con ned bubble owpattern. Following the work of Yao and Chang [36],the Bond number, D e[ r =g( q L q G )]1=2, along withthe Boiling number,D q=(Gh f g ), provided the basis for

heat transfer engineering vol. 23 no. 1 2002 7

Table1

Sum

maryof

investigations

onevaporationin

mini-andmicrochannels

Fluidand

ranges

ofChannelsize/

parameters

D( m

m) ,

G( kg/m

2s),

horizontal( unless

Author/year

q( kW/m

2)

otherw

isestated)

Heattransfer

Pressuredrop

Flowpatterns

Rem

arks

Lazarek

and

R-113,

Circular,

Heattransfer

Pressuredrop

Not

observed

Subcooledandsaturateddataobtained,h

almost

Black

[11],

GD125750,

DD3.1,

LD123

coeff.and

measuredand

constant

inthetwo-phaseregion,dependent

1982

qD14

380

and246

CHF

correlated

onheat

ux.B

ehaviorsimilartolarge-dia.

tubes

combination

ofnucleateandconvective

boiling.Pressuredrop

correlations

obtained.

Cornw

ell

R-113,

Parallelrectangular;

Heattransfer

Not

reported

Isolated

bubble,

The

heattransfercoef

cientw

asfoundtobe

andKew

GD124627,

75channels,

coeff.

con

nedbubble,

dependentontheexisting

owpattern.Inthe

[12],1992

qD333

1.20.9deep;

annular-slug

isolated

bubbleregion,hq0:7,low

erq

36channels,

effectin

con

nedbubbleregion,convection

3.251

.1deep

dominantinannular-slug

region.

Moriyam

aR-113,

Narrowrectangular

Heattransfer

Pressuredrop

Flattened

bubbles,

Two-phase

ow

boiling

datain

narrow

gaps

andInoue

GD2001,000,

channel,0.0350.11

coeff.

measuredand

w/coalescence,

obtained

andcorrelated

withan

annularlm

[13],1992

qD430

gap,widthD30,

components

liquidstrips,

ow

model.N

ucleateboilingignored,

LD

265

calculated

liquid

lm

although

adependence

ofhon

qwas

observed.

Wam

bsganss

R-113,

Circular,

has

aNot

reported

Not

reported

Exceptatthe

lowesth

eatand

mass

uxes,both

etal.[14],

GD50

100,

DD2.92

mm

function

ofnucleateboilingandconvectiveboiling

1993

qD8.890.7

x,G,and

qcomponentswerepresent.

Bow

ersand

R-113,

Mini-and

Heattransfer

Pressuredrop

Not

studied

Analyticaland

experimentalstudies

comparing

Mudaw

arqD1,0002,000,

microchannels,

rate

components

theperformance

ofmini-andmicrochannels.

[15],1994;

0.28

1.1ml/s

DD2.54

and

Minichannelsarepreferableunlessliquid

[16],1994;

0.51

inventoryor

weightconstraintsaresevere.

[17],1994

Mertzetal.

WaterandR-141b,

Rectangularchannels,

Heattransfer

Not

measured

Nucleateboiling,

Single-andmultichanneltestsections.Flowboiling

[18],1996

GD

50,100,200,

1,2,and3mmwide,

coeff.and

con

nedbubble

pulsationwas

observed

inmultichannels,w

ith300,qD3227

aspectratioup

to3

heatu

xandannular

reverseowin

somecases.Nucleateboilingdominant.

Ravigururajan

R-124,0.65ml/s,

270lmwide,1mm

Heattransfer

Not

studied

Not

studied

Experim

entswereconductedover00.9qualityand

etal.[19],1996

20400W

deep,20.52

mm

long

coeff.

5Cinletsubcooling.Wallsuperheat080

C.

Tranetal.

R-12,

Circular,DD2.46;

Heattransfer

Not

studied

Not

studied

Localheattransfercoeff.obtained

upto

xD0.94.

[20],1996

GD44

832,

rectangular,

coeff.

Heattransferin

nucleateboiling-dominantand

qD3.6129

DhD2.4

convectivedominantregions

obtained.N

ewcorrelationfornucleateboiling-dominantregion.

Kasza

etal.

Water,G

D21,

Rectangular,

Notreported

Not

reported

Bubbly,Slug

Increasedbubbleactiv

ityon

wallatn

ucleation

[7],1997

qD110

2.56.0

500

sitesinthethin

liquid

lm

responsibleforhigh

heattransferinsm

allchannels.

Tong

etal.

Water,G

D25,000

Circular,

Subcooled

Focuson

Not

studied

Pressuredrop

measuredinhighlysubcooled

ow

[21],1997

45,000,C

HFof

DD1.05

2.44

ow

boiling

pressuredrop

boiling,correlations

presentedforboth

5080

MW/m

2single-phase

andtwo-phase

ow

.

8

Bonjour

and

R-113,

Rectangular,0.52mm

Notstudied

Notstudied

3

ow

patterns

Nucleateboilingwithisolated

bubbles,

Lallemand

qD020

gap,60

wide,

withnucleate

nucleateboiling

withcoalescedbubblesand

[22],1998

120long,vertical

boiling

partiald

ryout,criteriaproposed

fortransitions.

Peng

and

Water,ethanol

Rectangular,

Heattransfer

Notreported

Not

observed

The

heattransferresults

indicatethatbothnucleate

Wang[23],

andmixtures

widthD0.20.4,

coeff.,heat

andforced-convectionboilingarepresent.No

1998

heightD

0.10.3,

ux

bubbleswereobserved,and

theauthorsproposea

LD50;triangular,

ctitious

boiling.The

authorsdidnotu

seproper

DhD0.20.6,LD120

microscopeandhigh-speed

videotechniques,

resulting

incontradictoryconclusions.

Peng

etal.

Theoretical

Theoretical

Bubblenucleation

Notstudied

Not

studied

Bubblenucleation

modeluses

avaporbubble

[24],1998

model

grow

ingon

aheater

surfacewithheatdiffusion

inthevaporphase.Thiscorrespondstopost-CHF

heattransferandisan

inaccuratemodelof

heat

transfer

during

nucleation

andbubblegrow

th.

Kam

idisand

R-113,pow

erCircular,

Single-and

Notreported

Not

studied

Extremelyhigh

heattransfer

coef

cientsup

toRavigururajan

25700W,

DD1.59,2.78,

two-phase,max

11kW

/m2 C

wereobserved.F

ullydeveloped

[25],1999

ReD

1901,250

3.97,4.62

h

11kW

/m2 C

subcooledboiling

andCHFwereobtained.

Kuznetsov

R-318C,

Annulus,

h

120

kW/m

2 C

Notstudied

Con

nedbubble,

Capillary

forces

importantin

ow

patterns,

andShamirzaev

GD200900,

0.9gap500

cell,

annular

thin

lm

suppresses

nucleation,leads

to[26],1999

qD

2110

convectiveboiling.

Lin

etal.

R-141b,

Circular,DD

1Heattransfer

Notstudied

Not

studied

Heattransfercoeff.obtained

asafunctio

n[27],1999

GD3002,000,

coeff.

ofqualityandheat

ux.T

rendsare

qD

10150

similarto

large-tube

data.

Dow

ingetal.

R-113,rangesnot

Circularmultichannels

Notstudied

Single-and

Not

studied

Asthehelicalcoilradiusbecamesm

aller,

[28],2000

clearlystated

inhelicalcoils,

Two-phase

pressuredrop

reduced

possibly

DhD0.23

1.86,

ow

duetorearrangem

entinowpattern.

helix

dia.D2.87.9

Hestronietat.

Water,

Triangularparallel

Measured,

Notreported

Periodicannular

Periodicannular

ow

observed

in[29],2000

ReD

2070,

chann,

D55

,butdata

microchannels.T

hereisasignicant

qD80

360

nD

21,26,D

hD

notreported

enhancem

entofheattransferduring

0.1290.103,LD15

ow

boiling

inmicrochannels.

Kennedy

etal.

Water,

Circular,

Onsetof

nucleate

Notreported

Not

studied

Heat

uxattheonseto

f

ow

instabilitywas

[30],2000

GD8004,500,

DD

1.17

and

boilingstarts

0.9of

theheat

ux

required

forsaturated

qD

04MW/m

21.45,LD160

instability

vapour

atexit,

similarly,G

atOFIwas

1.1

times

Gforsaturatedexitvaporcondition.

Lakshminarasim

hanR-11,

Rectangular,

Subcooled

and

Notmeasured

Boiling

incipience

Boiling

frontobservedinlaminar

ow

,not

etal.[31],2000

GD60

4,586

1

20357

saturated

observed

visiblein

turbulent

owdueto

comparable

ow

boiling

throughLCD

hbeforeandafter,saturated

ow

boiling

data

correlated

byKandlikar

( 1990)

correlation.

Kandlikar

Water,

Rectangular,

Subcooled

Measured

High-speedphotographyFlowoscillations

and

ow

reversallinked

tothe

etal.[32],2001

GD80

1160

mm

andsaturated

instantaneousvalues

onsingleand

severe

pressuredrop

uctuations,often

560kg/m

2s

ow

boiling

ofpressure

drop

multip

lechannels

leadingto

ow

reversalduring

boiling.

9

the transition from individual to con ned bubble ow.For a smaller Bond number, the channel dimension issmaller than the departure bubble diameter, resulting incon ned bubble ow pattern. For large Bond numbers,the channel size does not interfere with the bubble ow.A more detailed treatment of the forces acting on thebubble is needed to identify this boundary clearly.

Kuznetsov and Shamirzaev [26] studied the ow pat-terns during ow boiling of R318C in a 0.9-mm annulargap between two circular tubes. This work was an ex-tension of previous research on airwater systems byKuznetsov and Vitovsky [37]. The isolated bubble re-gionwas called the small bubble region. It was followedby long Taylors bubbles, similar to con ned bubbles(de ned by earlier investigators), which were elongatedin the ow direction. These bubbles spread along the pe-riphery of the annular gap and formed a cell structurereferred to as the cell ow regime. As the vapor qualityincreased, the annular ow pattern was established witha ripple of waves.

Hestroni et al. [29] studied the evaporation ofwater in multichannel evaporators. The evaporatorsconsisted of 2126 parallel ow passages with chan-nel hydraulic diameters of 0.1030.129 mm. Hestroniet al. observed periodic behavior of the ow patternsin these channels. The ow changed from single-phase ow to annular ow with some cases of dryout. Thedryout, however, did not result in a sharp increase inthe wall temperature. This clearly indicates that there isstill some evaporating liquid lm on the channel wallsthat could not be observed in the video images. Theseauthors also reported the presence of vapor phase in theinlet plenum.

Lakshminarasimhan et al. [31] studied the ow boil-ing in a narrow rectangular channel, 1 mm high 20 mm wide 357 mm long. They used liquid crystaldisplay (LCD) on the heated wall to observe the nu-cleation front and locate the onset of nucleate boiling(ONB). The ONB was clearly identi ed in the lami-nar ow region with subcooled R-11 entering the owchannel. As the ow rate increased to the turbulentregion, the ONB could not be identi ed through thistechnique due to the high heat transfer coef cient inthe subcooled single-phase region. However, it is pos-sible that the ONB may have occurred at discrete lo-cations rather than appearing as a clear identi ablefront.

Discussion on Flow Patterns and Flow PatternTransitions in Small-Diameter Channels

The three ow patterns shown earlier in Figure 1 rep-resent the characteristic ow patterns associated with

two-phase ow in minichannels. It is clear that discretebubbles, resulting from nucleation activity on the wall,are present in the subcooled boiling and low-quality re-gions. The presence of nucleation in the small-diametertubes is also evident through the available studies. Theobservations of nucleating bubbles in the thin liquid lms by Kasza et al. [7], shown in Figure 4, are alsovery revealing.

The experimental conditions employed by Kaszaet al. represent low-Reynolds-number conditions . Withtheir hydraulic diameter of 3.53 mm and a mass ux of21 kg/m2 s, the single-phase Reynolds number is 262at 1 atm pressure. The shear stress effects under theseconditions are expected to be quite low, and it shouldnot come as a surprise that the growth rate exponentfor nucleating bubbles re ects that under pool boilingconditions. In general, most of the visual studies are forlow ow rates, as the bubble activity cannot be easilytraced at higher mass uxes.

Kandlikar and Stumm [38], and Kandlikar andSpiesman [39], demonstrated the presence of nucleat-ing bubbles under highly sheared ow conditions ina rectangular channel. It was noted that bubble nucle-ation occurred when the nucleation criterion for avail-able cavity sizes was satis ed. The effect of the owand wall temperature on bubble characteristics was il-lustrated by Kandlikar [40] and is shown in Figures 5and 6.

Figure 5 shows the effect of owReynolds number onthe bubble growth rate. As the ow velocity increased, ow changed from laminar to transition region with anassociated increase in the single-phase heat transfer co-ef cient. This caused the bubble to grow much faster,reaching a departure condition in about 25 ms at Re D2,280, as opposed to 300C ms at Re D 1,267. The de-parture bubble diameter is also in uenced by the ow.As the ow velocity increases, the drag forces cause thebubbles to depart at smaller diameters.

Figure 6 further illustrates the sensitivity of the walltemperature conditions on the bubble growth rates. Ahigher wall temperature, with a greater associated heat ux, causes the bubbles to grow rapidly and reach thedeparture conditions much sooner. The departure sizesappear to be more dependent on the ow velocity forthe conditions depicted in these gures.

From the observations above, it may be concludedthat the nucleating bubbles are present in ow boilingunder high shear conditions . Kasza et al. [7] observedsuch bubbles in thin lms, shown in Figure 4b, con rm-ing that nucleation can occur in annular ow as well.Under these conditions, the nucleating bubble size de-creases, and bubble departure frequency increases. Thisfurther con rms the conclusions made by Kandlikarand Stumm [38] that a high speed camera with suitable


Figure 4 Flow patterns and bubble nucleation in the liquid lm observed by Kasza et al. [7].

magni cation is needed to observe the nucleating bub-bles (1) under high shear stress conditions , and (2) athigh wall temperatures. In fact, the use of high-speedphotography is essential in clearly observing the owpatterns in small-diameter tubes.

The bubbles departing in the ow can exist as in-dividual bubbles unless their size is smaller than thechannel dimension normal to the nucleating surface.Further growth of these bubbles results in their con-

Figure 5 Effect of owon bubble growth, subcooled ow ofwaterat 1 atm pressure in 3-mm 40-mm rectangular channel, Twall D108C, Tbulk D 80C, cavity radius 3.2 l m, Kandlikar [40].

nement by the channel walls under the con ned owpattern. In reality, the con ned ow pattern is similarto the early stages of the plug ow pattern seen in theconventional two-phase ow patterns for larger diame-ter tubes (>3 mm). Annular ow pattern then followsat higher qualities.

Flow Instabilitie s

The ow instability is another concern in the designof evaporators that employ small channels. The owinstabilitie s can be reduced considerably by increasingthe upstream pressure drop prior to the ow entering achannel. A large-diameter ow section, however, gen-erally precedes the test section in a number of experi-mental studies conducted on gas liquid ows in small-diameter tubes. In the study conducted by Lin et al. [33],air was introduced in a large mixing chamber upstreamof the test section to reduce the disturbances resultingfrom gas injection. The presence of such low-pressure-drop regions immediately before the test section leadsto signi cant ow instabilitie s that cause large pressuredrop excursions, and occasionally result in a negativepressure drop with a corresponding ow reversal in thechannel.


Figure 6 Effect of wall temperatures on bubble growth, subcooled ow of water at 1 atm pressure in 3-mm 40-mm rectangular channel,Twall D 108C, Tbulk D 80C, cavity radius 3.2 l m, Kandlikar [40].

The instability occurs in the negative-pressure-dropregion of the demand curve plotted as the pressure dropversus inlet ow velocity of the subcooled liquid.Kennedy et al. [30] studied the onset of ow insta-bility and noted that instability sets in at a slightlylower mass ux than the onset of signi cant voidcondition.

Cornwell and Kew [12] conducted experimentson ow boiling of R-113 in parallel microchannels.They observed that the ow was unstable at lower ow rates. The pressure drop uctuations were notreported.

Kandlikar et al. [32] viewed the ow boiling of wa-ter in electrically heated multichannel evaporators con-sisting of six parallel channels. The ow structure wasvisualized using a high-speed video camera up to amaximum speed of 1,000 frames per second. The typ-ical bubbly ow, slug ow, and annular ow patternswere observed. Nucleation was also observed in thebulk liquid as well as in the liquid lm. However, themost interesting discovery made, in an attempt to un-derstand the severe pressure uctuations (describedlater under Pressure Drop), was a visual con r-mation of complete ow reversal in some of thechannels.

Figure 7 shows the schematic of the multichannelevaporator investigated by Kandlikar et al. [32]. Theevaporator was heated electrically from the back wallof the test section. The front part was covered with ahigh-temperature-resistan t glass for ow visualization .

Figure 8 shows the sequence of the events that leadto ow reversal in the ow channels. Two adjacent cen-

tral channels are shown at 2-ms intervals in frames (a)through (e). Both channels (1) and (2) exhibit slug owin the visible section.

Vertical lines (y) and (z) indicate the initial bound-aries of a vapor slug in channel (2) of Figure 8a. Verticallines (x) and (w) are reference lines to aid visualizationof slug motion throughout the frames.

In Figure 8b, channel (1) has ow in the directionof bulk ow (left to right). The vapor slug in chan-nel (2) has expanded in the direction of bulk ow, yetthe inlet-side uid/vapor interface has not moved. The uid/vapor interface on the inlet side of the slug inchannel (2) is still stationary in Figure 8c, althoughthe outlet-side interface moves in the bulk ow direc-tion. In Figure 8d the ow in channel (1) moves alongthe direction of bulk ow, but the inlet-side uid/vaporinterface of the slug in channel (2) progresses in the

Figure 7 Multichannel evaporator investigated by Kandlikaret al. [32].


Figure 8 Successive frames (a) through (e) at 2-ms intervals oftwo channels interacting. G D 40 kg=m2 s, surface temperature D110.6C, entering water temperature D 24.7C, outlet water tem-peratureD 99.3C, x > 0.

direction counter to the bulk ow. In Figure 8e, theinlet uid/vapor interfaces in both channels move inthe direction counter to bulk ow. For this particularcase, it appears that both of the channels experience avapor-clogging condition where the differential pres-sure across the channels increases due to vapor gener-ation, and the mass ow rate is consequently reducedthrough these two channels. The reaction to this condi-tion in the other four channels would be an increased ow rate.

Concluding Remarks on Flow Patterns

The ow patterns observed in small channels in-dicate that the nucleating bubbles play an importantrole in small-diameter channels. The three predomi-nant ow patterns are (1) isolated bubbles, (2) con nedbubbles, and (3) annular-slug. Note that the ow pat-terns under highmass ux conditions (G> 500 kg/m2 s)have not been studied in the literature due to dif -culty in capturing the high-speed movement underthese conditions. Further work in this area isrecommended.

PRESSURE DROP IN SMALL-DIAMETER FLOWBOILING CHANNELS

Single Channel

Pressure drop in small-diameter tubes has been stud-ied by a number of investigators . Lazarek and Black[11] conducted systematic experiments to evaluate thethree components of pressure drop. The desired qual-ity was generated in the heated inlet section and thefrictional pressure drop was measured under adiabaticconditions in the discharge section. The frictional pres-sure was correlated using a correlation recommendedby Collier [41] with the Martinelli parameter v tt:

pTPpLO

D 1CCv tt

C1

v 2tt(1)

The subscript TP corresponds to the two-phase value,while LO corresponds to the value with the total owin the liquid phase. Lazarek and Black found that us-ing a value of C D 30 produces results that are in goodagreement with their experimental data. The value of Crecommended by Collier is 20 for large tubes.

The acceleration pressure drop was accurately pre-dicted using the Martinelli and Nelsons [42] separated ow model with a multiplier Ksa:

psaG2=(2 q L )

D Ksa

"q L

q G

x2exa ex

C(1 x )2

1 a ex

q L

q G

x2ina in

(1 xin)2

1 a in

#(2)

Here x is the vapor quality and a is the void fraction.Ksa is an empirical constant. Lazarek and Black foundthat a value of K D 2.5 correlated most of their datawithin 20%.

Moriyama and Inoue [13] measured pressure drop ofR-113 boiling in narrow annular gaps of 35110 l m.Their experimental values for frictional pressure dropwere correlated by slightly modifying Eq. (1). Fromtheir study, it is evident that the separated ow modelis applicable for the narrow gaps typically encounteredin microchannel applications .

On the other hand, Bowers and Mudawar [17] em-ployed a homogeneous ow model with fTP D 0.003as recommended by Collier [41]. Their results for bothminichannels and microchannels were correlated towithin 30% with this model.


Tong et al. [21] present an exhaustive treatment ofpressure drop during subcooled ow boiling in mini-channels. In addition, they presented a correlation topredict the two-phase pressure drop. Since the voidfraction was very small, a two-phase friction factor wasapplied. They observed a roughness effect on the single-phase laminar-to-turbulen t transition in these tubes. Theeffect of the tube diameter-to-length ratiowas also notedto be quite signi cant.

From the studies available in the literature, the ef-fect of channel dimension on two-phase pressure dropis not clearly established. Although several investiga-tors provide different correlation schemes to correlatetheir data, they do not provide a clear indication ofthe effect of small passage sizes on pressure drop. Theadded effect of channel wall roughness on pressuredrop, seen in the single-phase data, is also not incor-porated while analyzing the two-phase pressure dropparameters. These effects will become more importantas the channel size decreases from minichannel to mi-crochannel geometries.

Multiple Channels

As the tube diameter decreases, vapor slugs ll thetubes. Under two-phase ow conditions , ow insta-bilities occur when the pressure drop in the upstreamsection is relatively small. Introducing a large pressuredrop through a throttle valve in the liquid line immedi-ately prior to the test section considerably reduces theinstabilities . These instabilitie s have a signi cant effecton pressure drop and heat transfer under ow boilingconditions.

Figure 9 Differential pressure history for a six-channel (1-mm1-mm) parallel con guration. G D 48 kg=m2 s, Pmax=L D 4,688Pa/m, Pmin=L D 1,793 Pa/m, average surface temperature D125C, q 00 D 74:3 kW=m2, water inlet and outlet temperatures 25.0and 90.2C, Kandlikar et al. [32].

Figure 9 shows the pressure drop uctuations mea-sured in a multichannel evaporator with six parallel1-mm 1-mm square microchannels. Similar obser-vations were made by Kew and Cornwell [43] during ow boiling of R-141b in 2-mm square channels and in2.87-mm-diameter circular tubes. The pressure drop uctuations observed by Kandlikar et al. [32] are quitelarge and result in ow reversals as discussed earlierin the ow patterns section. The compressibility of thetwo-phase mixture, in adjacent channels, acts in a man-ner similar to the negative slope in the upstream sectionof a single evaporator tube. The large pressure drop uctuations lead to instantaneous localized ow rever-sal in some of the parallel channels. There are nomodelscurrently available that predict the pressure drop uc-tuations and the ow reversals under ow boiling con-ditions. Knowledge of these conditions is essential forsafe operation of evaporators employing minichannelsand microchannels.

HEAT TRANSFER IN SMALL-DIAMETER FLOWBOILING CHANNELS

Flow boiling in small-diameter tubes and compactheat exchanger passages has been a subject of interestin the automotive , aerospace, air liquefaction, chemi-cal and petroleum industries, and in electronics cool-ing applications . Nakayama and Yabe [44], and Kewand Cornwell [45] present a good overview of the re-cent advances in this area. Table 1 includes some ofthe recent works on ow boiling heat transfer inminichannels.

Flow boiling heat transfer in 13-mm-diameter chan-nels has been a subject of investigation for a long time.In one of the earlier articles, Bergles [46] studied thecritical heat ux in 0.584-, 1.194-, and 2.388-mm-diameter electrically heated tubes. He indicated thatwhen the bubble diameter approaches the tube diam-eter, considerable nonequilibrium vapor volume existsin the evaporator section, and ow oscillations cause apremature burnout in the small-diameter tubes.

Bowers andMudawar [17] studied ow boiling pres-sure drop and CHF in a minichannel of 2.54 mm diam-eter, and a microchannel of 510 l m diameter. Boilingcurves for the two channels were obtained at nearlyequal values of liquid Reynolds number. Their resultsare reproduced in Figure 10. Despite the large varia-tion in the tube diameter, the two curves overlap in theboiling region. It is believed that these experiments fallunder the fully developed nucleate boiling regime. Thedifferences between the two boiling curves are only ev-ident at low heat ux (near-single-phase region) andhigh heat ux values (approaching CHF condition).


Figure 10 Flow boiling characteristics in minichannel andmicrochannel evaporators, Bowers and Mudawar [15].

This indicates that in spite of the differences in the owcharacteristics of the channels, the ow boiling behav-ior is quite similar in the two geometries.

The detailed ow boiling data by Lazarek and Black[11] provide a clear comparison between the ow boil-ing characteristics of minichannels and regular tubes(>3 mm diameter). Figure 11 shows a comparison ofLazarek and Blacks ow boiling data in a 3.1-mm-diameter tube and Kandlikars [47] ow boilingcorrelation. The correlation represents the data quitewell, although some differences exist in the high-qualityregion. Although a detailed study is warranted, as a rst-order approximation, one may use the correlations

Figure 11 Comparison of ow boiling heat transfer coef cientdata by Lazarek and Black [11] with Kandlikar [50] correlation.

developed for the large-diameter tubes for predictingthe heat transfer coef cients in minichannels.

Cornwell and Kew [12] conducted experiments intwo sets of parallel channel geometries, 1.2 mm 0.9mmdeep, and 3.25mm 1.1mmdeep. Their resultsindicate that the ow boiling in such small channelsexhibits fully developed nucleate boiling characteris-tics in the isolated bubble region at lower qualities. Athigher qualities (when the bubbles ll the entire crosssection), and in the annular ow region, convective ef-fects dominate heat transfer. These characteristics aresimilar to those observed for the large-diameter tubes.The isolated and con ned bubble regions exhibit char-acteristics similar to the nucleate boiling-dominan t re-gion, while the annular-slug region exhibits the con-vective dominant trend seen in large-diameter tubes(Kandlikar, [47]).

Another aspect of ow boiling heat transfer in smallchannels is the oscillatory nature of the ow. The time-averaged value between two regions (i.e., between thecon ned bubble and the annular regions) would yielda combination of nucleate boiling-dominan t and con-vective boiling-dominan t regions. Purely ow pattern-based correlations need to include this averagingeffect. Since the large-diameter correlations combinethese effects, rather than using distinct boundaries, theyare expected to provide the basis for accuratecorrelation schemes for small-diameter tubes andchannels.

Continuing the work in this area, Lin et al. [27] ob-tained ow boiling data with R-141b in 1-mm-diametertubes. Their results indicate that the heat transfer co-ef cient exhibits behavior similar to that reported byCornwell and Kew [12]. The role played by bubbles isclearly an important one. Speci cally, they presenteddetailed results at G D 500 kg/m2 s with q from 18to 72 kW/m2. At high heat uxes, they observed con-siderable uctuations in the wall temperature readings,indicative of ow oscillations that cause changes in theinstantaneous values of local saturation temperature andheat transfer rate.

Wambsganss et al. [14] conducted extensive experi-ments on ow boiling of R-113 in a 2.92-mm-diametertube. Their results indicate that the heat transfer coef- cient was sensitive to both heat ux and mass uxchanges, except for the lowest mass ux result. At thelowest value, G D 50 kg/m2 s, changing the heat uxfrom 8 to 16 kW/m2 did not have any in uence on theheat transfer coef cient. One possible explanation isthat for this case, the nucleate boiling is in the partialboiling region at low heat fluxes, and the effect of heat ux is therefore quite small. For their other test condi-tions, the mass ux was varied from 100 to 300 kg/m2 s,and the heat ux was varied from 16 to 63 kW/m2.


For these tests, the heat transfer coef cient exhibited adependence on both heat ux and mass ux. This indi-cates the contributions from both nucleate boiling andconvective boiling mechanisms. They also comparedtheir data with the available correlations and found thatthe correlations by Liu and Winterton [48], Shah [49],and Kandlikar [50] predicted their results with a meandeviation of less than 20%. In particular, Wambsgansset al. found that the speci c correlation developed byLazarek and Black [11], who used their own small-diameter-tube data with R-113 in the correlation devel-opment, predicted the data with a mean error of 12.7%.The Chen [51] correlation predicted the results with amean deviation of 36%.

Mertz et al. [18] conducted extensive experimentswithwater andR-141bboiling in six differentminichan-nel con gurations. The ow boiling was observed asoscillatory phenomena in multichannels . It is interest-ing to note that although the heat transfer coef cientincreased with heat ux in almost all cases for single-channels, the trend forwater owing in themultichannelcon guration atGD 200 kg/m2 Cwas different. For allchannels in multichannel con guration, the heat trans-fer coef cient decreased with increasing heat fluxes. Itis suspected that the ow oscillations and reversals ob-served in multichannels are responsible for the degrada-tion in heat transfer. For R-141b boiling in multichannelcon guration, the heat ux effects wereweak and some-what mixed.

Mertz et al. [18] observed that the heat transfer co-ef cient for both uids in the multichannel con gu-ration was considerably higher than the correspond-ing single channel values under the same operatingconditions. Figure 12 shows the comparison for water(at 200 kg/m2 s in 2-mm 4-mm channels) in single-and multichannel con gurations under the same op-erating conditions. The oscillatory behavior found inthe multichannel evaporator is therefore believed to im-prove the heat transfer, although the improvement de-creases at higher heat fluxes. Another fact to note is thatthe heat transfer coef cient is lower for the 1-mm 1-mm multichannel con guration than for its 2-mm 4-mm counterpart as shown in Figure 12.

Tran et al. [20] conducted experiments with R-12 insmall circular and rectangular channels, both of2.46-mm hydraulic diameter. Their results indicatedtwo distinct regions, a convective boiling-dominan t re-gion at lower wall superheat values, and a nucleateboiling-dominan t region at higher wall superheat val-ues. They compared their data with the Kandlikar [50]correlation, and found that it exhibited similar trends,but underpredicted the results. One reason for this dif-ference is the fact that the single-phase heat transfercoef cients in small-diameter tubes is generally higher

Figure 12 Comparisons of the average heat transfer coef cienttrendlines for water in 2-mm 4-mm single- and multichannelcon gurations, and 1-mm1-mmmultichannel con guration.G D200 kg=m2 s, Tsat D 120 C, Mertz et al. [18].

than those predicted by the Dittus-Boelter type of corre-lations. It is recommended that the measuredsingle-phase heat transfer coef cients be used in thecorrelation as recommended by Kandlikar [47].

It is interesting to note that the heat transfer co-ef cients obtained by Tran et al. at higher qualitiesexhibited a dependence on heat ux alone. The mass ux had virtually no in uence on the heat transfer co-ef cient. These observations are supported by the vi-sual observations made by Kasza et al. [7], who stud-ied ow boiling of water in rectangular channels of2.5-mm 6-mm cross section. They concluded that theincreased bubble activity at nucleation sites in the thinliquid lm is responsible for high heat transfer coef- cient in small-hydraulic-diamete r tubes and channels.Kuznetsov and Shamirzaev [26] conducted experimentswith R-318C in an annular gap of 0.9 mm. They ob-served that at higher values of quality, nucleation wasseen to be suppressed. However, their experimental re-sults were in agreement with the correlation by Tranet al. [20],whichwas developed for the nucleate boiling-dominant region.

Kamidis and Ravigururajan [25] conducted owboiling experiments with R-113 in circular tubes of1.59, 2.78, 3.97, and 4.62 mm diameter. Their results


Figure 13 Comparison of Kamidis and Ravigururajan (1999) data with Kandlikar correlation (1990) for 1.59-mm-diameter tube, R-113.

indicate that very high heat transfer coef cients of theorder of 10 kW/m2 C are obtained in the ow boil-ing region. Figure 13 shows a comparison of their datafor 1.59-mm-diameter tube with the Kandlikar [50]correlation. For a Reynolds number of 5,720, the agree-ment is excellent. For Re D 2,370, the correlation un-derpredicts the data. It is suspected that theReynolds number is in the transition region where theturbulent single-phase heat transfer correlation is notapplicable.

Kennedy et al. [30] studied the instability during owboiling of water in circular tubes of 1.17 and 1.45 mmdiameter. Based on their results, they proposed that theinstability is initiated in the tube when the impressedheat ux is 90%of the value required to obtain saturatedvapor condition at the exit section.

Lakshminarasimhan et al. [31] conducted experi-ments with R-11 in 1-mm 20-mm rectangular chan-nels. They noted that the their saturated ow boilingdata was accurately predicted using the large-tubecorrelation by Kandlikar [50]. They also observed aclear boiling front with liquid ow in the laminar re-gion. In the turbulent region, the boiling front couldnot be clearly viewed due to the high heat transfercoef cient in the single-phase region prior tonucleation.

The experimental studies available in the literatureprovide some preliminary data on ow boiling heattransfer in small-diameter tubes and channels.

In the case of Lazarek and Blacks [11] andLakshminarasimhan et al. [31] data, the Kandlikar [50]correlation for large-diameter tubes predicted the re-sults satisfactorily. However, Tran et al. [20] indicateda signi cant enhancement over the large-diameter cor-relations. Pressure uctuations andmultichannel effectsare not clearly understood for small-diameter tubes.As noted by many investigators , including Lin et al.[27] and Mertz et al. [18], pressure uctuations havea signi cant effect on the ow characteristics and as-sociated heat transfer performance. The periodic llingof the ow channel with large vapor plugs, followedby all-liquid ow in the channel, make it very dif cultto apply ow pattern-based models to predict the heattransfer rates. Further research in this area is highlyrecommended.

Another class of ow channels that have receivedsome attention in literature are those with hydraulic di-ameters below 500 l m. These channels are referredto as microchannels, although the precise boundary isnot well de ned. There are very few quantitative stud-ies available for the microchannel geometry under owboiling conditions . Further efforts are needed in thisarea to generate high-quality experimental data in mi-crochannels under ow boiling conditions. This geom-etry has been investigated with its potential applicationin microelectronics cooling. Table 1 clearly indicatesthat there is very little quantitative data available formicrochannels.


Ravigururajan et al. [19] studied ow boiling in ami-crochannel 270 l mwide and 11 mmdeep. The working uid was R-124, and was tested over the entire qualityrange. They found that the heat transfer coef cient de-creased from a value of 11 kW/m2 C at x D 0.01 toabout 8 kW/m2 C at x D 0.65. Although no conclu-sions were drawn, this behavior may be the results ofthe two trends: (1) the nucleate boiling heat transfer isdominant, leading to its suppression at higher qualities;or (2) the higher vapor fraction leads to ow oscillationsin multichannels with a consequent change (increase?)in the heat transfer coef cient.

A number of investigators (for example, Peng andWang [23], Peng et al. [24]) have indicated that the ow boiling heat transfer inmicrochannelsmay be quitedifferent than that in larger-diameter tubes. They alsoindicated that the regular nucleate boiling phenomenondoes not exist in microchannels.

Peng and Wang [23] conducted experiments withwater, ethanol, and their mixtures in different shapedmicrochannel geometries (listed in Table 1). They notedthe presence of both nucleate boiling and convectiveboiling in various regimes. They did not observe anybubble activity in the rectangular and triangular pas-sages with hydraulic diameters between 0.1 to0.6 mm. In turn, they called this a ctitious boilingphenomenon.

It is dif cult to accept the notion of the ctitious boil-ing presented by Peng and Wang [23]. Similar studiesreported by Kandlikar and Stumm [38] and Kandlikarand Spiesman [39] with a channel height of 3 mmindicate that bubbles as small as 10 l m are seen todepart from the nucleating sites. The key to observingbubble activity in small channels is to employ high-speed photography along with a high-resolutionmicroscope.

The theoretical analysis presented by Peng andWang[23] considers a bubble nucleus that completely lls thetube. The microchannel dimension is of the order of100 l m, while the cavity sizes for active nucleation areon the order of a few micrometers or smaller. It is ex-pected that the nucleation criterion for ow boiling, es-tablished for large-diameter tubes, will hold true unlessthe tube diameter approaches the cavity dimensions.Such a conditionmay exist only in submicrometer-sizedtubes.

In conclusion, ow boiling in microchannels is anarea where further research is needed. The dif culty inobserving the bubbles and in the accurate measurementof heat fluxes at the wall make it very dif cult to un-derstand the mechanism of ow boiling heat transferin this geometry. With the availability of more accuratedata, we may be able to nd some of the answers in thenear future.

DESIGN CONSIDERATIONSIN MINICHANNEL EVAPORATORS

Mehendale et al. [52] and [53] present a goodoverview of the design considerations for heat exchang-ers employing mini- and microchannels.

Flow Instability in Multichannel Evaporators

The small-diameter multichannel evaporators differfrom the small-hydraulic-diamete r compact heat ex-changers in one vital aspect: there are no cross ow con-nections available for the uid to ow across the widthof the ow channel as it passes through the evapora-tor. This cross-connection helps the nucleating bubblesgrow in the crosswise direction without blocking theentire ow passage, as in the case of small-diameterchannels. This ow structure is clearly illustrated bythe ow pattern investigation conducted by Kuznetsovand Shamirzaev [26] in an annular gap between twoconcentric tubes. They observed a cell pattern that ef-fectively allows the bubbles and vapor to grow in thecross ow direction without blocking the ow. In thecase of square channels, as shown by Kandlikar et al.[32], the vapor bubble growth leads to large pressure uctuations that are not desirable for stable operationof the evaporator. The presence of ns or ribs in the gapis expected to further provide stability to the ow byincreasing ow resistance.

In the case of multichannel evaporators employingindividual small-diameter tubes or channels, the chan-nels running parallel to any given channel (which isexperiencing vapor expansion in a direction oppositeto the ow) act in a manner similar to reducing theupstream pressure drop characteristics in a two-phasesystem. Severe pressure drop uctuations, coupled withthe back ow of vapor into the inlet manifold, are notdesirable. These could lead to premature CHF in someof the channels where vapor may ow preferentially,without being accompanied by the liquid ow. Someof the systems that employ such evaporators may nottolerate such severe uctuations in the ow rate.

With these considerations , it is necessary to designmultichannel evaporators that avoid the severe pressure uctuations found in parallel channels. Further researchin this area is warranted.

Design Guidelines for Sizing Small-DiameterMultichannel Evaporators

Small channels present a number of advantages,mak-ing them attractive for speci c systems. Their compactsize, low weight, low liquid/vapor inventory, and fast


response are just some of the desirable features. In thissection, preliminary guidelines are presented for de-signing multichannel evaporators with small-diameterchannels. The design conditions considered in this anal-ysis are as follows.

Design Conditions

It is assumed that an existing single- or multichan-nel evaporator employing large-diameter (D) tubes isto be replaced with a multichannel evaporator employ-ing small-diameter (d ) tubes. Capital letter subscriptsrefer to the large-diameter tube, while lowercase sub-scripts refer to smaller-diameter tubes. For the quali-tative analysis presented here, it is assumed that bothgeometries employ circular tubes, and that one larger-diameter tube is being replaced by n number of smaller-diameter tubes. The total mass ow rate and the totalheat transfer rate are identical in both cases. The objec-tive is to arrive at the number of small-diameter tubesneeded to replace each large-diameter tube, and the newlength of the evaporator. Another consideration is theneed for equal pressure drop in the two cases. The anal-ysis is presented for a single-pass evaporator. It can beextended to a multipass evaporator con guration, butthe treatment will introduce many additional parame-ters. The purpose of the following exercise is to pro-vide some simple guidelines to help in designing thenew evaporator. Extensive design efforts will be neededto arrive at the nal design and all of the associateddetails.

Design Comparison

If n parallel channels are employed in the new evap-orator (for each tube in the original design), the mass ux and heat ux for the new heat exchangerwith small-diameter (d ) tubes would be different than those of theoriginal heat exchanger with large-diameter (D) tubes.Since the total mass ow rate remains constant betweenthe two designs, we get

n DGDGd

D2

d2(3)

The total heat transfer rates in the two cases are alsoidentical, since the evaporators are being designed forthe same heat duty. If we apply the heat transfer rateequations with the respective average heat transfer co-ef cients, and assume that the operating temperaturedifference in the two cases is identical, we can write

LdLD

DhDhd

1

n

D

d(4)

Substituting n from Eq. (3) into Eq. (4), the ratio ofthe lengths in the ow direction is given by

LdLD

DhDhd

GdGD

d

D(5)

For the same exit quality conditions, the total heattransferred in the heat exchanger remains the same. Theheat fluxes in the two cases are related by the followingequation:

qdqD

D1

n

D

d

LDLd

(6)

The ow boiling in the small-diameter tubes exhibitsa nucleate boiling-dominant region at low qualities.Here the heat transfer coef cient varies as q0:7. In thehigher-quality region, the ow becomes convectiveboiling-dominant , with the heat transfer coef cient in-dependent of q , and varying as G0:7. In general, thedependence of h may be expressed as h / qmG p. Theratio of the two heat transfer coef cients isgiven by

hdhD

DqdqD

m GdGD

p(7)

The exponents m and p depend on the ow boilingheat transfer characteristics under the prescribed oper-ating conditions . Their values range from m D 0 to 0.7,and pD 0 to 0.8 (Kandlikar, [40]). Substituting the heat ux ratio from Eq. (6) into Eq. (7), combining it withEq. (3), and then substituting the heat transfer coef -cient ratio into Eq. (5), the ratio of the two lengths isobtained as

LdLD

DGdGD

(1mp)=(1m) dD

(8)

Equation (8) provides a preliminary estimate of thelength of the heat exchanger needed to obtain the samevapor generation rate using a small-diameter evapora-tor. The number of small-diameter tubes replacing eachlarge-diameter tube is given by Eq. (3).

A few observations can be made regarding the effectof boiling characteristics on the length ratio presentedin Eq. (8). If the nucleate boiling is the dominant modein both cases, then p D 0. This results in a mass uxratio dependence given by (Ld=LD ) D (Gd=GD )(d=D ).On the other hand, if the heat transfer is convectivedominant, then m D 0 and p D 0.8. In the latter case,the mass ux ratio has a weak effect on the length ra-tio, (Ld=LD ) D (Gd=GD )0:2 (d=D ). However, the actual


variation lies between the two extreme cases discussedhere.

Another important factor to be considered in the de-sign of heat exchangers is the pressure drop. The designguideline provided by Eq. (8) does not address this is-sue. A similar analysis is now presented for pressuredrop comparison in the two cases.

The pressure drop analysis is a bit more complex. Tosimplify the analysis, the gravitational pressure dropis considered negligible when compared to the fric-tion and acceleration pressure drop terms. Assumingthe respective exit quality and exit void fractions to beequal in both cases, the pressure drop may be expressedin terms of the mass ux, tube length, tube diameter,exit quality, and uid properties. The frictional pres-sure drop varies as p f / fTPLG2=D, while the accel-eration pressure drop varies as p f /G2. In addition,the void fraction plays a role in the pressure drop terms.The two-phase friction factor may be considered to varyas fTP/G0:25. Assuming that the same equations ap-ply for the small- and large-diameter tubes, the ratio ofpressure drops may be expressed as

pdpD

DLdG1:75d

dC1F1( a d )C G2dC2F2( a d )

LDG1:75DDC1F1( a D )C G2DC2F2( a D )

(9)

The constants C1 and C2 include additional variablesin the respective pressure drop terms. F1 and F2 arefunctions of the void fractions in the two cases. Al-though the effects of mass ux, diameter, and lengthon pressure drop are not immediately obvious, assum-ing the frictional pressure drop to be dominant providessome degree of guidance. In addition, assuming the voidfractions and their effects to be similar, Eq. (9) may besimpli ed as follows:

pdpD

DLdG1:75d

d

LDG1:75D

D (10)

For the case of equal pressure drop between the twocon gurations, the length ratio is obtained as

LdLD

DGdGD

1:75 dD

(11)

Comparing Eqs. (8) and (11), it is clear that the ef-fect of mass ux is more severe on the pressure dropthan on the heat transfer. The diameter effect is samein both cases. If the mass ux is held constant forthe two con gurations, then the length ratio is iden-tical to the diameter ratio, Ld=LD D d=D. However, in

practical system designs, a higher pressure drop is gen-erally acceptedwith evaporators employing small chan-nels, and tube lengths larger than that given by Eq. (11)are employed.

The negative exponent in the mass ux ratio ofEq. (11) indicates that increasing the mass ux resultsin shorter tube lengths for the same pressure drop. Inother words, increasing Gd causes the pressure drop toincrease, and shorter tube lengths are needed tomeet thepressure drop requirements. From the heat transfer per-spective, a larger tube length may be needed to accom-modate higher mass fluxes. Consequently, the designmass ux is a compromise between these considera-tions and other system requirements.

The preceding discussion provides a preliminary ba-sis for the selection of a mass ux value for the smaller-tube-diameter heat exchanger being designed to replacean existing larger-tube-diameter evaporator. Needlessto say, a number of additional parameters, including uid properties, the local heat transfer coef cient andpressure drop relationships, differences in manifoldingand number of passes, and the differences in allow-able pressure drop will affect the design of the newevaporator with smaller-diameter tubes. Another ma-jor consideration in the design of the evaporator is theperformance on the hot- uid side. In the analysis pre-sented here, thewall temperatureswere considered to beidentical in both evaporators. The comparisons shouldtherefore be treated as qualitative in determining rst-order effects.

CONCLUSIONS

On the basis of a critical literature review and thework conducted by the author, the following conclu-sions are drawn:

1. Three ow patterns are commonly encountered dur-ing ow boiling in minichannels: isolated bubble,con nedbubble or plug/slug, and annular. The visualstudies available in the literature have been generallyconducted for low mass ux values in tubes of 1-mmor larger hydraulic diameters.

2. Large pressure drop uctuations are noted inmultichannel evaporators. Flow pattern obser-vations revealed a ow reversal in some channelswith expanding bubbles pushing the liquidvaporinterface in both the upstream and downstreamdirections.

3. Heat transfer studies in the minichannels indicatethat, as a rst-order estimate, heat transfer may bepredicted using the ow boiling correlations devel-oped for large-diameter tubes.


4. The heat transfer rate in multichannel evaporatorsis different from that in single-channel evaporatorsunder the same set of operating conditions. The roleof ow uctuations due to ow rate instabilitie s arenot clearly understood at this stage.

5. Severe pressure drop uctuations are not included inany pressure drop prediction schemes for minichan-nel evaporators. Both separated and homogeneous ow models have been used with some degree ofsuccess by previous investigators .

6. In designing evaporators with small-diameter chan-nels, the length-to-diamete r ratio depends on theheat transfer andpressuredrop characteristics.Largerpressure drops are generally accepted in evaporatorswith small-diameter channels.

FUTURE RESEARCH NEEDS

Future research needs are summarized below.

1. Conduct high-speed video studies to obtain ow pat-tern information under high-mass- ux conditions insmall-diameter tubes and channels.

2. Compare the performance of single-tube evapora-tors and multichannel evaporators under the sameoperating conditions and identify the reasons for thedifferences in their performance.

3. Study the effects of inlet ow conditions and mani-fold design on the performance of the multichannelevaporator.

4. Conduct more experiments with minichannel evap-orators to obtain accurate ow boiling heat trans-fer and pressure drop data as a function of qual-ity, heat ux, mass ux, and tube/channel hydraulicdiameter.

5. Critical heat ux is an important factor in the designof evaporators. Although not covered in this articledue to space constraints, there is a need to obtainmore experimental data for CHF in single and par-allel minichannels.

NOMENCLATURE

C constant in Eq. (1)C1 and C2 constants in Eq. (9)D diameter of large-diameter tubed diameter of small-diameter tubee gap size, mF1 and F2 constants in Eq. (9)g acceleration due to gravity, m/s2

G mass ux, kg/m2 sKsa pressure drop multiplier in acceleration

pressure drop, Eq. (2)

h ffg latent heat of vaporization, J/kgh average heat transfer coef cient in the

evaporator, W/m2 CL length of the evaporator tuben number of parallel small-diameter tubes

for each large-diameter tubep pressure drop, N/m2

q heat ux, W/m2

x qualitya void fractionq density, kg/m3

r surface tension, N/mv tt Martinelli parameter fD ( q V =q L )0:5

( l L=l V )0:1[(1 x )=x]0:9g

Subscripts

D large-diameter tubed small-diameter tubeex exitf frictionin inletL liquidLO all ow as liquidTP two-phasett turbulent-turbulentV vapor

REFERENCES

[1] Baker, O., Simultaneous Flow of Oil and Gas, Oil Gas J.,vol. 53, pp. 185190, 1954.

[2] Hewitt, G. F., and Roberts, D. N., Studies of Two-Phase FlowPatterns by Simultaneous X-Ray and Flash Photography, UKAEA Rep. ASRE-M2159, 1969.

[3] Taitel, Y., Barnea, D., and Dukler, A. E., Modeling Flow Pat-tern Transition for Gas-Liquid Transitions for Steady UpwardGas-Liquid Flow in Vertical Tubes, AIChE J., vol. 26, no. 3,pp. 345354, 1980.

[4] Fukano, T., Kariyasaki, A., andKagawa,M., FlowPatterns andPressure Drop in Isothermal Gas-Liquid Flow in a HorizontalCapillary Tube, ANS Proc. 1989 Natl. Heat Transfer Conf.,vol. 4, pp. 153161, 1989.

[5] Wambsganss, M. W., Jendrzejczyk, J. A., and France, D. M.,Two-Phase FlowPatterns and Transitions in Small, Horizontal,Rectangular Channels, Int. J. Multiphase Flow, vol. 17, no. 3,pp. 327342, 1991.

[6] Triplett, K. A., Ghiaasiaan, S. M., Abdel-Khalik, S. I.,LeMouel,A., andMcCord, B. N.,Gas-Liquid Two-Phase FlowinMicrochannels Part II: Void Fraction and Pressure Drop, Int.J. Multiphase Flow, vol. 25, pp. 395410, 1999.

[7] Kasza, K. E., Didascalou, T., and Wambsganss, M. W.,Microscale Flow Visualization of Nucleate Boiling in SmallChannels: Mechanisms In uencing Heat Transfer, in R. K.Shah (ed.), Proc. Int. Conf. on Compact Heat Exchanges forthe Process Industries, pp. 343352, Begell House, NewYork,1997.


[8] Hewitt, G. F., Fluid Mechanics Aspects of Two-Phase Flow,in S. G. Kandlikar, M. Shoji, and V. K. Dhir (eds.), Handbookof Boiling and Condensation, Chap. 9, Taylor and Francis,New York, 1999.

[9] Mandhane, J. M., Gregory, G. A., and Aziz, K., 1974, A FlowPattern Map for Gas-Liquid Flow in Horizontal Pipes, Chem.Eng. Prog., vol. 45, pp. 3948, 1974.

[10] Taitel, Y., and Dukler, A. E., A Model for Predicting FlowRegime Transitions in Horizontal and Near Horizontal Gas-Liquid Flow, AIChE J., vol. 22, pp. 4755, 1976.

[11] Lazarek, G. M., and Black, S. H., Evaporative Heat Transfer,Pressure Drop and Critical Heat Flux in a Small DiameterVertical Tube with R-113, Int. J. Heat Mass Transfer, vol. 25,no. 7, pp. 945960, 1982.

[12] Cornwell, K., and Kew, P. A., Boiling in Small Parallel Chan-nels,Proc. CECConf. on EnergyEf ciency inProcess Technol-ogy, Athens,Greece,October 1992, ElsevierAppliedSciences,pp. 624638.

[13] Moriyama, K., and Inoue, A., The Thermohydraulic Char-acteristics of Two-Phase Flow in Extremely Narrow Chan-nels (The Frictional Pressure Drop and Heat Transfer of Boil-ing Two-Phase Flow, Analytical Model), Heat TransferJpn.Res., vol. 21, no. 8, pp. 838856, 1992.

[14] Wambsganss, M. W., France, D. M., Jendrzejczyk, J. A., andTran, T. N., Boiling Heat Transfer in a Small Diameter Tube,ASME J. Heat Transfer, vol. 115, no. 4, pp. 963972, 1992.

[15] Bowers, M. B., and Mudawar, I., High Flux Boiling in LowFlow Rate, Low Pressure Drop Mini-channel and Micro-channel Heat Sinks, Int. J. Heat Mass Transfer, vol. 37, no. 2,pp. 321334, 1994.

[16] Bowers, M. B., and Mudawar, I., Two-Phase Electronic Cool-ing Using Mini-Channel and Micro-channel Heat SinksPart 1. Design Criteria and Heat Diffusion Constraints, ASMEJ. Electronic Packaging, vol. 116, pp. 290297, 1994.

[17] Bowers, M. B., and Mudawar, I., Two-Phase Electronic Cool-ing Using Mini-Channel and Micro-channel Heat SinksPart 2. Flow Rate and Pressure Drop Constraints, ASME J.Electronic Packaging, vol. 116, pp. 290297, 1994.

[18] Mertz, R.,Wein, A., and Groll, M., Experimental Investigationof Flow Boiling Heat Transfer in Narrow Channels, Calore eTechnologia, vol. 14, no. 2, pp. 4754, 1996.

[19] Ravigururajan, T. S., Cuta, J., McDonald, C. E., and Drost,M. K., Effects of Heat Flux on Two-Phase Flow Charac-teristics of Refrigerant Flows in a Micro-Channel Heat Ex-changer, 1996,Natl. Heat Transfer Conf., vol. 7,HTD-Vol. 329,pp. 167178, ASME, New York, 1996.

[20] Tran, T. N., Wambsganss, M. W., and France, D. M., SmallCircular- and Rectangular-Channel Boiling with Two Refrig-erants, Int. J. Multiphase Flow, vol. 22, no. 3, pp. 485498,1996.

[21] Tong, W., Bergles, A. E., Jensen, M. K., Pressure Drop withHighly Subcooled Flow Boiling in Small-Diameter Tubes,Exp. Thermal Fluid Sci., vol. 15, pp. 202212, 1997.

[22] Bonjour, J., and Lallemand, M., Flow Patterns during Boil-ing in a Narrow Space between Two Vertical Surfaces, Int. J.Multiphase Flow, vol. 24, pp. 947960, 1998.

[23] Peng, X. F., and Wang, B. X., Forced Convection and Boil-ing Characteristics in Microchannels, Heat Transfer 1998,Proc. 11th IHTC, August 2328, 1998, Kyongju, Korea, vol. 1,pp. 371390.

[24] Peng, X. F., Hu, H. Y., and Wang, B. X., Boiling NucleationDuring LiquidFlow inMicrochannels, Int. J.HeatMass Trans-fer, vol. 41, no. 1, pp. 101106, 1998.

[25] Kamidis, D. E., and Ravigururajan, T. S., Single and Two-phase Refrigerant Flow in Mini-channels, Proc. NHTC2000:33rd Natl. Heat Transfer Conf., Albuquerque, NM, August2022, 2000, Paper NHTC2000-12100 ; pp. 18.

[26] Kuznetsov, V. V., and Shamirzaev, A. S., Two-Phase Flow Pat-tern and Flow Boiling Heat Transfer in Noncircular Channelwith a Small Gap, Two-Phase FlowModeling and Experimen-tation, pp. 249253, 1999.

[27] Lin, S., Kew, P. A., and Cornwell, K., Two-Phase Evaporationin a 1 mm Diameter Tube, 6th UK Heat Transfer Conf. inEdinburgh, September 1999.

[28] Downing, R. S., Meinecke, J., and Kojasoy, G., The Effects ofCurvature on Pressure Drop for Single and Two-Phase Flow inMiniatureChannels,Proc. NHTC 2000: 34th Natl. Heat Trans-fer Conf., Pittsburgh, PA, August 2000, Paper NHTC2000-12100.

[29] Hetsroni, G., Segal, Z., and Mosyak, A., Nonunifrom Tem-perature Distribution in Electronic Devices Cooled by Flowin ParallelMicrochannels, Packaging Electronic Photonic De-vices, EEP-vol. 28, pp. 19, 2000.

[30] Kennedy, J. E., Roach, G. M., Jr., Dowling, M. F., Abdel-Khalik, S. I., Ghiaasiaan, S. M., Jeter, S. M., and Quereshi,Z. H., The Onset of Flow Instability in Uniformly HeatedHorizontal Microchannels, ASME J. Heat Transfer, vol. 122,pp. 118125, 2000.

[31] Lakshminarasimhan, M. S., Hollingsworth, D. K., and Witte,L. C., Boiling Incipience in Narrow Channels, HTD-Vol. 366-4, Proc. ASME Heat Transfer Division 2000, ASME IMECE2000, vol. 4, pp. 5563.

[32] Kandlikar, S. G., Steinke, M. E., Tian, S., and Campbell,L. A., High-Speed Photographic Observation of Flow BoilingofWater in ParallelMini-Channels, ASMENatl. Heat TransferConf., June 2001.

[33] Lin,S., Kew, P.A., andCornwell, K., Two-Phase FlowRegimesand Heat Transfer in Small Tubes and Channels,Heat Transfer1998, Proc. 11th Int. Heat Transfer Conf., Kyongju, Korea,1998, vol. 2, pp. 4550.

[34] Barnea, D., Luninsky, Y., and Taitel, Y., Flow Pattern in Hori-zontal and Vertical Two-Phase Flow in Small Diameter Pipes,Can. J. Chem. Eng., vol. 61, pp. 617620, 1983.

[35] Mishima,K., andHibiki, T., SomeCharacteristics of Air-WaterTwo-Phase Flows in Small Diameter Tubes, Int. J. MultiphaseFlow, vol. 22, no. 4, pp. 703712, 1996.

[36] Yao, S.-C., and Chang, Y., Pool Boiling Heat Transfer in aCon ned Space, Int. J. Heat Mass Transfer, vol. 26, no. 6,pp. 841848, 1983.

[37] Kuznetsov, V. V., and Vitovsky, O. V., Flow Pattern of Two-Phase Flow in Vertical Annuli and Rectangular Channel withNarrow Gap, in G. P. Celata and R. K. Shah (eds.), Two-Phase Flow Modelling and Experimentation 1995, Pisa, Italy,Edizioni ETS, 1995.

[38] Kandlikar, S. G., and Stumm, B. S., A Control Volume Ap-proach to Predict Departure Bubble Diameter in Flow Boiling,ASME J. Heat Transfer, vol. 117, pp. 990997, 1995.

[39] Kandlikar, S. G., and Spiesman, P. H., Effect of Surface Char-acteristics on Flow Boiling Heat Transfer, Engineering Foun-dation Conf. on Convective and Pool Boiling, Irsee, Germany,May 1825, 1997.

[40] Kandlikar, S. G., Flow Boiling in Circular Tubes, in S. G.Kandlikar,M.Shoji, andV.K.Dhir (eds.),Handbook ofBoilingand Condensation, Taylor & Francis, Philadelphia, PA, 1999.

[41] Collier, J. G.,Convective Boiling and Condensation, McGraw-Hill, London, 1981.


[42] Martinelli, R. C., and Nelson, D. B., Prediction of Pres-sure Drop during Forced Convection Boiling of Water, ASMETrans., vol. 70, pp. 695702, 1948.

[43] Kew, P. A., and Cornwell, K., On Pressure Drop Fluctuationsduring Boiling in Narrow Channels, in G. P. Celata, P. DiMarco, and A. Mariani, (eds.), 2nd European Thermal Sci-ences and 14th UIT Natl. Heat Transfer Conf., Pisa, Italy,pp. 13231327, Edizioni ETS, 1996.

[44] Nakayama, W., and Yabe, A., Flow Boiling in Narrow Chan-nels for Thermal Management of Microelectronic Equipment,in S. G. Kandlikar, M. Shoji, and V. K. Dhir (eds.), Handbookof Phase Change: Boiling and Condensation, pp. 403411,Taylor & Francis, Philadelphia, PA, 1999.

[45] Kew, P. A., and Cornwell, K., Flow Boiling in Compact HeatExchangers, in S. G. Kandlikar, M. Shoji, and V. K. Dhir(eds.),Handbook of PhaseChange: Boiling and Condensation,pp. 412427, Taylor & Francis, Philadelphia, PA, 1999.

[46] Bergles,A. E., Subcooled Burnout in Tubes of Small Diameter,ASME Paper 63-WA-182, 1964.

[47] Kandlikar, S. G., Development of a Flow Boiling Map forSaturated and Subcooled Flow Boiling of Different Fluidsin Circular Tubes, J. Heat Transfer, vol. 113, pp. 190200,1991.

[48] Liu, Z., andWinterton, R. H. S.,Wet Wall Flow Boiling Corre-lation with Explicit Nuclear Term, 5th Miami Symp. on Mul-tiphase Transport and Particulate Phenomena, 1988.

[49] Shah, M. M., Chart Correlation for Saturated Boiling HeatTransfer: Equations and Further Study, ASHRAE Trans.,vol. 88, pp. 185196, 1982.

[50] Kandlikar, S. G., A General Correlation for Saturated Two-Phase Flow Boiling Heat Transfer Inside Horizontal and Ver-

tical Tubes, ASME J. of Heat Transfer, vol. 112, pp. 219228,1990.

[51] Chen, J. C., A Correlation for Boiling Heat Transfer to Satu-ratedFluids inConvective Flow, I&ECProcessDesignDevel.,vol. 5, no. 3, pp. 322329, 1966.

[52] Mehendale, S. S., Jacobi, A. M., and Shah, R. K., Heat Ex-changers atMicro- andMeso-Scales, in R. K. Shah (ed.),Com-pact Heat Exchangers and Enhancement Technology for theProcess Industries, pp. 5574, Begell House, NewYork, 1999.

[53] Mehendale, S. S., Jacobi, A. M., and Shah, R. K., FluidFlow and Heat Transfer at Micro- and Meso-Scales withApplications to Heat Exchanger Design, Appl. Mech. Rev.,vol. 53, pp. 175193, 2000.

Dr. Satish G. Kandlikar is a Professor inMechanical Engineering at Rochester Institute ofTechnology in Rochester, New York. He has beenwith R.I.T. since 1980. Prior to coming to R.I.T.,he obtained his ph.D. in 1975 from the IndianInstitute of Technology, Bombay, India, wherehe continued to become Associate Professor be-fore coming to R.I.T. He received the Eisenhartoutstanding teaching award at R.I.T. in 1997.

Dr. Kandlikar is a fellow of the ASME and heads the Heat Transfer Chapterof the Rochester Section of the ASME. He is involved in research in theareas of ow boiling, pool boiling, critical heat ux, microchannels , andcooling of electronic components . He has published over 60 conference andjournal articles and has delivered several keynote lectures. He is also thechief editor of the Handbook of Phase Change: Boiling and Condensation,published by Taylor & Francis. He is the current Heat and History Editor ofHeat Transfer Engineering journal.


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