散熱器擴散熱阻的計算

散熱器擴散熱阻的計算散熱器擴散熱阻的計算Accident？Considerthescenariowhereadesignerwishestoincorporateanewlydevelopeddeviceintoasystemandsoonlearnsthataheatsinkisneededtocoolthedevice.Thedesignerfindsaratherlargeheatsinkinacatalogwhichmarginallysatisfiestherequiredthermalcriteria.Duetootherconsiderations,suchasfannoiseandcostconstraints,anattempttouseasmallerheatsinkprovedfutile,andsothelargerheatsinkwasacceptedintothedesign.Aprototypewasmadewhich,unfortunately,burned-outduringtheinitialvalidationtest,theproductmissedthenarrowintroductiontime,andtheprojectwascanceled.WhatwentwrongThereasonscouldhavebeenmulti-fold.But,underthisscenario,themainculpritcouldhavebeenthespreadingresistancethatwasoverlookedduringthedesignprocess.Itisveryimportantforheatsinkuserstorealizethat,unlesstheheatsinkiscustomdevelopedforaspecificapplication,thermalperformancevaluesprovidedinvendor'scatalogsrarelyaccountfortheadditionalresistancescomingfromthesizeandlocationconsiderationsofaheatsource.Itisunderstandablethatthevendorsthemselvescouldnotpossiblyknowwhatkindofdevicestheuserswillbecoolingwiththeirproducts.RIntroductionSpreadingorconstrictionresistancesexistwheneverheatflowsfromoneregiontoanotherindifferentcrosssectionalarea.Inthecaseofheatsinkapplications,thespreadingresistanceoccursinthebase-platewhenaheatsourceofasmallerfootprinfootprintareaismountedonaheatsinkwithalargerbase-platearea.Thisresultsinahigherlocaltemperatureatthelocationwheretheheatsourceisplaced.Figure1illustrateshowthesurfacetemperatureofaheatsinkbase-platewouldrespondasthesizeoftheheatsourceisprogressivelyreducedfromlefttorightwithallotherconditionsunchanged:thesmallertheheatsource,themorespreadinghastotakeplace,resultinginagreatertemperatureriseatthecenter.Inthisexample,theeffectoftheedgesurfacesoftheheatsinkisignoredandtheheatsourceisassumedtobegeneratinguniformheatflux.Incaseswherethefootprintofaheatsinkneednotbemuchlargerthanthesizeoftheheatsource,thecontributionofthespreadingresistancetotheoveralldevicetemperaturerisemaybeinsignificantandusuallyfallswithinthedesignmargin.However,inanattempttoremovemoreheatfromtoday'shighperformancedevices,alargerheatsinkisoftenusedand,consequently,theimpactofspreadingresistanceontheperformanceofaheatsinkisbecominganimportantfactorthatmustnotbeignoredinthedesignprocess.Itisnotuncommontofindinmanyhighperformance,highpowerapplicationsthatmorethanhalfthetotaltemperatureriseofaheatsinkisattributedtothespreadingresistanceinthebase-plate.Theobjectivesofthisarticleare:1)tounderstandthephysicsandparametersassociatedwithspreadingresistance2)toprovideasimpledesigncorrelationforaccuratepredictionoftheresistance3)todiscussandclarifytheconceptofspreadingresistancewithanemphasisonthepracticaluseofthecorrelationinheatsinkapplicationsThecorrelationprovidedhereinwasoriginallydevelopedinreferences1and2.Thisarticleisanextensionoftheearlierpresentation.SpreadingResistanceBeforeweproceedwiththeanalysis,letusattendtowhatthetemperaturedistributionsshowninFig.1aretellingus.Thefirstobviousone,asnotedearlier,isthatthemaximumtemperatureatthecenterincreasesastheheatsourcebecomessmaller.Anotherimportantobservationisthat,asthetemperaturerisesinthecenter,thetemperaturesalongtheedgesoftheheatsinkdecreasesimultaneously.Itcanbeshownthatthishappensinsuchawaythatthearea-averagedsurfacetemperatureoftheheatsinkbase-platehasremainedthesame.Inotherwords,theaverageheatsinkthermalperformanceisindependentofthesizeofaheatsource.Infact,aswillbeseenlater,itisalsoindependentofthelocationoftheheatsource.Thespreadingresistancecanbedeterminedfromthefollowingsetofparameters:footprintorcontactareaoftheheatsource,Asfootprintareaoftheheatsinkbase-plate,Apthicknessoftheheatsinkbase-plate,tthermalconductivityoftheheatsinkbase-plate,kaverageheatsinkthermalresistance,R0Wewillassume,forthetimebeing,thattheheatsourceiscentrallymountedonthebase-plate,andtheheatsinkiscooleduniformlyovertheexposedfinnedsurface.Thesetwoassumptionswillbeexaminedinfurtherdetail.Figure2showsatwo-dimensionalsideviewoftheheatsinkwithheat-flowlinesschematicallydrawninthebase-platewhosethicknessisgreatlyexaggerated.Atthetop,thecorrespondingsurfacetemperaturevariationacrossthecenterlineofthebase-plateisshownbythesolidline.Thedottedlinerepresentstheaveragetemperatureofthesurfacewhichis,again,independentoftheheatsourcesizeandcanbeeasilydeterminedbymultiplyingRwiththe0totalamountofheatdissipation,denotedasQ.AsindicatedinFig.2,themaximumconstrictionresistanceR,whichcaccountsforthelocaltemperatureriseovertheaveragesurfacetemperature,istheonlyadditionalquantitythatisneededfordeterminingthemaximumheatsinktemperature.Itcanbeaccuratelydeterminedfromthefollowingcorrelation.Figure2-TwodimensionalschematicviewoflocalresistanceortemperaturevariationofaheatsinkshownwithheatflowLinesNotethatthecorrelationaddressesneithertheshapeoftheheatsourcenorthatoftheheatsinkbase-plate.Itwasfoundintheearlierstudythatthiscorrelationtypicallyresultsinanaccuracyofapproximately5%overawiderangeofapplicationswithmanycombinationsofdifferentsource/sinkshapes,providedthattheaspectratiooftheshapesinvolveddoesnotexceed.Seereferences1and2forfurtherdiscussions.ExampleProblemConsideranaluminumheatsink(k=200W/mK)withbase-platedimensionsof100x100xmmthick.Accordingtothecatalog,thethermalresistanceofthisheatsinkunderagivensetofconditionsis°C/W.Findthemaximumresistanceoftheheatsinkifusedtocoola25x25mmdevice.SolutionsWithnootherspecificdescriptions,itisassumedthattheheatsourceiscentrallymounted,andthegiventhermalresistanceof°C/Wrepresentstheaverageheatsinkperformance.Fromtheproblemstatement,wesummarize:A=x=m2sA=x=m2pt=mk=200W/mKR=°C/W0Therefore,Hence,themaximumresistance,R,is:totalR=R+R=+=°C/WtotalocReadersshouldnotethefarrighttemperaturedistributioninFig.1whichistheresultofanumericalsimulationforthepresentprobleminrectangularcoordinates.EffectofSourceLocationInthefollowingtwosections,wewilllimitourexaminationtothecurrentexampleproblem.Asweshallsee,theresultofthislimitedcasestudywillallowustodrawsomegeneralyetusefulconclusions.Supposethesameheatsourceintheaboveexamplewasnotcentrallylocated,butmountedadistanceawayfromthecenter.Obviously,themaximumtemperaturewouldfurtherriseascomparedtothatfoundintheaboveexample.Figure3showsthelocalresistancescorrespondingtotwosuchcases:Figure3-Heat-sinklocalresistanceshowingtheeffectofsourcelocation:fromLtoR,heatsourceat,0)and,thefirstoneisforthecasewheretheheatsourceismountedmidwayalongtheedge,andtheother,whereitismountedononecorneroftheheatsink.Forthesetwospecialcases,themaximumspreadingresistancecanbecalculatedbyusingEq.(1)forRwithinputcparameterstandRmodifiedasshownbelow:c0RCxRAAktCRC)ccps0withwithforthefirstcase,andC=2forthesecondcase.Itistobenotedthatthisexpressionisindependentofthesourcesize.Numerically,forthecurrentproblemwitha25x25mmheatsource,itresultsinthemaximumspreadingresistancesofand°C/W,orthetotalresistancesofand°C/Wforthefirstandsecondcases,respectively.Forbothcases,itcanbeshownthattheaveragesurfaceresistancehasnotchangedfromunity.Forotherintermediatesourcelocations,numericalsimulationswerecarriedoutandaplotisprovidedinFig.4forthecorrectionfactorCwhichcanbeusedtocomputethetotalresistanceasfR=R+CR(4)total0fcwhereRisdeterminedfromEq.(1),givenforthecasewiththeheatcsourceplacedatthecenter.Figure4-CorrectionfactorasafunctionofsourcelocationThecoordinatesinFig.4indicatethelocationofthecenteroftheheatsourcemeasuredfromthecenterofthebase-plateinmm:thecasewithacentrallylocatedheatsourcecorrespondsto(0,0),andthecasesshowninFig.3correspondto,0)and,forthefirstandsecondcases,respectively.OnlyonequadrantisshowninFig.4astheywouldbe,owingtotheassumptionofuniformcooling,symmetricalabout(0,0).Ascanbeseenfromthefigure,thecorrectionfactorincreasesfrom1astheheatsourceisplacedawayfromthecenter.Itisworthwhilenotingthattheincreaseis,however,veryminimaloverawideregionnearthecenter,andmostincreasesoccurclosertotheedges.UnlikeCintheearlierexpression,Ciscasedependent.itdependsfontheheat-sourcesize).However,itwasfoundthattheplotsofCfobtainedformanyothercasesexhibitessentiallythesameprofileasthatshowninFig.4,withmagnitudesatthecornersdeterminedfromEq.(3),andthedomainoftheplotdefinedbythemaximumdisplacementoftheheatsource.Basedonthisobservation,ageneralconclusioncanbemade:forallpracticalpurposes,aslongastheheatsourceisplacedclosertothecenterthantotheedgesoftheheatsink,thecorrectionalincreaseinthespreadingresistancemaybeignored,andC=1maybeused.Asnotedabove,thiswouldintroducefasmallerrorofnogreaterthan5-10%inthespreadingresistancewhich,inturn,isafractionofthetotalresistance.Sofar,wehaveassumedauniformcoolingovertheentirefinned-surfaceareaofthebase-plate.Althoughthisisausefulassumption,itisseldomrealizedinactualsituations.Itiswellknownthat,duetothethinnerboundarylayerandthelessdown-streamheatingeffect,adevicewouldbecooledmoreeffectivelyifitismountedtowardtheairinletside.Again,anumericalsimulationiscarriedoutusingourexampleproblemwiththeboundarylayereffectincluded.Figure5showstheresultingmodifiedcorrectionfactorasafunctionofthedistancefromthecenteroftheheatsinktotheheatsourceplacedalongthecenterlineaty=0:x=mmcorrespondstothefrontmostleadingedgelocationoftheheatsourceandx=mmtherearmosttrailingedgeplacement.Figure5-Correctionfactormodifiedforboundarylayereffectaty=0Ascanbeseenfromthefigure,itispossibletorealizeasmallimprovementbyplacingtheheatsourceforwardofthecenterlocationwhereC<1.However,itwasexperiencedinpracticethatfaccommodatingaheatsourceawayfromthecenterandensuringitsmountingorientationoftencauseadditionalproblemsduringmanufacturingandassemblyprocesses.SummaryandDiscussionAsimplecorrelationequationispresentedfordeterminingspreadingresistancesinheatsinkapplications.Asamplecalculationiscarriedoutforacasewithaheatsourceplacedatthecenteroftheheatsinkbase-plateandameanstoestimatethecorrectionfactortoaccountfortheeffectofchangingtheheat-sourcelocationisprovided.ItistobenotedthatthecorrelationprovidedhereinisageneralsolutionwhichreducestothewellknownKennedy'ssolution3whenRapproaches0:themathematicalequivalentofisothermal0boundarycondition.Kennedy'ssolutionisvalidonlywhenRis0sufficientlysmallsuchthatthefin-sideoftheheatsinkbase-plateisclosetoisothermal.Otherwise,Kennedy'ssolution,representingthelowerboundaryofthespreadingresistance,mayresultingrossunderestimationoftheresistance.Theearlierstudyrevealedthat,dependingontherelativemagnitudeoftheaverageheatsinkresistance,thespreadingresistancemayeitherincreaseordecreasewiththebase-platethickness.Iftheheatsinkresistanceissufficientlysmall,asinliquidcooledheatsinkapplications,thespreadingresistancealwaysincreaseswiththethickness,andanoptimumthicknessdoesnotexist.Ontheotherhand,iftheh