Optimal numerical design of forcedconvection heat sinks

OptimalNumericalDesignofForced

ConvectionHeatSinks

WilliamB.KruegerandAvramBar-Cohen,Fellow,IEEE

Abstract—Theobjectiveofthispaperistodescribethede-velopmentofacomputationallyefficientcomputer-aideddesign(CAD)method,whichusesafiniteelementnumericalmodel(FEM)coupledwithempiricalcorrelations,tocreateanoptimumheatsinkdesign,subjecttomultipleconstraints.Athermaloptimization“challenge”problem,representativeofanticipatedheatsinkrequirementsinthenearfuture,issolvedtodemonstratetheproposedmethodology.Particularemphasisisplaceduponmicro-processorcentralprocessingunit(CPU)chipcoolingapplicationswhere,inadditiontothermalrequirements,theheatsinkdesignspecificationincludesconstraintsuponsize,totalmass,andaircoolantpressuredropacrosstheheatsink.

IndexTerms—Automateddesign,designmethodology,numer-icalmethods,optimization,thermalmanagement.

Designvariableoroptimizationinput.

Dimensionlessflowlengthforpressuredrop.Dimensionlesslengthforconvection.Incrementallength.

Fluid(air)density(mass/volume).Ratioofflowareas.

I.INTRODUCTION

T

NOMENCLATURE

Totalductflowarea.Obstructedductarea.

Degreescentigradetemperature.Specificheat(air)(heat/(mass-C)).Hydraulicdiameter(m).

Frictionfactor(dimensionless).

Averageconvectioncoefficientoverflowlength

-.

Losscoefficientsforentranceandexitoffinarray.Thermalconductivity(W/m-C).Flowlength(m).Meters.

Massflowrate(mass/time).

AverageNusseltnumberoverflowlength(dimen-sionless).

Pascalsofpressure.

Prandtlnumber(dimensionless).Thermalresistance.

Reynoldsnumber(dimensionless).

Thermalresistance(junctiontoambient).Meanflowvelocity(/time).Watts(powerorheatflow).Pressuredrop(Pa).Temperature(C).

Temperaturedifference.Heatflow(heat/time).

ManuscriptreceivedSeptember1,2003;revisedJanuary15,2004.ThisworkwasrecommendedforpublicationbyAssociateEditorP.Sathyamurthy.

W.B.KruegeriswiththeDepartmentofMechanicalEngineering,UniversityofMinnesota,TwinCities,MN55812USA(e-mail:wmbkrueger@aol.com).A.Bar-CoheniswiththeDepartmentofMechanicalEngineering,UniversityofMaryland,CollegePark,MA20742USA(e-mail:abc@eng.umd.edu).DigitalObjectIdentifier10.1109/TCAPT.2004.830969

HECENTRALfocusofthisworkisonthedesign,andoptimizationofconvectiveaircoolingsystemsforuseinhighperformanceelectroniccoolingapplications.Theprimarymotivationforthisstudystemsfromthegrowingrequirementsoftheelectronicsindustrytocoolcompact,highpowerdensity,componentsandcircuits,andinparticularmicroprocessorsandpowermodules.[1],[2]indicatethatthegrowthtrendinintegratedcircuit(IC)technologyoverthelastdecadesisexpectedtoextendwellintothe21stcentury.Intheearly1990s,ahigh-endcentralprocessorunitorchip(CPU)dissipatedapproximately30Wofheat.Increasesinclockspeed,chipsize,switchingspeed,andtransistordensityhaveincreasedthepowerdissipationtoapproximately100Wcurrently;with200Wanticipatedinthefirstdecadeofthe21stcentury.Similarly,maximum,currentelectronicdeviceheat

areexpectedtodoubleinthefluxesoftypically25

nextfewyearstoapproximately50[1],[2].

TheconsequenceofthisICgrowthtrendisthatelectroniccoolingcomponentsandsystemswiththecapabilitytoremovefarhigherheatfluxes,volumetricheatdensitiesandtotalheatloads,willberequired.However,themaximumdeviceoperatingtemperaturesarenotexpectedtoincreaseforthecur-rentlypredominantcomplementarymetal-oxidesemiconductor(CMOS)technologyintheelectronicsindustry.Therequiredambientoperatingtemperatureenvelopeisalsonotexpectedtodecreaseinthenearfuture.Ifanything,thedemandforelectronicsystemstooperateinevermoreharshenvironmentsisexpectedtoactuallyincreasetheambienttemperatures.Thus,moreeffective(lowerthermalresistance)coolingsystemswillberequired.

Aircoolingofelectronicsofferslowermanufacturingcost,easeofmaintenance,reliability,andnoenvironmentalconcernsrelativetothealternativesofwatercooling,vaporcompres-sionrefrigeration,ordirectcoolingwithfluorocarbonliquids.Pragmatically,thelimitlesssupplyofairfromthesurroundingstypicallymeansthatnocostswillbeincurredforthecoolantmaterialorthecoolantshippingandtransportation.Finally,themajorityoflandbasedelectronicsystemsusetheatmosphereasanultimatethermodynamicreservoirorheatsink.Assuch,di-rectdissipationofheatintoairtendstosimplifycoolingsystem

1521-3331/04$20.00©2004IEEE

418IEEETRANSACTIONSONCOMPONENTSANDPACKAGINGTECHNOLOGIES,VOL.27,NO.2,JUNE2004

Fig.1.Challengeproblemgeometryandmateriallocations.

design.Whileliquidcoolingsystems,active(coldplate)refrig-eration,refrigeratedorchilledair,andimmersioncoolingareexpectedtoplayaroleinfutureelectroniccoolingsystems,thewidelyacceptedaircoolingofelectronicsisalsoexpectedtoremainpopularifnotpredominant,despitetherelativelypoorthermalpropertiesofair.Successfulrealizationofthehighlyde-mandingcoolingrequirementsoffutureelectroniccomponentswillrequirelowthermalresistance,electronicheatsinksthatarecapableofmeetingstringentlimitsonheatsinkmass,volumeorsize,andaircoolantpressuredrop.Whilecurrentheatsinkdesignsandgeometriesincludeawidevarietyoffinshapesandbasematerialdistributions,parallelplateheatsinks,ofthetypeshowninahalfplanemodelofFig.1continuetobeonepopularchoice[2]andprovideaconvenientgeometryforthedevelop-mentofoptimizationprocedures.

Theheatsinkgeometryusedtodevelopanddemonstratetheoptimumnumericaldesignmethodology,ofthisstudy,isillus-tratedinFigs.1and2.ThesiliconCPUchipservesastheheatsourceatthebottomofFig.1.Dissipatedpowerorheatiscon-ductedthroughthecoppercoreatthecenterofthealuminumbaseintothealuminumfinarray.Thecoolantairflowthenre-movesorconvectsheatoutofthefinarraytotheambient.Thegeometryoftheproposedheatsinkdesigncanberepre-sentedbyavertical,parallelfinarrayonasolidbase.Thepro-posedheatsinkbaseisrectangularatthefinarray,withaformedvolumeofrevolution,createdbyrotatingacurvedsplinearoundtheverticalaxisofsymmetry.Thevolumeofrevolutioncreatedbytherotatedsplineisinspiredbytheleastmaterialradialfinprofiledescribedin[3],whichservesasastartingpointforthisdesignsynthesis.Theflatrectangularplategeometry(betweentherevolvedbaseandfinarray)isusedtointerfacethevolumeofrevolutiontothesquarespecificationenvelope.Thispartic-ulardesignspecificationhasbeendefinedasamicroprocessorheatsink“challengeproblem”forthe2005timeframe[1],[2],asfollows.

—Maximumheatsinkarea

m(0.1m0.1m.—Maximumheatsinkheightm(totalfinsand

base).

—Maximumspaceclaim

cubicmeters(0.1mwide,0.1mlong,0.05mhigh).

—MaximumCPUchipoperatingtemperature

.Fig.2.Challengeproblemdesignvariables.

—

Maximumambienttemperature(inside

enclosure).

—MaximumCPUchippowerdissipation

.—Maximumdesiredheatsinkmass(finsand

base).—Maximumallowablefanhead(pressuredrop)

.(0.15inofwater).

—Coolingairflowratecubicm/s[40cubic

ft/min(c.f.m.)].

Asindicatedabove,thepreviousdesignspecificationrequire-mentsareindeedachallengingproblem,exceedingmostcur-rentheatsinkcapability.Whilethepreviousproblemstatementessentiallyoutlinesthe“challenge”specificationrequirements,severalkeyissuesarelefttothediscretionofthedesigner.

Thetotalrequiredchippowerdissipation

of200Wisspecified,howevernomentionismadeofthedistribution(intimeorspace)ofthedissipatedheatoverthemicro-processorchipsurface.Notethatamaximumspecifiedchiptemperature

of90Catalocalambienttemperatureof40C,allowonetodeterminethemaximumthermalresistanceimpliedbythisspecification

(1)

Asindicatedin(1),themaximumallowablethermalresis-tancepermittedhereinis0.25C/W.Thisthermalresistance

metricorfigureofmerit

representsthetotalthermalre-sistanceallowablefromthechipjunctiontothecoolanttempera-tureorlocalambient.Individualcomponentsof

include:thechipconductiveresistance,chiptoheatsinkcontactresis-tance,theheatsinkandfinarrayconductiveresistance,finarrayconvectiveresistance,andcoolantsensibleheatgainequivalent

resistance.InSectionsIIandIIIofthispaper,

willbeusedasanobjectiveormeritfunctionfortheoptimizationofthepro-posedheatsinkdesign.

Fandriven,forcedconvectionaircoolingisspecifiedforheatremovalfromtheheatsink.Ourconventionwillbetousethemaximumspecifiedairflowrateandallowablepressuredrop,asevenlydistributedacrosstheheatsinkinletsandoutlets.Inkeepingwiththeusualdecouplingbetweenthe“mechanical”sideandthe“electrical”side,thecoolantorairflowisbetween

KRUEGERANDBAR-COHEN:OPTIMALNUMERICALDESIGNOFFORCEDCONVECTIONHEATSINKS419

thefins,andovertheupperorfinnedsurfaceoftheheatsinkbase,notovertheotherheatsinksurfaces.

ExaminationofFig.1indicatesseveraltrade-offsarepossibleorevenrequiredtoachieveasuccessfuldesign.Alargenumberoffinswillprovidealowexternalorconvectiveresistanceduetothelargeextendedsurfaceheattransferarea.Howevertheef-fectiveflowareawillbereducedbythefinthicknessesandanexcessivepressuredropmayresult.Thevolumetricflowrateofthecoolingairwillalsoheavilyinfluenceboththepressuredropandoverallthermalresistance.Ahighcoolingairflowratewillresultinahighflowvelocity,highheattransfercoefficient,

smallsensiblecoolantheatgain,andlow

.Again,theallow-ablepressuredropmaybeexceeded.Conversely,alowcoolantflowratewillhavetheoppositeeffectwithlowerheattransfer

coefficients,largersensibleheatgains,higher

,andlowerpressuredrops.

Thealuminumbasegeometryalsoimpactstheheatsinkper-formance.Athickerbasewillresultinlower(lateralorradial)conductiveheatspreadingresistancefromtheCPU.However,thethickerbasewillalsomovethefinsfurtherfromthechipheatsource,increasingtheaxialorverticalcomponentoftheheatsinkbase’sconductiveresistance.Giventhefiniteallow-ableheatsinkheight(0.05m),athickerbasealsomeansashorterfinarrayheightwithhigherconvectiveresistance(duetodecreasedfinarea),andalargerpressuredropduetothere-ducedflowarea;seeFig.1.Increasingthecoppercorediam-eterwillcertainlydecreasetheinternalconductiveresistanceoftheheatsinkbaseduetothehigherthermalconductivityof

copper(400

-)relativetoaluminum(170-).However,thedensityofcopperisapproximatelythreetimesthatofaluminum,soasevereweightpenaltywillresultfromalargecoppercorediameter.Additionally,afullerorlesstaperedbaseprofilewillresultinlowerinternalconductiveresistance,howeverthemassoftheheatsinkmayeasilyexceedthepaltryspecificationlimitof250g.Thesedesigntrade-offsaremerelyafewoftheissuesthatmustberesolvedinthedesignofthisproposedheatsink,andillustratethepotentialforoptimizationtechniquescoupledwithaFEMtocreateasuperiorheatsinkdesignbysearchingtheapplicabledesignspacefortheoptimaldesign,thusresolvingthepreviouslydiscussedtrade-offs.

II.OPTIMIZATIONMODEL

ThissectionwilldescribethefiniteelementmodelusedtocreatetheoptimalheatsinkdesignsdescribedinSectionsII-A–Eofthispaper.Morespecifically,theheatsinkgeometryforthechallengeproblemheatsinkdesigncanbecharacterizedbyatotalof9inputordesignvariables;(X1,X2,X3,X4,X5,X6,X7,X8,X9).Thesedesignvariablesarethebasicinputstotheoptimizationroutinessubsequentlydiscussed.

A.DesignVariables

Fig.2illustratesthelocationandorientationofthedesignvariables.Thevariable(X1)representstheouterradiusofthefullthicknesscircularbossatthechiplocation.X3isthecoppercoreouterradius,expressedasafractionofthedistancefrom

thechipperimetertotheouterradiusofthecircularbossor(X1).Theminimumchipsizeof0.02msquareisusedhereinforcalculationordemonstrationpurposesinthispaper.ThismodelcouldeasilyaccommodateotherCPUchipsizes.Thedesignvariable(X2)representsthesolidbasethickness,(X4)thenumberoffins(halfplanemodel),and(X5)the(uniform)thicknessofeachcoolingfin.Theaircoolantvolumetricflowrate(X6)istreatedasadesignvariableorinputinthisstudy.Thetaperedbasecurvatureisdefinedbythreeintermediatesplinepointsareplacedateven,radialincrementsovertheta-peredportionoftheheatsinkbase.Theheightofthefirstsplinepoint(dimensionA1inFig.2)issimplydeterminedbydesignvariable(X7),beingafractionofthebasethicknessmultipliedbythebasethicknessordesignvariable(X2).

Theheightofthesecondormiddlesplinepoint(B1inFig.2)isalsodeterminedbytheratio(designvariableX8)multipliedbytheremainingfractionoftheremainingbasethickness;seeFig.2.Inotherwords,thedifferencebetweenthefirstsplinepointheightandthetotalremainingbasethicknessismultipliedbyaratioor(X8)todeterminethesecondsplinepointheight.Thefinaldesignvariable(X9)isalsoaratio,determiningthefinalsplinepointheight(C1inFig.2)usedinasimilarmannerto(X8).Havingdeterminedthethreesplinepointheightsasafunctionofthebasethicknessordesignvariable(X2),afourthorder,continuous,splineconnectsthesplinepoints.There-sultingsplineformstheouterradialsurfaceofrevolutionorheatsinkbasegeometry.Thischaracterizationofthetaperedheatsinkbasecurvatureresultsinamonotonicallydecreasing(out-ward)thickness,capableofproducingawidevarietyofbasegeometries.TheSectionsII-Bdiscussesthematerialselectionsusedinthisstudy.

B.MaterialSelectionandProperties

Fig.1indicatesthemateriallocationsandgeometryusedinthisstudy.Thefactorsinfluencingthematerialselectionsofthispaperaremassdensity,andthermalperformance.Incontrasttothemassdensityconsiderations,thermalperformancefavorstheuseofcopper,foratleastaportionoftheproposedheatsinkasindicatedinTableI(materialproperties),wherethehigherthermalconductivityofcopperwillreducetheinternalconduc-tiveresistanceoftheheatsinkbase,attheexpenseofgreatermass.Ourapproachtotheallocationofthehigherconductivity,higherdensitycopperversusthelowerconductivityandlowerdensityaluminumwasindicatedintheformulationofdesignvariablesinofSectionII-A.

ThismodelwillinitiallyassignacoppercoreregionatthelocationofthehighestheatfluxorattheCPUchip-to-heatsinkinterface.Preliminaryfeasibilitycalculationsprecludedtheob-viousandsimpleallaluminumbasedesignbaseduponthere-quiredvalue.

Theoptimalamountofcopperwillbedeterminedbysolu-tionoftheoptimizationproblemforthedesignvariable(X3)orthecoppercoreradius.Iftheupperlimitof(X3)isapproached,reformulationoftheoptimizationmodeltoextendthecopperregionwouldbeindicated.Anintermediatesolutionoftheop-timalvaluefortheradiusofthecoppercore(X3)withinthespecified0.1to0.9(10%to90%ofthecircularbossradius)wouldindicatereasonableuseofcoppermaterialinthisproblem

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TABLEI

MATERIALPROPERTIES[2]

formulation.TheremainingmaterialdiscussionpertainstothechipinterfacematerialshowninTableI.

Theactualchipattachmenttotheheatsinkisamechanicalclampingdeviceasopposedtoadiscretematerialjoint.Theclampforceisintendedtoreducethethermalcontactresistancebetweenthesiliconchipandheatsink.Itwillbeassumedthat

thebestattainablecontactresistancefora1

chipsizeis0.05C/W,andinverselyproportionaltothechiparea.Placingathinlayerof“interface”material,ofappropriatethermalcon-ductivity,betweenthechipandheatsinkemulatesthisthermalcontactresistanceintheFEMmodel.Inthecomputationsdis-cussedherein,a0.1mmlayerwitha20W/mKthermalcon-ductivitywasused.Sinceanyactualinterfacematerialusedonthephysicalsystemislikelytohavenegligiblemass,the“inter-face”materialisomittedfromanymasscalculations.Inadditiontomaterialproperties,theeffectoftheboundaryconditionsandsolutiontechniques(discussedinSectionsII-C–E)isimportanttoproperheatsinkoptimization.C.SolutionTechniques

Thegoverningequationusedforsolutionofthisoptimiza-tionmodelisthewellknownLaplacianconductionequation,orsecondorderpartialdifferentialtemperatureequation,withthefiniteelementanalysisnumericalapproximationtechnique.SeveralfactorssupporttheuseofthefiniteelementmethodandLaplacianconductionequationinthispaper.Firstly,complexandvariablegeometrydiscussedinSectionII-B,precludesanyexistingclosedformsolutiontechnique,oruseofanapprox-imationtechniquesuchastheseparationofvariablesmethod.Anumericalapproximationtechniqueisindicatedforaccuratesolutionoftheheatconductionequationoveracomplicatedge-ometryasstudiedherein.

Secondly,theoptimizationprocesswithninedesignvari-ableswillrequiremanyFEMmodelevaluationsmandatingafastsolutiontechnique.AtypicalsolutiontimeforthisLaplacianmodelisapproximatelyfifteenminutesontheUniversityofMinnesotaMENETsystems;SiliconGraphics(b)R10000processorrunningat150mHzwith500mbytesofmemory.Conjugatesolutions(theNavier–Stokesandenergyequations)foramuchsimplerfinarray,withonlyaconstantbasetemperature,requireapproximately2horafactorofeighttimesmorecomputertime,onthesameequipment.The

excessivecomputationtimeofaconjugatesolvercoupledwithmanymodelevaluationsrequiredbytheoptimizationalgorithmmilitatesafastLaplaciansolution.Anadditionalfactorarguingagainsttheuseofconjugatesolutionsinthispaperisthelackofspecificationorknowledgeabouttheupstreamanddownstreamflowconditionsandgeometry.Ifsuchinformationwereavailable,theadditionalcapabilityofconjugatesolversindeterminingairflowpressuredropsandconvectioncoefficientswouldbeavaluableaddition.However,withthisincomplete“challenge”specification,theadditionalcomplexityandcomputetimeofaconjugatesolverarenotjustified,andidealizationsorsimplificationsmustbemadeforsolutionofthisproblem,regardlessofthesolutionalgorithmselected.Hence,wewillselecttheLaplaciangoverningequa-tion,andFEMapproximationforuseherein.

ThisselectionofaLaplaciansolutionalgorithmrequiresad-ditionalmathematicalmodelsforthecalculationofpressuredrops,sensibleheatgainofthecoolantflow,convectioncoef-ficients,andheatsinkmasscalculations.Mathematicalmodelsfortheseadditionalcalculationswillbe“embedded”orcalcu-latedinternallybytheFEMandarereferredtohereinas“em-beddedmodels.”These“embeddedmodels”fundamentallypro-videtheadditionaldata(beyondthescopeoftheLaplaciansolver)requiredbythe“challengeproblem”specification.Notethatallofthe“embedded”modelsinthisstudyrequirevariousgeometricdimensions(finspacing,finheight,arraylength,etc.)forcalculationofthehydraulicdiameter,heatsinkmass,andotherpertinentquantities.Thesedimensionsareavailablein-ternallyintheFEMeitherasadirectdesignvariableinput,orindirectly,asaresultofthegeneratedmodelgeometry.D.EmbeddedModels

Inordertoprovideacompletesolutionpursuanttothe“chal-lenge”specification,wewillrequireanestimationofthepres-suredropacrossthefinarray.Theairflowratelimitationsandsmallgeometryspecified,forcetheflowregimetobelaminar.Fortunately,theproblemoflaminarflowbetweenparallelplateshasbeenextensivelystudiedincontemporaryliterature.[4],[5]outlineacorrelationforthelaminarflowpressuredropacrossasimilarparallelplatefinarray.Thepressureandvelocitydis-tributionisassumedtobeuniformacrosstheinletofthefinarray.Theupstreamanddownstreamflowgeometryaretakenasasimplerectangularducts;0.1mwide,withtheductheightequaltothefinarrayheight.Alloftheaircoolantenteringthefinarrayattheinletexitsouttheoppositeend;no“bypass”iscon-sideredherein.Therequiredductingsurfacesonthefinarrayinlet,outlet,andtopoffinarrayareomittedforclarityonallfigures.

Asper(2),[4],[5]thepressuredropincludesskinfrictionanddevelopingfloweffectsaswellasentryandexitlosses.The

termin(2)accountsforthepressuredropduetoflowareacontractionexperiencedbyflowenteringthefinarrayfroman

inletduct.The

termin(2)estimatestheskinfrictionanddevelopingflowlosses,andthetermestimatestheoutletorexpansionpressuregain.Theoutletpressuregainiscausedbytheaircoolantflowexpansionwhenthecoolantexitsthefinarrayintoanexhaustduct.Insummary,thecorrelationpresented

KRUEGERANDBAR-COHEN:OPTIMALNUMERICALDESIGNOFFORCEDCONVECTIONHEATSINKS421

in[4],[5],forlaminarflow,pressuredropacrossaductedfinarrayissimilarto

(2)(3)(4)

Equation(4)defines

thedimensionlessstream-wisedistanceasrequiredin(3).Theentranceandexitlosstermsofthepres-suredropcorrelationhavebeencurvefitfromdatain[6]forlaminarflowasper

(5)(6)(7)

Empiricalandanalyticalverificationof(2)arecontainedin[4]and[5]with(2)–(7)providingacompactcomputationallyeffi-cientpressuredropcalculation.

Aconvectionboundaryconditionisalsorequiredtomodeltheheatdissipationfromthefinarrayanduppersurfaceoftheheatsink.TheFEMappliestherequiredconvectiveboundaryconditiontothefinsurfacesaswellasthe“wetted”topoftheheatsinkbase.ThepreviouslyselectedLaplaciansolverre-quiresaprioriestimationoftheconvectiveheattransfercoeffi-cientresultingfromtheairflowinthefinarraytoimplementaconvectiveboundarycondition.Thispaperusesanempir-icalconvectioncorrelationforlaminardevelopingparallelplateflow[7](alsorecommendedin[5]),andsummarizedasfollows.Theaverageheattransfercoefficientalongtheflow-wiselengthofthefinarrayisestimatedby

(8)

In(8),

istheaverageNusseltnumberovertheflowlength,thehydraulicdiameter,andthethermalconductivityofair.Calculationofisaccomplishedby

(9)(10)

Equation(10)definesadimensionlesslengthinthestreamwiseflowdirectionrequiredin(9).Theconstantterm(7.55)in(10)indicatesthefullydevelopedNusseltnumber,withthequotienttermof(9)beingthecorrectionduetodevelopingflow.Theaircoolantfluidpropertiesareevaluatedatanaverage65Ctem-perature,baseduponthespecified,40Cambienttemperature,and90Cmaximumchiptemperature.

Theremainingcomponentoftherequiredconvectiveboundaryconditionisthe(variable)bulktemperatureoftheaircoolant.Inthisstudy,theenergybalance(11),andanassumedlinearlyvariable(increasingalongtheflowdirection)bulk

temperaturewasusedtoapproximatethesensibleheatgainofthecoolantairflow.

Thesensibleheatgainoftheairisaresultoftheconvectiveheattransferfromthe(hotter)finarraytothe(cooler)airflow.Thistemperaturegainofthecoolantairflowcanhaveasignifi-canteffectupontheproposedheatsink’sthermalperformance

.However,theLaplaciansolverisincapableofdirectlycalculatingthesensibleheatgainoftheairoritsconsequentialincreaseinthebulktemperature.Thefinal“embedded”modelindicatedistheenergybalanceequation

(11)

In(11),isthetotalheatflowtothecoolantairflow,whichisalsothetotalheatflowthroughtheheatsinkforthissteadystatesolution,isthemassflowrate(convertedfromaninputordesignvariableX6foratmosphericair),thespecificheat

ofair,and

thetotaltemperaturegainofthecoolantairflow.The“embedded”modelforthesensibleheatgainofthecoolantisaniterativeprocessconsistingofthefollowingsteps.

Atthefirstsolutionofagivensetofdesignvariableinputs,thecoolantheatgainissimplysettozerooratypicalconvec-tiveboundarycondition,themodelsolved,andthetotalheat

flowcalculated.Equation(11)isthensolvedfor

,giventheotherknownterms.Thetemperaturegain

islinearlyapplied(anapproximation)alongthefinflowpassages,andthemodelresolvedforaseconditeration.Again,theaircoolantinlettemperatureisspecifiedat40C.Ifattheendoftheseconditer-ationthetotalheatflow

iswithintwopercentofthefirstit-eration,iterationiscompleteandthemodelwillproceedtopostprocessing.Ifthedifferencebetweenthecalculatedheatflowattheendofanyiteration,andtheprecedingiteration’sheatflow

,isgreaterthantwopercent,(11)isresolvedfor,theboundaryconditionsreapplied,andanotheriterationstarted.Thetwopercentconvergencetoleranceissimplyarea-sonablealbeitarbitraryvalue,anyconvergencecriteriavaluecouldbeused.Attypical,coolantflowratesof0.019cubicm/s(40c.f.m.),twoorthreeiterationsarerequiredtocorrectlyestimatetheaircoolanttemperaturegain.Attheminimumflowrateconsideredhereinof0.007cubicm/s(15c.f.m.),approximatelyfiveiterationswererequiredformostdesigngeometries.Thereasonformoresolutioniterationswithlowerflowratesisthattheinitialiteration’scoolanttemperaturegainbeingzeroisapoorapproximationatlowflowrateswhichinfacthavealargecoolanttemperaturegain.Highercoolantflowrateswithverylowtemperaturegainstendtobebetterapproximationsoftheinitialiteration,andconsequentlyrequirefewersolutioniterations.Theremainingboundaryconditionsusedinthispaperarethehalfplanesymmetrycondition,andthepreviouslydiscussed“junction”temperaturespecification.Ahalfplanesymmetrymodelisusedhereinsimplytoreducecomputationrequirements.Thesimpleadiabaticboundarycon-ditionatthesymmetryplane(seeFig.1)accomplishesthispur-posewhilethespecifiedjunctiontemperaturewasdiscussedinSectionsII-A–C.TheCPUchiptemperature(lowerfaceofthesiliconchipinFig.1)isspecifiedattherequired90Ctemper-atureasper(1),andthepreviouslydiscussedspecification.TheSectionII-Ebrieflydiscussesthenumericalstabilityandmodelverificationeffortsofthisstudy.

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E.NumericalStabilityandModelVerification

Thenumericalstabilityofthefiniteelementsolutionmodelwasalsoevaluatedattheoptimumdesignsolution.Attheoptimumdesignsolution,approximately20000nodesordegreesoffreedomwererequiredforanumericallyaccuratesolution,withapproximately12000secondorder,isopara-metricsolidthermalelementsmodelingthesolidbasestructureand2000thermalshellelementsbeingusedforthefinarray.The20000degree-of-freedommodelexhibitedexcellent

numericalstabilityattheoptimumdesign,withthe

meritfunctiondecreasingbylessthan0.001C/Wat8200degreesoffreedom,andincreasingbyapproximately0.001C/W(0.4%ofthenominal0.250value)whenthedegreesoffreedomwereincreasedto65000.Assuch,thenumericalstabilityofthisoptimumsolutionisdemonstrated.

ModelvalidationwasaccomplishedhereinbycomparingtheoptimaldesignofSectionIII,andseveralrandomlygeneratedheatsinkdesignstothecorrespondingoutputsofotheranalyt-icalmethods.Conjugatenumericalsolutions(ICEPAK)andan-alyticalfinarraymethods(UniversityofMinnesotaTHERMNSsoftware)bothagreedwiththecurrentmodelwithinafewper-centonthecalculatedvaluesofconvectioncoefficients,pressuredrops,andheatflows.Havingdiscussedallofthepertinentfea-turesofthisheatsinkanalysismodel,andsolutiontechniques,wewillproceedtotheactualoptimizationtechniquesandre-sultsofthisoptimizationstudy.

III.OPTIMIZATIONTECHNIQUESANDRESULTS

Thethermalmodel,discussedanddevelopedinpreviously,waspreparedforoptimizationandseveraloptimizationrunsweremadetodetermineanoptimaldesign.Brieflyrecallingthediscussionoftheintroduction,thefollowingoptimizationcriteriawereidentifiedinthatsectionandareimplementedherein.Theobjectiveormeritfunction(tobeminimized)istheoverallthermalresistancefromthe“junction”temperatureto

ambienttemperatureor

.Aspreviouslydiscussed,representsathermalfigureofmeritorindexastohowwell

agivenheatsinkwillperform.Wewillminimize

(theobjectiveormeritfunction)subjecttotheconstraintsthat

notexceed0.25C/W,themaximumpressuredropnotexceed38Pa,andthetotalheatsinkmassnotexceed250gofmass.

Thelastthreeconstraintson

,pressuredropandmassarecommonlyreferredtoassideconstraints,orconstraintson

calculatedoutputs.Theuseof

asbothanobjectiveormeritfunctionandsideconstrainttendstoprohibittheoptimizationroutinefromproducingoptimaldesignswithlowmassand

lowcoolantpressuredrop,butexcessivelyhigh

values.Havingdiscussedtheoutputsoftheoptimizationroutinewewillturnourattentiontotherequiredinputs.

Theoptimizationinputsofthisstudyarethepreviouslydis-cusseddesignvariablesX1throughX9;seeFigs.1and2.Inthissection,wewilluseoptimizationtechniquestodeterminethebestsetofinputvariablevaluesordesignvector(X1through

X9)tominimize

(theoutput),subjecttothepreviouslydiscussedsideconstraintsonpressuredrop,thermalresistanceandheatsinkmass.Agivenheatsinkdesignwhichexceedsanyoftheprevioussideconstraintsissaidtobeinfeasible.Inthiscontext,theterminfeasiblesimplymeansoneormoreofthesideconstraintswasviolatedorexceeded.A0.1%toler-anceonfeasibilitylimitswasusedintheoptimizationroutine,technicallyallowingforslightlyhighervaluesofthesidecon-straintstobefeasible.Thefollowingparagraphssummarizethetwodifferentoptimizationalgorithms[8]usedinthisstudy;sub-problemtechniques,andfirstorderorgradientoptimization.Attheinitiationofthefirstorderalgorithm[8],theuserisrequiredtomakeaninitialguessattheoptimumdesign.Theoptimizationmodelisevaluatedattheinitialguess,andtheob-jectivefunctiondetermined.Theindividualdesignvariablesaresubsequentlyslightlyperturbatedaroundtheinitialdesign.TheFEMissolvedateachperturbationforthepurposesofdeter-miningthederivativesoftheobjectivefunctionandsidecon-straintswithrespecttothedesignvariables.Thefirstorderorgradientequationalongwithastepsizealgorithmisthenusedtodeterminethenextiterationpointordesignvector(setofdesignvariables);asrequiredtominimizetheobjectivefunction.Thisprocessiscontinueduntiltheoptimizationconvergencecrite-rionissatisfied.Firstorderoptimizationrequiresthattheopti-mizationmodelbeevaluatedby(1thenumberofdesignvari-ables)ateachiterationpoint.Assuch,firstorderoptimizationcanberegardedasacomputationallyintensive,localapproxi-mationoftheFEMbeingoptimized.

Conversely,inthesub-problemoptimizationmethod,eachdesigniteration,involvesonlyasinglesolutionoftheFEM,andaglobalquadraticapproximation(overtheallowedrangeofdesignvariablesorinputs)isachieved.Thesub-problemmethodofoptimization[8]canbedescribedasanadvanced,zero-ordermethodinthatitsimplyrequiresthevaluesofthedependentvariables(objectivefunctionandsideconstraints)nottheirderivatives.Atthestartofasub-problemoptimization,arequisitenumberofFEMsolutionsaremade,tocreateadatabaseforsubsequentdependentvariablecurvefittingorap-proximation.Thenumberofdesignvariablesor(optimizationinputs)plustwoadditionalsolutionsarerequiredforasimplequadraticapproximation.Inthisstudy,wehaveninedesignvariablesrequiringelevenFEMmodelsolutionsforinitialquadraticapproximation.Thedependent(output)variablesarefirstreplacedwithquadraticapproximationsbymeansofleastsquaresfitting,andtheconstrainedminimizationproblemisconvertedtoanequivalentunconstrainedproblemusingpenaltyfunctions.Aftertheinitialcurvefit,theapproximationfunctionisminimized(todeterminetheestimatedoptimumdesign),theFEMupdatedandsolvedatthe(newly)estimatedoptimumdesign.AftereachsubsequentiterationorsolutionoftheFEM,theapproximatedquadraticmodel(calledthesub-problem)isupdated,minimizationoftheobjectivefunctionperformed,andtheFEMredirectedtoanewdesignuntilconvergenceisachievedorterminationisindicated.

Severalinitialattemptsweremadeatoptimizingthisheatsinkdesignusingthefirstordergradientmethod.Noneofthesecalculationsproducedafeasibledesign.Thesub-problemopti-mizationmethodwasthensuccessfullydeployedwiththeinitialpurposeofsimplyfindingthefeasibledesignspace.Anoptimaldesignfortheheatsink“challenge”problemwassuccessfullyfound,andisindicatedinTableII.TableII,alsoshowsthattheoptimumdesignsatisfiedallofthespecifiedsideconstraints,

KRUEGERANDBAR-COHEN:OPTIMALNUMERICALDESIGNOFFORCEDCONVECTIONHEATSINKS423

TABLEII

SUMMARYOFOPTIMIZATIONRESULTS

withinthespecifieddesignvariablelimits.Thetotalcalcula-tiontimefortheoptimizationrun,wasapproximatelyfourhoursontheUniversityofMinnesotaMENETcomputerpreviouslydescribed.

Convergenceofthesub-problemoptimizationmodelisplottedinFig.3.Notethatthefirstelevenmodeliterationsaresimplyrandomdesignevaluationssolvedtocreateadatabaseforthequadraticorsub-problemapproximation.Thetwelfthsolutionisthefirstattemptatactualoptimization,withiterationnumber29reachingtheoptimaldesign.Designiterations12through27producedinfeasibledesignswhereoneormoreofthesideconstraintswereexceeded.

Designsensitivitycalculationswereperformedontheop-timumdesignofTableIIandrevealedthatnoneoftheindi-vidualdesignvariablescouldbeindividuallyalteredbymorethanapproximately10%fromtheiroptimumvalueswithoutproducinganinfeasibledesign.Thusthefeasibledesignspaceofthisproblemisverysmallcomparedtoanyreasonablerangeoftheinputvariables.

Inordertoillustratethesmallsizeofthefeasibledesignspace,considertheninevariabledesignspaceasaninedimen-sional“hyper-cube;”withascalededgelengthofunity.Givenaplusorminus10%tolerance(20%ortwotenths(0.2)ofthetotalrange)oneachdesignvariable,thefeasibledesignspaceasa“volume”fractionofthetotaldesignspacecanbeapprox-imatedas

ofthetotalde-signspace.Thisrealization(sometimescalledthecurseofdi-mensionality)tendstoexplaintheinitialfailureoffirst-orderorgradientbasedmethodsatfindingafeasibledesignspace.Theglobalapproximationinherentinthesub-problem[8]methodwasabletolocatetheverysmallfeasibledesignspace,whilethelocalapproximationnatureofthefirstorderoptimizationmethod[8]wasunabletofindasinglefeasibledesignvector.Havingfoundtheverylimitedfeasibledesignspaceandop-timaldesignvector,nofurther(significant)improvementcouldbemadebyeitherrepeatedsub-problemorfirstorderoptimiza-tioncalculations.

Fig.3.Optimizationhistory.

BrieflyreturningtotheoptimizationhistoryplotofFig.3,afewcommentsareinorder.Theinfeasibledesignsproducediniterations12through27areinfactverysimilardimensionallytothefinaloptimumdesign.Thesub-problemoptimizationtech-niquefundamentallyconvergedtoanearlyoptimumdesignatiteration12,(withonlyminorviolationsofthesideconstraints)andthefollowingiterationssimply“fine-tuned”theheatsinkdesignintotheoptimumconditionindicatedinTableII.Hadthesideconstraintsbeenrelaxedtoallowdeviationsorincreasesontheorderof15%overthespecifiedvaluesforheatsinkmass,coolantpressuredrop,andthermalresistance,convergencetoanoptimumdesignwouldhaveoccurredatanearlieriteration,oratamuchfasterrate.Fewerdesigniterationswouldberequired,withrelaxedsideconstraints,howeveronlyasimilaritytotheexactoptimumdesignofTableIIwouldhavebeenattained,not

theexactvalue.Secondly,thevariationof

showninFig.3isnotparticularlylargeduetotworeasons.First,thedesignvari-ablelimitsofTableIIwereestablishedaprioritooptimiza-tioncalculations,baseduponanticipatedmanufacturingcon-straintsandpreliminaryfeasibilitycalculations.Awiderrangeonthedesignvariableswouldgreatlyincreasethecalculated

values.Usingasnarrowarangeonthedesignvariablesaspracticaltendstoallowforamoreaccuratequadraticapprox-imationof

;asrequiredforsub-problemapproximation.Secondly,thefirstelevenrandomlygenerateddesignsplottedinFig.3,tendtoreflect“average”designs(ordesignpointsnearthemiddleofthedesignspace),sincetheprobabilityofallnine

designvariables(andtheirconsequent

outputs)beingran-domlyassignedtoextreme(highorlow)valuesisverylow,andconsequentlynotobservedinFig.3.Anadditionaltopicofin-terestisthesensitivityoftheobjectivefunctiontoperturbationsoftheinputvariables.

GiventheoptimumdesignoutlinedinTableIIabove,the

variationof

withthemajordesignvariables,abouttheop-timumdesignofTableII,isshowninFig.4.

InpreparingFig.4theentirerangeofeachdesignvariableisnormalizedtounity,duetothelargenumericalvariationintherangesoftheindividualdesignvariablesasindicatedinTableII.Eachdesignvariableisvariedindividually,andtheoptimizationmodelsubsequentlysolvedtocreatetheplotteddata.Aseachdesignvariable,ofFig.4,isincreasedinitsrange,theobjective

424IEEETRANSACTIONSONCOMPONENTSANDPACKAGINGTECHNOLOGIES,VOL.27,NO.2,JUNE2004

Fig.4.Variationinobjectivefunctionwithdesignvariablesattheoptimaldesignvector.

functionoroverallthermalresistanceclearlytendstodecreasewithincreasingdesignvariables.Thesalienttrendsorimpactofeachmajordesignvariable,attheoptimaldesignvector,isindicatedinFig.4withtheanticipatednonlinearityofoutput

asafunctionofinputvariablesbeingevident.

OnemightbetemptedtouseFig.4(orsimilarplots)foraheuristicdesignapproachinlieuoftheoptimizationrou-tinespreviouslydiscussed.SuchanapproachwouldquicklyencounterthelimitationsofFig.4whichincludethefactthatmanyofthedesignpointsinFig.4areinfactinfeasible

designs,andtheplottedvariationsin

are“centered”abouttheoptimaldesignvector.TheplottedcurvesofFig.4wouldmostcertainlyvaryinshape(andsignificance)if“centered”atotherregionsofthedesignspace.

Anotheralternativeapproachtothisdesignmethodologymightusethepopularfactorialdesigntechnique.Alinearfactorialdesign,forthisninevariableproblemwouldrequire

FEMmodelevaluations,orapproximatelyanorder

ofmagnitudemorecomputationthanthe29sub-problemitera-tionspreviouslycited;seeFig.3.Additionally,alinearfactorialwouldnotaccuratelyestimatethenonlinearresponsesindicatedinFig.4.Ifaquadraticfactorialmodel,wereusedforthisninevariableproblem,thenonlinearresponsescouldbeestimated,

however

FEMmodelevaluationswouldberequired,posinganimpracticalcomputationalburden.Partialfactorialexperimentaldesignswillbemorecomputationallyefficientatthe“expense”ofneglectingspecificvariableinteractions,whichcouldeasilycausesignificantdifficultiesindeterminingtheoptimaldesign.Finally,specializedresponsesurfaceexperimentaldesignmethodsmaybeappropriateal-ternativestothesub-problemmethodpresentedherein,butarecertainlylesswellknownoracceptedrelativetotheproposedsub-problemmethod.

Fig.5.Temperaturesolutionofoptimumdesign.

Giventhesecomplexities,theuseofdesignoptimizationalgorithms,suchasthesub-problemandfirstordermethod,closelycoupledwithfiniteelement(orothernumerical)models,areseenashighlyeffectivetoolstodetermineorcreateafeasibleoptimalelectronicheatsinkdesignmeetingtheappropriateproblemconstraints.

Fig.5showstheoveralltemperaturesolutionfortheoptimumheatsink.TheplottedtemperaturecontoursinFig.3spanthetotaltemperaturerangeofthisproblem;40Cambientto90Cchiptemperature.Theeffectofthesensibleheatgainofthecoolingairflowisapparentwiththefintemperaturecontoursvaryingbothparallelandtransversetotheairflowdirection.Theinletendoftheheatsinkiscoolerthantheexhaustoroutletend,asexpected,duetotheheatingofthecoolingairflow.

Thusfarwehavelimitedourdiscussiontotheoptimizationmodel,processanddirectresults.AnimportantinferencecanbemadebyexaminingFig.5,thetemperaturesolutionoftheoptimumdesign.Fig.5showshightemperaturesnearthechiplocation,withremoteportionsofthebaseandfinsoperatingatmuchlowertemperatures.Theseobservationsalsotendtore-inforcethenotionofhighheatdissipationnearthechiploca-tionwithfairlylowheatspreading,andconsequentlylessheattransferfromthefintips,andremotecornersofthebase.Whiletheoptimaldesignpresentedearlierisindeedthebestsetofin-putsordesignvector(tominimize

),withinthedesignvari-ableconstraintsandsideconstraints,Fig.5indicatesthepos-sibilityofstillmoreimprovement.Thispotentialshortcomingisdueinparttotheoptimizationdesignvariablespecificationsordecisionsherein,whichrequireuniformfinthickness,shape,spacing,anduniformaircoolantflowratesineachfinpassage.Shapingthefinlengths,varyingfinspacing,varyingthefinpro-file,andmorecomplexbasegeometriesareallalternativestoimprovethefinproposedheatsinkdesignoreffectiveness.In-deed,thesetopicswillbeexploredinsubsequentpapers.

IV.CONCLUSION

Theobjectiveofthispaperwastodevelopanddemonstrateacomputationallyefficientmethodologyforthecomputer

KRUEGERANDBAR-COHEN:OPTIMALNUMERICALDESIGNOFFORCEDCONVECTIONHEATSINKS425

aidednumericaldesignofelectronicheatsinks,withmultipleconstraints.SectionsIIandIIIaccomplishedthistaskbyuseofaFEMcoupledwithempiricalcorrelations,andoptimizationtechniques.Theproposedmethodologywasdemonstratedbysolutionofaheatsinkdesignchallengeproblem.Overallspeci-ficationcompliancewasdemonstratedbytheproposedoptimaldesign,aswellasasomewhatcomprehensiveheatsinkdesignmethodology,addressingthesimultaneousrequirementsforthermalperformance,maximummass,specifiedspaceclaim,andmaximumallowablecoolantpressuredropinapractical,computationallyefficientmanner.Thefinalcomment,ontheproposedmethodologyistherecognitionthatalthoughonlythe“challenge”problemsolutionisdemonstratedherein,othersimilardesignproblemscanalsobesolvedinasimilarmannerbythetechniquesoutlinedinthispaper.

REFERENCES

[1]A.Bar-Cohen,“Thermalpackagingforthe21stcentury:Challengesand

options,”inProc.5thTherminic—InternationalWorkshopThermalIn-vestigationsofIC’sandSystems,Rome,Italy,1999.

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ofheatsinksinelectroniccooling,”ASMEProc.Adv.Electron.Packag.,vol.2,1990.

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HeatTransfer.NewYork:Wiley,1987.

[6]W.M.KaysandA.L.London,CompactHeatExchangers,3rd

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WilliamB.KruegerreceivedtheM.S.andPh.D.degreesinmechanicalengineeringfromtheUniver-sityofMinnesota,Minneapolis,in1997and2002,respectively.

Thefocusofhisgraduatestudieswasinheattransfer,numericalmethods,andoptimizationtechniques.Since1999,hehasbeenself-employedasanindependentconsultingengineerprovidingthermalandstructuraldesignandanalysisservicesforanumberofleadingcorporations.Priorto1999,hewasemployedinprimarilyintheproductdesign

anddevelopmentcapacitybymanyofhiscurrentconsultingclientele.Hisprofessionalinterestsincludecomputeraideddesign,designmethodologies,optimizationtechniques,andproductdevelopmentmethodologies.

AvramBar-Cohen(M’85–SM’87–F’93)receivedtheB.S.(withhonors),M.S.,andPh.D.degreesfromtheMassachusettsInstituteofTechnology,Cambridge,in1968and1971,respectively,allinmechanicalengineering.

HeisProfessorandChairofMechanicalEn-gineeringattheUniversityofMaryland,CollegePark,wherehecontinueshisresearchinthethermalmanagementofMicro/Nanosystems.HebeganhisprofessionalcareerattheRaytheonCompanyinMassachusettsin1968andforthepast35yearshas

beeninvolvedinthedesign,analysis,andoptimizationofthermalsystems,withemphasisonthethermalpackagingofelectronicequipment.Hehaslecturedwidely,publishedextensivelyinthearchivalheattransferandpackagingliterature,andtaughtmanyShortCoursesonthissubject,atuniversitiesandmajorconferencesintheU.S.andabroad.HeservedasGeneralManagerandExecutiveConsultantforpackagingandphysicalmodelingatControlDataCorporation,1984-19,heldasuccessionofacademicappointments,fromLecturertoProfessor,intheDepartmentofMechanicalEngineeringattheBenGurionUniversityoftheNegev(Israel),1973-1988,andwasonthefacultyattheMassachusettsInstituteofTechnology,1977-1978,andtheNavalPostgraduateSchool,1982.FiftygraduatestudentshavecompletedtheirM.S.andPh.D.degreesunderhisdirectionattheBenGurionUniversity,MIT,andtheUniversityofMinnesota,respectively.Heisco-author(withA.D.Kraus)ofDesignandAnalysisofHeatSinks(NewYork:Wiley,1995)andThermalAnalysisandControlofElectronicEquipment(NewYork:McGraw-Hill/Hemisphere,1983),andhasco-edited13booksinthisfieldincludingAdvancesinThermalModelingofElectronicComponentsandSys-tems(NewYork:ASMEPress)andThermalManagementofMicroelectronicandElectronicSystems(NewYork:Wiley).Hehasauthoredandco-authoredsome250journalpapers,refereedproceedingspapers,andchaptersinbooks,andhasdeliverednearly50Keynote,Plenary,andInvitedLecturesatmajortechnicalConferencesandInstitutions.Priortoacceptinghiscurrentposition,heservedastheDirectoroftheCenterfortheDevelopmentofTechnologicalLeadershipandheldtheSweattChairattheUniversityofMinnesota,whereheearlierservedasProfessorofMechanicalEngineeringandDirectoroftheThermodynamicsandHeatTransferDivision.HeservedastheASMEVicePresidentforResearch(1998-2001)andhadearlierservedonASME’sBoardofResearchandTechnologyDevelopment,aswellastheASMEBoardonProfessionalDevelopment,andwasinstrumentalinrevivingtheHTDK-16CommitteeonHeatTransferinElectronicComponentsintheearly1980s.HewasafoundingmemberandcurrentlyservesontheAdvisoryBoardofASME’sNanotechnologyInstituteandrepresentsASMEontheAssemblyforInternationalHeatTransferConferences(2002–2006).Hisinterestsincludethermaldesign,ebullientheattransfer,andthermalphenomenainmicroelec-tronic,photonic,andbiologicalsystems,aswellastechnologyforecastingandmanagementoftechnology.

Dr.Bar-Cohenreceivedthe2001IEEECPMTSocietyOutstandingSustainedTechnicalContributionsAward,the2000ASMEWorcesterReedWarnerMedalforoutstandingcontributionstotheliteratureintheareaofheattransfer,theASMEHeatTransferMemorialAward,theASMECurriculumInnovationAwardin1999,theASME/IEEEITHERMAchievementAwardin1998,theASMEEdwinF.ChurchMedalin1994,andtheTHERMIAwardfromtheIEEE/Semi-ThermConferencein1997.HeisaFellowofASME,theEditor-in-ChiefoftheIEEETRANSACTIONSONCOMPONENTSANDPACKAGINGTECHNOLOGIES,aDistinguishedLecturerforIEEEand,inthepast,forASME,wastheFoundingChairmanoftheITHERMConferencein1988,andservedastheGeneralChairmanforthefirstInternationalIntersocietyPackagingConference(InterPack)in1995.