传热学习题解答11.docx

传热学习题解答11.docx

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传热学习题解答11

Chapter1

BASICSOFHEATTRANSFER

ThermodynamicsandHeatTransfer

1-1CThermodynamicsdealswiththeamountofheattransferasasystemundergoesaprocessfromoneequilibriumstatetoanother.Heattransfer,ontheotherhand,dealswiththerateofheattransferaswellasthetemperaturedistributionwithinthesystemataspecifiedtime.

1-2C（a）Thedrivingforceforheattransferisthetemperaturedifference.（b）Thedrivingforceforelectriccurrentflowistheelectricpotentialdifference（voltage）.（a）Thedrivingforceforfluidflowisthepressuredifference.

1-3CThecalorictheoryisbasedontheassumptionthatheatisafluid-likesubstancecalledthe"caloric"whichisamassless,colorless,odorlesssubstance.Itwasabandonedinthemiddleofthenineteenthcenturyafteritwasshownthatthereisnosuchthingasthecaloric.

1-4CTheratingproblemsdealwiththedeterminationoftheheattransferrateforanexistingsystemataspecifiedtemperaturedifference.Thesizingproblemsdealwiththedeterminationofthesizeofasysteminordertotransferheatataspecifiedrateforaspecifiedtemperaturedifference.

1-5CTheexperimentalapproach（testingandtakingmeasurements）hastheadvantageofdealingwiththeactualphysicalsystem,andgettingaphysicalvaluewithinthelimitsofexperimentalerror.However,thisapproachisexpensive,timeconsuming,andoftenimpractical.Theanalyticalapproach（analysisorcalculations）hastheadvantagethatitisfastandinexpensive,buttheresultsobtainedaresubjecttotheaccuracyoftheassumptionsandidealizationsmadeintheanalysis.

1-6CModelingmakesitpossibletopredictthecourseofaneventbeforeitactuallyoccurs,ortostudyvariousaspectsofaneventmathematicallywithoutactuallyrunningexpensiveandtime-consumingexperiments.Whenpreparingamathematicalmodel,allthevariablesthataffectthephenomenaareidentified,reasonableassumptionsandapproximationsaremade,andtheinterdependenceofthesevariablesarestudied.Therelevantphysicallawsandprinciplesareinvoked,andtheproblemisformulatedmathematically.Finally,theproblemissolvedusinganappropriateapproach,andtheresultsareinterpreted.

1-7CTherightchoicebetweenacrudeandcomplexmodelisusuallythesimplestmodelwhichyieldsadequateresults.Preparingveryaccuratebutcomplexmodelsisnotnecessarilyabetterchoicesincesuchmodelsarenotmuchusetoananalystiftheyareverydifficultandtimeconsumingtosolve.Attheminimum,themodelshouldreflecttheessentialfeaturesofthephysicalproblemitrepresents.

HeatandOtherFormsofEnergy

1-8CTherateofheattransferperunitsurfaceareaiscalledheatflux

.Itisrelatedtotherateofheattransferby

.

1-9CEnergycanbetransferredbyheat,work,andmass.Anenergytransferisheattransferwhenitsdrivingforceistemperaturedifference.

1-10CThermalenergyisthesensibleandlatentformsofinternalenergy,anditisreferredtoasheatindailylife.

1-11CFortheconstantpressurecase.ThisisbecausetheheattransfertoanidealgasismCpTatconstantpressureandmCpTatconstantvolume,andCpisalwaysgreaterthanCv.

1-12Acylindricalresistoronacircuitboarddissipates0.6Wofpower.Theamountofheatdissipatedin24h,theheatflux,andthefractionofheatdissipatedfromthetopandbottomsurfacesaretobedetermined.

AssumptionsHeatistransferreduniformlyfromallsurfaces.

Analysis（a）Theamountofheatthisresistordissipatesduringa24-hourperiodis

（since1Wh=3600Ws=3.6kJ）

（b）Theheatfluxonthesurfaceoftheresistoris

（c）Assumingtheheattransfercoefficienttobeuniform,heattransferisproportionaltothesurfacearea.Thenthefractionofheatdissipatedfromthetopandbottomsurfacesoftheresistorbecomes

DiscussionHeattransferfromthetopandbottomsurfacesissmallrelativetothattransferredfromthesidesurface.

1-13EAlogicchipinacomputerdissipates3Wofpower.Theamountheatdissipatedin8handtheheatfluxonthesurfaceofthechiparetobedetermined.

AssumptionsHeattransferfromthesurfaceisuniform.

Analysis（a）Theamountofheatthechipdissipatesduringan8-hourperiodis

（b）Theheatfluxonthesurfaceofthechipis

1-14Thefilamentofa150Wincandescentlampis5cmlongandhasadiameterof0.5mm.Theheatfluxonthesurfaceofthefilament,theheatfluxonthesurfaceoftheglassbulb,andtheannualelectricitycostofthebulbaretobedetermined.

AssumptionsHeattransferfromthesurfaceofthefilamentandthebulbofthelampisuniform.

Analysis（a）Theheattransfersurfaceareaandtheheatfluxonthesurfaceofthefilamentare

（b）Theheatfluxonthesurfaceofglassbulbis

（c）Theamountandcostofelectricalenergyconsumedduringaone-yearperiodis

1-15A1200Wironisleftontheironingboardwithitsbaseexposedtotheair.Theamountofheattheirondissipatesin2h,theheatfluxonthesurfaceoftheironbase,andthecostoftheelectricityaretobedetermined.

AssumptionsHeattransferfromthesurfaceisuniform.

Analysis（a）Theamountofheattheirondissipatesduringa2-hperiodis

（b）Theheatfluxonthesurfaceoftheironbaseis

（c）Thecostofelectricityconsumedduringthisperiodis

1-16A15cm20cmcircuitboardhouses120closelyspaced0.12Wlogicchips.Theamountofheatdissipatedin10handtheheatfluxonthesurfaceofthecircuitboardaretobedetermined.

Assumptions1Heattransferfromthebacksurfaceoftheboardisnegligible.2Heattransferfromthefrontsurfaceisuniform.

Analysis（a）Theamountofheatthiscircuitboarddissipatesduringa10-hperiodis

（b）Theheatfluxonthesurfaceofthecircuitboardis

1-17Analuminumballistobeheatedfrom80Cto200C.Theamountofheatthatneedstobetransferredtothealuminumballistobedetermined.

AssumptionsThepropertiesofthealuminumballareconstant.

PropertiesTheaveragedensityandspecificheatofaluminumaregiventobe=2,700kg/m3and

kJ/kg.C.

AnalysisTheamountofenergyaddedtotheballissimplythechangeinitsinternalenergy,andisdeterminedfrom

where

Substituting,

Therefore,515kJofenergy（heatorworksuchaselectricalenergy）needstobetransferredtothealuminumballtoheatitto200C.

1-18Thebodytemperatureofamanrisesfrom37°Cto39°Cduringstrenuousexercise.Theresultingincreaseinthethermalenergycontentofthebodyistobedetermined.

AssumptionsThebodytemperaturechangesuniformly.

PropertiesTheaveragespecificheatofthehumanbodyisgiventobe3.6kJ/kg.°C.

AnalysisThechangeinthesensibleinternalenergycontentofthebodyasa

resultofthebodytemperaturerising2Cduringstrenuousexerciseis

U=mCT=（70kg）（3.6kJ/kg.C）（2C）=504kJ

1-19Anelectricallyheatedhousemaintainedat22°Cexperiencesinfiltrationlossesatarateof0.7ACH.Theamountofenergylossfromthehouseduetoinfiltrationperdayanditscostaretobedetermined.

Assumptions1Airasanidealgaswithaconstantspecificheatsatroomtemperature.2Thevolumeoccupiedbythefurnitureandotherbelongingsisnegligible.3Thehouseismaintainedataconstanttemperatureandpressureatalltimes.4Theinfiltratingairexfiltratesattheindoorstemperatureof22°C.

PropertiesThespecificheatofairatroomtemperatureis

=1.007kJ/kg.C（TableA-15）.

AnalysisThevolumeoftheairinthehouseis

Notingthattheinfiltrationrateis0.7ACH（airchangesperhour）andthustheairinthehouseiscompletelyreplacedbytheoutdoorair0.724=16.8timesperday,themassflowrateofairthroughthehouseduetoinfiltrationis

Notingthatoutdoorairentersat5Candleavesat22C,theenergylossofthishouseperdayis

Ataunitcostof$0.082/kWh,thecostofthiselectricalenergylostbyinfiltrationis

1-20Ahouseisheatedfrom10Cto22Cbyanelectricheater,andsomeairescapesthroughthecracksastheheatedairinthehouseexpandsatconstantpressure.Theamountofheattransfertotheairanditscostaretobedetermined.

Assumptions1Airasanidealgaswithaconstantspecificheatsatroomtemperature.2Thevolumeoccupiedbythefurnitureandotherbelongingsisnegligible.3Thepressureinthehouseremainsconstantatalltimes.4Heatlossfromthehousetotheoutdoorsisnegligibleduringheating.5Theairleaksoutat22C.

PropertiesThespecificheatofairatroomtemperatureis

=1.007kJ/kg.C（TableA-15）.

AnalysisThevolumeandmassoftheairinthehouseare

Notingthatthepressureinthehouseremainsconstantduringheating,theamountofheatthatmustbetransferredtotheairinthehouseasitisheatedfrom10to22Cisdeterminedtobe

Notingthat1kWh=3600kJ,thecostofthiselectricalenergyataunitcostof$0.075/kWhis

Therefore,itwillcostthehomeownerabout19centstoraisethetemperatureinhishousefrom10to22C.

1-21EAwaterheaterisinitiallyfilledwithwaterat45F.Theamountofenergythatneedstobetransferredtothewatertoraiseitstemperatureto140Fistobedetermined.

Assumptions1Waterisanincompressiblesubstancewithconstantspecificheatsatroomtemperature.2Nowaterflowsinoroutofthetankduringheating.

PropertiesThedensityandspecificheatofwateraregiventobe62lbm/ft3and1.0Btu/lbm.F.

AnalysisThemassofwaterinthetankis

Then,theamountofheatthatmustbetransferredtothewaterinthe

tankasitisheatedfrom45to140