Measurement and correlation of critical heat flux in two-pha

InternationalJournalofHeatandMassTransfer47(2004)

2045–2059

/locate/ijhmt

Measurementandcorrelationofcriticalheat uxin

two-phasemicro-channelheatsinks

WeilinQu,IssamMudawar

*

BoilingandTwo-phaseFlowLaboratory,SchoolofMechanicalEngineering,1288MechanicalEngineeringBuilding,PurdueUniversity,

WestLafayette,IN47907-1288,USA

Received17October2003;receivedinrevisedform11December2003

Abstract

Criticalheat ux(CHF)wasmeasuredforawater-cooledmicro-channelheatsinkcontaining21parallel215·821lmchannels.Testswereperformedwithdeionizedwateroveramassvelocityrangeof86–368kg/m2s,inlettemper-aturesof30and60°C,atanoutletpressureof1.13bar.AsCHFwasapproached, owinstabilitiesinducedvaporback owintotheheatsink’supstreamplenum,whichsigni cantlyalteredthecoolanttemperatureatthechannelinlets.Theback ownegatedtheadvantagesofinletsubcooling,resultinginaCHFvirtuallyindependentofinlettemperaturebutwhichincreaseswithincreasingmassvelocity.Duetothevaporback owandotheruniquefeaturesofparallelmicro-channels,ingthenewheatsinkwaterCHFdataaswellaspreviousdataforR-113inheatsinkswithmultiplecircularmini-andmicro-channels,anewCHFcorrelationisproposedwhichshowsexcellentaccuracyinpredictingexistingheatsinkdata.Ó2004ElsevierLtd.Allrightsreserved.

1.Introduction

Thepastdecadehaswitnessedunprecedentedimprovementsintheperformanceofcomputerproces-sorswhichwerebroughtabout,forthemostpart,byarestlesspursuitofmicro-miniaturizationofcomponentsintheprocessoritself.Theseadvanceshaveledtoalarmingincreasesintheamountofheatthatisdissi-patedandhastoberemovedfromtheseprocessors.Thelargeincreaseinheatdissipationperunitsurfaceareaandperunitvolumeisnotlimitedtocomputerproces-sors.Infact,thistrendisevidentinmanycutting-edgepowerandswitchingdevicesaswellaslaserdiodear-rays.Heatdissipationratesinthesedeviceshavealreadyescalatedtolevelsthatcannolongerbemanagedwithconventionalcoolingtechniques.New,morepowerfulcoolingsystemsarethereforeneededtobothmeetthechallengesofemergingtechnologiesaswellasmake

Correspondingauthor.Tel.:+1-765-494-5705;fax:+1-765-494-0539.

E-mailaddress:mudawar@ecn.purdue.edu(I.Mudawar).

*possiblefurtherdevelopmentsinthesetechnologiesthatwillundoubtedlybringaboutfurtherincreasesinheatdissipation.

Severalcoolingschemeshavebeendevelopedinre-centyearsthatcapitalizeuponthemeritsofphasechangetoachievethedesiredcoolingperformance.Theseincludepoolboilingthermosyphons,channel owboiling,jet,andsprays.Two-phasemicro-channelheatsinksareaspecialclassofchannel owboilingsystems.Theyo eruniqueadvantagesthatclearlysetthemapartfromotherhigh-performancecoolingsystems.Atypicalmicro-channelheatsinkconsistsofahigh-conductivityslabcontainingmultiple,parallelchannelswithcross-sectionaldimensionsof10–1000lm.Theheat-dissipat-ingdeviceisattachedtotheplanarsurfaceoftheheatsink,fromwhichtheheatisconductedtoaliquidcoolantthatissuppliedthroughthechannels.Highdeviceheat uxescausethecoolanttoboilalongthemicro-channel.Twokeymeritsofboilinginmicro-channelsare(1)verylargeconvectiveheattransfercoe cients(i.e.,lowdevicetemperatures)and(2)relati-velysmalltemperaturerisealongthechannelcompared

0017-9310/$-seefrontmatterÓ2004ElsevierLtd.Allrightsreserved.

doi:10.1016/j.ijheatmasstransfer.2003.12.006

2046W.Qu,I.Mudawar/InternationalJournalofHeatandMassTransfer47(2004)2045–2059

NomenclatureAAchAhAtCC0cPdde

parameterinempiricalcorrelationsmicro-channelcross-sectionalareamicro-channelheatedinsidearea

planformareaofheatsink’stopsurfaceparameterinempiricalcorrelationsvoiddistributionparameter

speci cheatatconstantpressureinnerdiameterofcircularchannel

heatedequivalentdiameterofrectangularchannel

F1toF4parametersinempiricalcorrelationsggravitationalconstantGmassvelocityinmicro-channelh uidenthalpyHcellheightofheatsinkunitcellHchheightofmicro-channelhfenthalpyofsaturatedliquidhfglatentheatofvaporizationDhsub;ininletsubcoolingHw1thicknessofplasticcoverplateHw2distancefromthermocoupletomicro-chan-nelbottomwallKinletsubcoolingparameter

K1toK3parametersinempiricalcorrelationskfthermalconductivityofliquidksthermalconductivityofcopperheatsinkLheatedlengthofmicro-channel_mtotalmass owrateMnumberofdatapointsMAEmeanabsoluteerrornparameterinempiricalcorrelationsNnumberofmicro-channelsinheatsinkPpressurePhinsideheatedperimeterofchannelPp;outpumpexitpressurePRreducedpressureinBowringcorrelationPWtotalelectricalpowerinputtoheatsink’s

cartridgeheaters

e ectiveheat uxbasedonheatsink’stopplanformarea

00qeff;mCHFbasedonheatsink’stopplanformarea00qpmeanheat uxbasedonchannelheatedin-sidearea00qp;mCHFbasedonchannelheatedinsidearea00qp;m0CHFbasedonchannelheatedinsidearea

forzeroinletsubcooling

00

qp;m01toq00p;m05parametersinempiricalcorrelationstc1totc4thermocouplesTtemperatureTsatsaturationtemperatureTtcithermocouplereading(i¼1to4)Tw;tcichannelbottomwalltemperatureatther-mocouplelocationWcellwidthofheatsinkunitcellWchwidthofmicro-channelWwhalf-widthofwallseparatingmicro-chan-nelsWeWebernumberxethermodynamicequilibriumqualityzstream-wiselocationGreeksymbolskcharacteristicwavelengthqdensityrsurfacetensionSubscriptsexpexperimental(measured)fliquidgvaporininletoutoutletmmaximum(criticalheat ux)predpredictedssolid(copperheatsink)tcithermocouple(i¼1to4)q00eff

tosingle-phasemicro-channelcooling.Coupledwith

theirintrinsicallysmallthickness,thesetwoadvantagesgreatlyreduceoverallthermalresistancebetweenthedeviceandcoolant,reducecoolant owrateandinventoryrequirements,andprovideahighdegreeoftemperatureuniformityalongthe owdirection.Theseattributeshavemadetheseheatsinksaprimecon-tenderforcompact,lightweightcoolingsystemsinsuchapplicationsassatellites,avionics,andportablecom-puters.Thesepracticalmeritsoftwo-phasemicro-channelheatsinkshaveattractedconsiderableattentioninre-centyearsonseveralissuesconcerningtheirphasechangecharacteristics.Theseincludeboilingincipience[1,2],dominant owpatterns[3–5],hydrodynamicinstability[6–9],heattransfer[10–14],andpressuredrop[9,12,15–19].Theissueofcriticalheat ux(CHF),however,hasreceivedverylimitedattention,despitethegreatimportanceofthisparametertothedesignandsafeoperationofaheatsink.

W.Qu,I.Mudawar/InternationalJournalofHeatandMassTransfer47(2004)2045–20592047

CHFgenerallyreferstotheoutcomeofeventsthatcauseasudden,appreciabledecreaseintheheattransfercoe cientforasurfaceonwhichboilingisoccurring.Foraheat- ux-controlledsystem,suchasthecasewithmostpracticaltwo-phasemicro-channelheatsinks,exceedingCHFcanleadtoasuddenlargeincreaseinsurfacetemperature,which,formostcoolants,canleadtocatastrophicsystemfailure.TheabilitytodetermineCHFisthereforeofvitalimportancetothesafetyoftwo-phasemicro-channelheatsinkssinceonlywithsuchknowledgecanaheatsinkbedesignedwithanaccept-ablemarginofsafetyrelativetomaximumheat uxdissipationorminimumcoolant owrate.

Two-phasemicro-channelheatsinksgenerallyin-volve owboilinginstraight,constant-cross-sectional-areachannelswithconstantmass owrateanduniformheatdistributionalongthe owdirection.Forsuchsystems,CHFgenerallycommencesatthechanneloutlet[20,21].Accordingtowhetherthebulk uidatchanneloutletissubcooledorsaturatedwhenCHFoccurs, ow-boilingCHFcanbeclassi edaseithersubcooledCHForsaturatedCHF.ThetwotypesofCHFaretriggeredbydrasticallydi erentmechanisms.SubcooledCHFindicatessituationswherethebulk uidtemperatureatthechanneloutletissub-cooledwhenCHFoccurs.Thisconditionisrepresentedbyathermodynamicequilibriumquality,whichisde- nedasxhÀhf

e¼

h;ð1Þ

fg

thatislessthanzeroattheoutlet,xe;out<0.ConditionsthatoftenleadtosubcooledCHFincludelargemassvelocity,highinletsubcooling,and/orchannelswithasmalllength-to-diameterratio.Atthechanneloutlet,thebulk uidremainsinmostlyliquidstatewithalargenumberofverysmallvaporbubblescon nedtotheheatedwall.ResearchershaveproposedseveraltheoriestoexplainthetriggermechanismforsubcooledCHF:intenseboilingcausesthebubble-liquidboundarylayertobeseparatedfromtheheatedwallandtheresultingstagnantliquidtoevaporate[22],bubblecrowdingwithintheboundarylayerinhibitsliquidreplenishmentnearthesurfacecausingtheformationofaninsulatingvaporlayer[23],anddryoutofaliquidsublayerbeneathlargevaporbubblescausesthelocalwalltemperaturetoriseappreciably[24].HallandMudawar[25]providedacomprehensivereviewofthecurrentstateofknowl-edgeofsubcooledCHFforwater owboilinginchan-nels,andderivedastatisticalcorrelationbasedontheentireworldsubcooledCHFdatabaseavailableuntil1999.

SaturatedCHFisencounteredinsituationswherexe;outP0whenCHFoccurs.Conditionsthatcom-monlyleadtosaturatedCHFincludesmallmass

velocity,lowinletsubcooling,and/orchannelswithalargelength-to-diameterratio.Thecorresponding owpatternatthechanneloutletismostlyannularwiththevaporphaseoccupyingmostofthechannelcorewhiletheliquid owsasathin lmalongthechannelwall.Dryoutoftheliquid lmneartheoutletiswidelyre-gardedasthetriggermechanismforsaturatedCHF[20,21].Micro-channelheatsinksareespeciallypronetothistypeofCHFsincetheyareusedinapplicationsdemandingminimal owratesandsmallcoolantinventory.

Asthetransportprocessbehind owboilingCHFisextremelycomplex,CHFpredictionsrelyheavilyonempiricalcorrelationsthatarederivedfromexperi-mentalCHFdatabases[21,25].AvailablesaturatedCHFdatafor owboilinginmini/micro-channelswerecompiledbythepresentauthorsandaresummarizedinTable1.Inthispaper,mini-channelsrefertochannelswithcharacteristiccross-sectionaldimensionsfromabout1to3mm,andmicro-channelslessthan1mm.Thedatabasecontains438saturatedCHFdatapoints,including392forwater owinsinglecircularmini-channels(d¼1–3mm),22forRefrigerantR-113insinglecircularmini-channels(d¼3:15mm),and24forR-113incircularmini-(d¼2:54mm)andmicro-channel(d¼510lm)heatsinks.SourcesandparameterrangesfortheCHFdataarealsoprovidedinTable1.InadditiontothoselistedinTable1,Nariaietal.[32]andYuetal.[33]alsoconductedexperimentalstudiesonsaturatedCHFofwaterinsinglecircularmini-channels.However,theirdataareexcludedfromthedatabaseastheywerenotavailableinfullycharacterizedtabularform.CloseexaminationofTable1revealsasevereshortageofdataformicro-channels,andclearlypointstoaneedforfurtherexperimentalstudy.WiththeexceptionofBowersandMudawar’swork[15],allothersaturatedCHFdatawereobtainedusingsinglechan-nels.CHFinaheatsinkcontainingmultipleparallelchannelsmaybesigni cantlydi erentfromthatinasinglechannel,asboilingandtwo-phase owarelessstableintheformer.AnotheraspectofthedatabaseisthatalltheavailablesaturatedCHFdataareforcircularchannels,whilechannelsinpracticalheatsinksaremostlyrectangularbecauseoftheireaseoffabrication.Finally,themajorityofthesaturatedCHFdataareformini-channelswhoseinnerdiametersareconsider-ablylargerthanthoseemployedinmicro-channelheatsinks.

Thepresentstudyexplores owboilingCHFforawater-cooledtwo-phasemicro-channelheatsink.Theprimaryobjectivesofthepresentstudyare:(1)topro-videnewsaturatedCHFdatafor owboilinginaheatsinkcontainingrectangularmicro-channels,(2)toassesstheaccuracyofpreviousempiricalCHFcorrelationsforbothsinglemini-channelsaswellasmini/micro-channelheatsinks,and(3)todevelopanewCHFcorrelation

2048W.Qu,I.Mudawar/InternationalJournalofHeatandMassTransfer47(2004)2045–2059

Table1

ParameterrangesofsaturatedCHFdatafor owboilinginmini/micro-channelsReference

No.ofdata

d(mm)

L=d

G(kg/m2s)94.930379.84370.05180.0365.02725.0776.02738.0246.61036.9232.0503.0

Pout(bar)1.017.9113.813.831.071.029.472.03.3610.421.144.141.061.37

Tin(°C)22.225.6153.87165.6219.3383.7822.9288.048.9072.5023.9094.3037.2637.26

xe;out0.0200.9800.2100.2650.2070.8910.6600.9900.3621.1820.2900.8870.5811.528

2

q00p;m(W/cm)

(a)Water owboilinginsinglecircularmini-channels

Lowdermilk1881.3050.0etal.[26]2.44250.0Weatherhead61.14100.0[27]1.14100.0Becker[28]822.40166.7

3.00208.3

Lezzietal.681.00239.0[29]1.00975.0Roachetal.481.17110.5[30]1.45137.0(b)R-113 owboilinginsinglecircularmini-channelsLazarekand223.1540.0Black[31]3.1540.0

23.0

2504.8732.0732.0114.0513.028.5236.386.0369.818.333.635.54105.50

(c)R-113 owboilingincircularminiandmicro-channelheatsinksBowersand240.513.9429.8Mudawar[15]2.5419.61476.3

thatisparticularlysuitedformini/micro-channelheatsinks.

2.Experimentalapparatus2.1.Testmodule

Fig.1(a)illustratesthelayeredconstructionofthemicro-channelheatsinktestmodule.Themicro-chan-nelswerecutintothe4.48cmlongand1.0cmwidetopsurfaceofanoxygen-freecopperblock.Twenty-one215lmwideand821lmdeepmicro-slotsweremachinedwithinthe1-cmwidthofthetopsurface.Heatwassuppliedtothemicro-channelsfromtwelvehigh-power-densitycartridgeheatersthatwereinsertedintoboresintheundersideofthecopperblock.

Thecopperbockwasinsertedalongthecentralhol-lowedsectionofathermallyinsulatingG-7 berglassplastichousing.Asmallprotrudingplatformaroundtheperipheryoftheheatsinkensuredthatthetopsurfaceoftheheatsinkwas ushwiththetopsurfaceofthehousing.Thehousingcontainedadeepplenumleadingtoanothershallowplenumbothupstreamanddown-streamoftheheatsinktoensureeven owdistribution.Apolyetherimidethermoplastic(GEUltem1000)coverplatewasboltedatoptheheatsink.Asidefromformingthetopsurfacefortheinpidualmicro-channels,thissemi-transparentcoverplateprovidedvisualaccesstothe owboilinginsidethemicro-channels.Afterthetestmodulewasassembled,multiplelayersofceramic berwerewrappedaroundthecopperblocktoreduceheatlosstotheambient.

FourTypeKthermocouples,indicatedinFig.1(a)astc1totc4(fromupstreamtodownstream),wereinsertedbelowthetopsurfaceoftheheatsinktomeasurethestream-wisetemperaturedistributionalongthecentralplane.Errorassociatedwiththethermocouplereadingswassmallerthan±0.3°C.Thecartridgeheaterswerepoweredbya0–110VACvariacandtheirtotalelectricalpowerinputmeasuredbya0.5%accuracywattmeter.LocatedinthedeepplenumsweretwoabsolutepressuretransducersandtwoType-Kthermocouplesforinletandoutletpressureandtemperaturemeasurements,respectively.Theuncertaintyforthesepressureandtemperaturemeasurementswas3.5%and±0.3°C,respectively.

PriortoperformingtheCHFmeasurements,aseriesofsingle-phasetestswereconductedwithinthesame parisonbetweenelectricalpowerinputandtheincreaseinwaterenthalpyduringthesesingle-phasetestsshowedheatlosswassmallerthan4%.Allheat uxdatapresentedinthisstudywerethereforebasedonthemeasuredelectricalpowerinput.2.2.Flowloop

Deionizedwaterwassuppliedtothetestmoduleusingthe owloopillustratedschematicallyinFig.1(b).Thebulkofthewaterresidedinareservoirwhichalsoservedasadeaerationchamber.Agearpumpprovidedthenecessarypressureriseatthemoduleinletoverthedesiredrangeof owrates.Thewater owratewasmeasuredbyoneoftworotametersthatwerearrangedinparallel.Measurementuncertaintyofthe owmeterswasbetterthan4%.Twocontrolvalves,onesituated

upstreamandtheotherdownstreamofmodule,playedavitalroleinthe owregulation.Thedownstreamvalvewasusedtoregulatetheheatsink’soutletpressure.Throttlingtheupstreamvalveeliminatedatypeofinstability,severepressuredroposcillation,whichiscausedbyinteractionbetweenthetwo-phase owintheparallelmicro-channelsandtheupstreamcompressiblevolumeintheloop.Anothermildparallel

channel

instabilitypersistedinthemicro-channelsevenwiththethrottlingoftheupstreamvalve.Thislatterinstabilitycausedrandomaxialoscillationsoftheboundarybe-tweentheliquidanddownstreamtwo-phasemixture,buthadarelativelymilde ectonheatsinkpressuredrop.These owinstabilitiesweredescribedinaprevi-ouspaperbythepresentauthors[9],andwillbead-dressedbrie ylaterinthispaper.2.3.Experimentalprocedure

BeforemakinganyCHFmeasurements,thewaterinthereservoirwasbroughttoavigorousboilinsidethereservoirforaboutonehourtopurgeanydissolvedgasesintotheambient.Subsequently,the owloopcomponentswereadjustedtoyieldthedesiredoperatingconditionsaccordingtoTable2.

Usingtheupstreamvalve,thepumpexitpressure,Pp;out,waselevatedtoabout2.0bartopreventtheaforementionedseverepressuredroposcillation.Afterthe owbecamestable,theheaterpowerwasadjustedtoalevelbelowincipientboiling.Thepowerwasthenin-creasedinsmallincrementsandthe owloopcompo-nentswerecontinuouslyadjustedtomaintainthedesiredoperatingconditions.Followingeachpowerincrement,theheatsinkwasallowedsu cienttimetoreachsteady-state,andtheinletandoutletpressures,PinandPout,inletandoutlettemperatures,TinandTout,andheatsinktemperatures,Ttc1toTtc4,wereallrecordedusinganHPdataacquisitionsystemthatwasinterfacedtoaPC.EachtestwasterminatedwhenCHFwasencoun-teredinthemicro-channelheatsink.AfterCHFwastriggeredatthechanneloutlet,itpropagatedupstreamalongthechannel.Withashorttimedelay,thether-mocoupleclosesttothechanneloutlet(tc4)sensedasuddenunsteadytemperaturerise.ThetestwasthenterminatedonceCHFreachedthelocationoftc4toavoidoverheatingofthetestmodule.

ThewatermassvelocityGwasdeterminedfromthe

_,numberofmicro-channels,measuredmass owrate,m

N,andcross-sectionalarea,Ach,ofamicro-channel.G¼

_m:NAch

ð2Þ

bythewattmeter,PW,pidedbythetopplanformareaoftheheatsink,At¼1:0Â4:48cm2.q00eff¼

PW

:At

ð3Þ

Thesecondde nitionisameanheat uxaveragedoverthemicro-channelheatedinsidearea,q00p,asillustratedinFig.2foraheatsinkunitcellcontainingasinglemicro-channelaswellassurroundingsolid-dimensionsoftheunitcellaregiveninTable3.Whileq00effprovidesaglobalmeasureoftheheatsink’sthermalperformance,q00pismoreusefulwheninvestigatingempirical owboilingCHFcorrelations.ReferringtoFig.2,q00pcanberelated

00

toqeffbyq00p

q00effWcell

¼:Wchþ2Hch

ð4Þ

TheCHFvaluesreportedinthisstudyrepresentthe

00

highestheat ux(q00eff;morqp;m)measuredforstable owboilingbeforethelastpowerincrementthatprecipitatedtheunsteadytemperaturerise.

Twode nitionsareusedinthepresentstudyforheat uxtotheheatsink.The rstisan‘‘e ective’’heat ux,q00eff,de nedasthetotalelectricalpowerinputmeasured

Table2

OperatingconditionsforpresentstudyCoolantDeionizedwater

Inlettemperature,Tin(°C)Massvelocity,G(kg/m2s)30.060.0

86–36886–368

Outletpressure,Pout(bar)1.131.13

Pumpexitpressure,Pp;out(bar)2.02.0

Table3

Dimensionsofmicro-channelheatsinkunitcellWw(lm)Wch(lm)Hw1(lm)125

215

12,700

3.Resultsanddiscussion3.1.Boilingcurve

Fig.3(a)and(b)showtypicalboilingcurvesobtainedatthefourthermocouplelocationsforamassvelocityof228kg/m2sandinlettemperaturesof30and60°C,respectively.Thee ectiveheat ux,q00di erencebetweenthelocalchanneleff,isplottedversusthebottomwalltemperature,Tw;tci,andinlettemperature,Tin.ReferringtoFig.2,Tw;tciwasevaluatedfromq00effandthermocouple

Hch(lm)Hw2(lm)821

2354

readingsTtcibyassumingone-dimensionalheatcon-ductionbetweenthermocouplelocationandchannel

bottomwallimmediatelyabove.Tq00Hw2

w;tci¼TtciÀ

effk:ð5Þ

s

TheinlettemperatureTinwasmeasureddirectlybythethermocouplelocatedintheupstreamplenum.However,astheheat uxapproachedCHF,theparallel-channelinstability,whichhadbeenmildoverawiderangeofheat uxes,becamequiteintense.Thiscausedasigni cantamountofvaporfromthemicro-channelsto owbackwardsintotheupstreamplenumandmixwiththeincomingsubcooledliquid.Thiswasclearlymanifestbyupstreamplenumthermocouplereadingtemperaturessigni cantlyhigherthanthatoftheincomingliquid,Tin.Undertheseconditions,theincomingliquidtemperatureisassignedthevalueofTin.Thisissuewillbediscussedinmoredetailinthenextsection.

Fig.3(a)and(b)showtheslopesofallboilingcurvesarefairlyconstantatlowheat uxescorrespondingtothesingle-phaseliquidcoolingregime.Withincreasingheat ux,theslopeoftheboilingcurvebeginsincreasingatztc4,indicating owboilingisinitiatedneartheoutlet.Furtherheat uxincreasescausesimilarslopechangesfortheupstreamthermocouplelocationsinuniformsuccession.Astheheat uxapproachesCHF,theslopebeginstodecreaseagain,indicativeofreducedheattransfere ectiveness,whichalsobeginsatztc4andpropagatesupstreamatslightlyhigher uxes.Eventu-ally,CHFisdetectedatztc4.CHFvaluesforthecon-ditionsgiveninFig.3(a)and(b)areq00respectively.eff;m¼184:5and

184.4W/cm2

,3.2.Hydrodynamicinstability

Inapreviousstudybythepresentauthors[9],twotypesof owinstabilitywereidenti edintheheatsinktestmoduleasdescribedintheprevioussection.The rst-severepressuredroposcillation-wastheresultofinteractionbetweenthetwo-phase owintheheatsinkandtheupstreamcompressiblevolumeinthe owloop.Thisinstabilityproducedsevere owoscillationsacrosstheheatsink,whichoccurredwhenthecontrolvalveupstreamofthemodulewasfullyopen.Theboilingboundarybetweentheliquidanddownstreamtwo-phasemixtureinallchannelsshowedsevere uctuation,movingbackandforthinunisonbetweentheinletandoutlet.Bythrottlingtheupstreamcontrolvalve,this

severe owoscillationwasvirtuallyeliminated,andtheboilingboundary uctuatedbetweenmicro-channelsinarandombutmildmanner.Thissecondtypeofinsta-bilitywasclassi edasmildparallelchannelinstability,resultingfrommicro-channelinteractionsthatareintrinsictotheheatsinkitself.

Allthepresenttestswerethereforeconductedwiththeupstreamcontrolvalvethrottled.Duringthetests,how-ever,itwasobservedthattheparallelchannelinstability,whichwasverymildoveralargeportionoftheheat uxrange,becamesevereasCHFwasapproached.Fig.4showsaschematicofthemicro-channelinletatthesehighpre-CHFheat uxes.Vaporwasobservedto owback-wardsfromtheinpidualmicro-channelsintotheup-streamshallowplenum,eventuallyformingathickintermittentvaporlayer.Thislayerwasbrokenupintomanysmallvaporbubbles,whichpropagatedfurtherupstreamevenintodeepplenum,whereitmixedwiththeincomingliquid.Theupstreamplenuminteractionsbe-tweenthevaporandincomingliquidsigni cantlyalteredthe uidtemperatureinthedeepplenum.Fig.5showstheupstreamplenumthermocouplereadingsarefairlycon-stantoverabroadrangeofheat uxesbutbegintoin-creasesigni cantlyforthelasttwoorthreeheat uxincrementsimmediatelypriortoCHF.RecallthattheboilingcurvesshowninFig.3(a)and(b)werereferencedrelativetoaTinvalueequaltothemeanthermocouplereadingscorrespondingtolowerheat uxes.ThesevaluesareshownashorizontallinesinFig.5.

3.3.CHFcharacteristics

TheCHFdatameasuredduringthepresentstudyaregiveninTable4alongwiththecorrespondingoperatingconditions.Inlettemperature,Tin,isbasedontheaver-ageofmeasuredinlettemperaturesbeforethepre-CHFlossofsubcoolingdepictedinFig.5beginstotakee ect.Outletquality,xe;out,isevaluatedusingEq.(1),wheretheoutlet uidenthalpy,hout,isdeterminedbyapplyinganenergybalancefortheentireheat

sink.

W.Qu,I.Mudawar/InternationalJournalofHeatandMassTransfer47(2004)2045–2059

Table4

PresentCHFdataforwaterinrectangularmicro-channelheatsinkTin(°C)32.1630.6631.6631.4630.6530.6030.5430.6530.6359.0060.6960.5058.9660.6959.3460.8859.9459.63

G(kg/m2s)85.9124.2159.2194.5228.0263.2299.5336.1368.485.9124.2159.2194.5228.0263.2299.5336.1368.4

Pin(bar)1.2131.2311.2711.2851.3101.3311.3091.3311.3241.2231.2491.3101.3141.3661.3751.3981.3931.375

Pout(bar)1.1311.1271.1331.1291.1351.1301.1231.1321.1391.1311.1351.1411.1311.1401.1321.1351.1431.133

xe;out0.5240.3980.3760.3100.2880.2500.2140.1780.1720.5620.4340.4240.3610.3440.2950.2830.2330.214

2

q00eff;m(W/cm)

2053

2

q00p;m(W/cm)

107.64

126.48154.94164.93184.48193.64200.00201.66216.76105.66121.69153.21164.60184.43189.59207.33201.59207.8526.9131.6238.7441.2446.1348.4250.0150.4254.2026.4230.4338.3141.1646.1247.4151.8450.4151.97

hout¼hinþ

q00effAt

:_m

ð6Þ

ThethermophysicalpropertiesusedinEq.(1)were

basedontheoutletpressurePout.Table4showsxe;outvaluesatCHFareallpositive,indicatingsaturatedCHFconditions.Inaddition,increasingmassvelocityGfrom85.9to368.4kg/m2sdecreasesxe;outfrom0.524to0.172forTin¼30°Cand0.562to0.214forTin¼60°C.

Fig.6showsCHFincreasesmonotonicallywithincreasingGforbothinlettemperatures.However,whatisquitesurprisingisinlettemperature,Tin,hasvirtuallynoe ectonCHF.

Interestingly,theseCHFtrendsrelativetomassvelocityGandinlettemperatureTinmirrorthoseof

BowersandMudawarforRefrigerantR-113incircularminiandmicro-channelheatsinks[15].WhilethetrendofincreasingCHFwithincreasingGisquitecommon,thelackofinlettemperaturee ectonCHFseemstobeuniquetotwo-phasemini/micro-channelheatsinks,notsinglemicro/mini-channels.Akeydi erencebetweenheatsinksandsinglechannelsistheaforementionedampli cationofparallelchannelinstabilitypriortoCHF.Asdiscussedearlier,thisampli cationcausesback owofvaporintotheupstreamplenum,whichresultsinstrongmixingofthevaporwiththeincomingliquid.Regardlesshowsubcooledtheincomingliquidis,themixingactionappearstoincreasethetemperatureoftheliquidclosetothelocalsaturationtemperatureasitapproachesthechannel

inlet.

2054W.Qu,I.Mudawar/InternationalJournalofHeatandMassTransfer47(2004)2045–2059

3.4.AssessmentofpreviousCHFcorrelations

Inthissection,theapplicabilityofpreviousCHFcorrelationstopredictingsaturated owboilingCHFinsinglemini-channelsaswellasinmini/micro-channelheatsinksisexaminedthroughcomparisonofcorrela-tionpredictionswithexperimentalCHFdata.

SummarizedinTable5aretheBowring[34,35]andtheKattoandOhnocorrelations[36],whicharethemostpopularamongnumerouscorrelationsdevelopedforsaturated owboilingCHFinsingle(isolated)cir-cularchannels[20].Thesetwocorrelationsare rstcomparedwithsaturatedCHFdataforwaterandR-113insinglecircularmini-channelsthatwerecompiledbythepresentauthorsandpresentedearlierinTable1.Fig.7(a)showstheBowringcorrelationagreesquitewellwiththeCHFdatainthelowCHFrange,butshowspoorpredictivecapabilityinthehighCHFrange.The

meanabsoluteerror(MAE)forthiscorrelation,whichisde nedas

00

1Xjq00p;m;predÀqp;m;expj

MAE¼Â100%;ð7Þ

q00Mp;m;expis28.3%foratotalofM¼414datapoint.Fig.7(b)

showstheKattoandOhnocorrelationyieldssuperiorpredictionsovertheentireheat uxrange.TheMAEforthiscorrelationis17.3%withmostofthedatapointsfallingwithina±40%errorband.

Fig.8(a)and(b)comparethepredictionsoftheBowringandtheKattoandOhnocorrelationswiththepresentCHFdataofwaterinthemicro-channelheatsink.Asthepresentchannelshapeisrectangular,ahe-atedequivalentdiameter,de,de nedas[37]de¼

4Ach4Ach

¼;PhWchþ2Hch

ð8Þ

Table5

Correlationsforsaturated owboilingCHFinsinglecircularchannelsReference[34,35]

q00p;m¼

AÀ0:25dGDhsub;in

2:317ðdGh=4ÞF

:077F3dG1

Dhsub;in¼hfÀhin;A¼fgC¼0

24[36]

n¼2:0À0:5PR;PR¼0:145Pout;PoutinMPa

È18:942É1:309FPRexp½20:89ð1:0ÀPRÞ þ0:917;F2¼Pexp½2:444F1¼1:917

ð1:0ÀPRÞ þ0:309R

ÈÉ117:0231:649

F3¼PRexp½16:658ð1:0ÀPRÞ þ0:667;F4¼F3PR

Dhsub;in00

q00¼q1:0þKp;mp;m0fg

À0:0431q00p;m01¼CðGhfgÞWe 0:133qgq00WeÀ1=3p;m02¼0:1ðGhfgÞf 0:133

0:27qg00À0:433ðL=dÞ

qp;m03¼0:098ðGhfgÞfWe 0:6qgÀ0:1731

qp;m04¼0:0384ðGhfgÞfWe 0:513qgðL=dÞ0:27

q00¼0:234ðGhÞWeÀ0:433fgp;m05fÀÁ2LWe¼G;C¼0:25forL<50;C¼0:25þ0:0009LÀ50for506fC¼0:34forL>1500:833ð0:0124þd=LÞð1:52Weþd=LÞ0:261K1¼CWeK3¼1:12K2¼ðq=qÞWeÀ1=3ðq=qÞWeÀ0:173

g

f

g

f

À0:233

L

6150

For

qgf

<0:15:

000000

Whenq00p;m01<qp;m02,qp;m0¼qp;m01

000000000000000000Whenq00p;m01>qp;m02,ifqp;m02<qp;m03,qp;m0¼qp;m02;ifqp;m02>qp;m03,qp;m0¼qp;m03

WhenK1>K2,K¼K1;whenK1<K2,K¼K2Forg>0:15:f

000000

Whenq00p;m01<qp;m05,qp;m0¼qp;m01

000000000000000000Whenq00p;m01>qp;m05,ifqp;m05>qp;m04,qp;m0¼qp;m05;ifqp;m05<qp;m04,qp;m0¼qp;m04q

WhenK1>K2,K¼K1;whenK1<K2,ifK2<K3,K¼K2;ifK2>K3,K¼K3

isemployedtoreplacechanneldiameterdinthetwocorrelations.Fig.8(a)and(b)showbothcorrelationsoverpredictthepresentCHFdatabyalargemargin.Thislargedeviationmaybeattributedtotheafore-mentionedpre-CHFampli cationoftheparallelchan-nelinstabilityaswellastherectangularshapeofthepresentmicro-channels.AlsoshowninFig.8(a)and(b)arecomparisonsofthepredictionsofthetwocorrela-tionswiththesaturatedCHFdataforR-113inmini/micro-channelheatsinksmeasuredearlierbyBowersandMudawar[15].Thecorrelationsgenerallyunder-predicttheR-113dataaswell,eventhoughmanydatapointsarelocatedwithina±40%errorband.

-parisonsbetweencorrelationpredictionsandthepresentCHFdataintherectangularmicro-channelheatsinkareshowninFig.9(a)–(d).Amongthefourcorrelationstested,thecorrelationbySudoetal.[39]showsthebest

agreement(MAEof19.8%)withthedata.However,acloseexaminationofthesamecorrelation,Table6,showsitrelatesCHFtomassvelocityandthermo-physicalpropertiesofthecoolant,butnoneofthechannelgeometricalparameters.Sincesaturated owboilingCHFisa ectedbybothchannellengthLandheatedequivalentdiameterde[20],theseeminglyaccu-ratepredictionsofthiscorrelationarenotsu cienttojustifyitsuseforheatsinkdesign.

Theaboveassessmentofpriorcorrelationspointstotheneedfordevelopinganewcorrelationthatisspe-ci callytailoredtomini/micro-channelheatsinksthatcontainmultiple,parallelchannels.3.5.NewCHFcorrelation

AnewCHFcorrelationisdevelopedbasedonthepresentCHFdataforwaterintherectangularmicro-channelheatsink,aswellasBowersandMudawar’sCHFdataforR-113inthecircularmini/micro-channelheatsinks.Drasticdi erencesbetween

the

thermophysicalpropertiesofwaterandR-113,Table7,aswellasthedi erencesinbothchannelshape,channeldiameter,andL=dratioareallespeciallyusefulindevelopingacorrelationwithabroadapplicationappealbasedonthesetwoCHFdatabases.ThenewCHFcor-relationadoptsthefunctionalformoftheKattoandOhnocorrelation[36].AsshowninTable5,theKattoandOhnocorrelationforzeroinletsubcoolingisgivenby

&'

q00qgLp;m0

;ð9Þ¼f;We;

GhfgqfdewhereWeistheWebernumberbasedonthechannelheatedlengthL,G2LWe¼:

rqf

ð10Þ

q00p;m

¼

q00p;m0

Dhsub;in

:1þK

hfg

ð11Þ

SinceCHFforbothmini/micro-channelheatsinkda-tabasesshowsnodependenceoninletsubcooling,thesedatabasesarecorrelatedaccordingtoEq.(9),i.e.with-outthesubcoolingmultiplier.

1:11 À0:36

q00qgLp;m

¼33:43WeÀ0:21;

deGhfgqf

ð12Þ

AssumingCHFincreaseslinearlywithincreasinginlet

subcoolingyields

wheredeshouldbesetequaltodforcircularmini/micro-channelheatsinks.

Fig.10comparesthepredictionsofthisnewCHFcorrelationwiththe owboilingCHFdataforbothwaterinthepresentrectangularmicro-channelheatsinkandR-113intheBowersandMudawarcircularmini/micro-channelheatsinks.TheoverallMAEof

4%

W.Qu,I.Mudawar/InternationalJournalofHeatandMassTransfer47(2004)2045–2059

Table6

Correlationsforsaturated owboilingCHFinsinglerectangularchannelsReference[37]

Dhsub;in00

q00¼q1:0þKp;mp;m0fg

100À0:0431q00p;m01¼0:25ðGhfgÞeqp;m02¼CðGhfgÞWee

0:133qg1

q00WeÀ1=3p;m03¼0:15ðGhfgÞfe

0:133qgðL=deÞ0:171

q00WeÀ0:433p;m04¼0:26ðGhfgÞfe

L

>50e

0:556ð0:0308þde=LÞ0:261

K1¼1;K2¼K3¼ðqg=qfÞWe000000

Whenq00p;m01<qp;m02,qp;m0¼qp;m01,K¼K1

0000000000

Whenq00p;m01>qp;m02,ifqp;m02<qp;m03,qp;m0¼qp;m02,K¼

0000000000

ifq00m02>qm03,ifqp;m03<qp;m04,qp;m0¼qp;m03,K¼K3

000000

ifq00p;m03>qp;m04,qp;m0¼qp;m04

2057

C¼0:25for

L

e

<50;C¼0:34for

K2

[38]

þq q

C0¼1:35À0:35g

f

q00p;m

¼

Ach

hGDhsub;in

hfgfg

h

10

q i

qggðqfÀqgÞdeÀ0:11

[39][40]

0:005hfgG0:611½kqggðqfÀqgÞ 0:195q00p;m¼q

r

k¼ðqfÀ

qgÞg

hq i

Dhsub;inA¼h0:458G1:0Àq00þ2:412kqggðqfÀqgÞp;mhfgfg

Table7

ThermophysicalpropertiesofsaturatedwaterandsaturatedR-113atoneatmosphereProperties

Saturationtemperature,Tsat(°C)Densityofliquid,qf(kg/m3)Densityofvapor,qg(kg/m3)

Latentheatofvaporization,hfg(kJ/kg)Surfacetension,r(N/m)

Liquidspeci cheatatconstantpressure,cp(kJ/kgK)Thermalconductivityofliquid,kf(W/mK)

Water100.0957.90.602257

0.05894.2170.68

R-11347.61507.37.48158

0.01470.9220.07

tions,channelgeometries,channelsizes,andlength-to-diameterratios.

4.Conclusions

Inthisstudy,experimentswereperformedtomeasureCHFforwater owboilinginarectangularmicro-channelheatsink.PreviousempiricalCHFcorrelationswereexaminedforsuitabilitytopredictingsaturatedCHFinsinglemini-channelsaswellasinmini/micro-channelheatsinks.AnewempiricalcorrelationwasdevelopedforCHFintwo-phasemini/micro-channelheatsinks.Key ndingsfromthestudyareasfollows:(1)Themildparallelchannelinstabilityintrinsictomi-cro-channelheatsinkwithmultiple,parallelchan-nelsisgreatlyampli edasheat uxapproachesCHF.Thiscausesthevaporto owbackwardsinto

clearlydemonstratesitsexcellentpredictivecapabilityfordi erent uids,circumferentialheatingcondi-

2058W.Qu,I.Mudawar/InternationalJournalofHeatandMassTransfer47(2004)2045–2059

theinletplenum,mixwiththeincomingliquid,andincreasetheliquidtemperaturetothelocalsaturationtemperatureastheliquidentersthemicro-channels.(2)

CHFinmini/micro-channelheatsinksincreaseswithincreasingmassvelocitybut,becauseofthelossofsubcoolingduetothebackwardvapor ow,CHFisvirtuallyindependentofinlettemperature.Thisisafundamentaldepartureofmini/micro-channelheatsinkbehaviorfromthatofsinglemini-channels.(3)

TheKattoandOhnocorrelation[36]isfairlyaccu-rateatpredictingsaturatedCHFinsinglecircularmini-channels.

(4)

TwowidelyusedcircularchannelCHFcorrelationsandfourrectangularchannelCHFcorrelationsweretestedrelativetothepresentrectangularmicro-channelheatsinkdata.AcorrelationbySudoetal.[39]forCHFinsinglerectangularchannelsshowedthebestagreementwiththeexperimentaldata.However,thiscorrelationisnotrecommendedforheatsinkdesignbecauseofitsfailuretoaccountforchannellengthordiameter.

(5)

Anewempiricalcorrelationisproposedbasedonexperimental owboilingCHFdataforwaterandR-113inmultiple-channelmini/micro-channelheatsinks.TheoverallMAEofthiscorrelationof4%demonstratesitsexcellentpredictivecapabilityfordi erent uids,circumferentialheatingconditions,channelgeometries,channelsizes,andlength-to-diameterratios.

Acknowledgements

TheauthorsaregratefulforthesupportoftheO ceofBasicEnergySciencesoftheUSDepartmentofEn-ergy(Awardno.DE-FG02-93ER14394A7).

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