Heat transfer cengel solution manual

Complete Solution Manual to Accompany
v v v v




HEAT TRANSFER v
SECONDv


EDITION
A Practical Approach
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YUNUS A. CENGEL
v v

,Preface
Thisvmanualvisvpreparedvasvanvaidevtovthevinstructorsvinvcorrectingvhomeworkvassignments,vbutvi
tvcanvalsovbevusedvasvavsourcevofvadditionalvexamplevproblemsvforvusevinvthevclassroom.vWithvth
isvinvmind,vallvsolutionsvarevpreparedvinvfullvdetailvinvavsystematicvmanner,vusingvavwordvproces
sorvwithvanvequationveditor.vThevsolutionsvarevstructuredvintovthevfollowingvsectionsvtovmakevitv
easyvtovlocatevinformationvandvtovfollowvthevsolutionvprocedure,vasvappropriate:

Solutionv-
Thevproblemvisvposed,vandvthevquantitiesvtovbevfoundvarevstated.vA
ssumptionsv-
vThevsignificantvassumptionsvinvsolvingvthevproblemvarevstated.vPropertiesv-

Thevmaterialvpropertiesvneededvtovsolvevthevproblemvarevlisted.vA
nalysisv-
Thevproblemvisvsolvedvinvavsystematicvmanner,vshowingvallvsteps.v
Discussionv- Commentsvarevmadevonvthevresults,vasvappropriate.

Avsketchvisvincludedvwithvmostvsolutionsvtovhelpvthevstudentsvvisualizevthevphysicalvproblem,va
ndvalsovtovenablevthevinstructorvtovglancevthroughvseveralvtypesvofvproblemsvquickly,vandvtovma
kevselectionsveasily.
Problemsvvv designatedvvv withvvv thevvv CD
iconvinvthevtextvarevalsovsolvedvwithv
thev EESv software,v andv electronicv solutions
completev withv parametricv studiesvar
evavailablevonvthevCDvthatvaccompaniesvthevtext.vComprehensivevproblemsvdesignatedvwithvthe
vcomputer-

EESviconv[pickvonevofvthevfourvgiven]varevsolvedvusingvthevEESvsoftware,vandvtheirvsolutionsv
arevplacedvatvthevInstructorvManualvsectionvofvthevOnlinevLearningvCenterv(OLC)vatvwww.mh
he.com/cengel.vAccessvtovsolutionsvisvlimitedvtovinstructorsvonlyvwhovadoptedvthevtext,vandvin
structorsvmayvobtainvtheirvpasswordsvforvthevOLCvbyvcontactingvtheirvMcGraw-
HillvSalesvRepresentativevatvhttp://www.mhhe.com/catalogs/rep/.
Everyveffortvisvmadevtovproducevanverror-
freevSolutionsvManual.vHowever,vinvavtextvofvthisvmagnitude,vitvisvinevitablevtovhavevsome,vandv
wevwillvappreciatevhearingvaboutvthem.vWevhopevthevtextvandvthisvManualvservevtheirvpurposevi
nvaidingvwithvthevinstructionvofvHeatvTransfer,vandvmakingvthevHeatvTransfervexperiencevofvbot
hvthevinstructorsvandvstudentsvavpleasantvandvfruitfulvone.
Wevacknowledge,vwithvappreciation,vthevcontributionsvofvnumerousvusersvofvthevfirstve
ditionvofvthevbookvwhovtookvthevtimevtovreportvtheverrorsvthatvtheyvdiscovered.vAllvofvtheirvsugg
estionsvhavevbeenvincorporated.vSpecialvthanksvarevduevtovDr.vMehmetvKanogluvwhovcheckedvt
hevaccuracyvofvmostvsolutionsvinvthisvManual.

YunusvA.vÇengel

Julyv2002

, Chapterv1vBasicsvofvHeatvTransfer


Chapter 1 v



BASICS OF HEAT TRANSFER
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ThermodynamicsvandvHeatvTransfer

1-1 CvThermodynamicsvdealsvwithvthevamountvofvheatvtransfervasvavsystemvundergoesvavprocessvfromvoneveq
uilibriumvstatevtovanother.vHeatvtransfer,vonvthevothervhand,vdealsvwithvthevratevofvheatvtransfervasvwellvasvthev
temperaturevdistributionvwithinvthevsystemvatvavspecifiedvtime.

1-2 Cv(a)vThevdrivingvforcevforvheatvtransfervisvthevtemperaturevdifference.v(b)vThevdrivingvforcevforvelectricv
currentvflowvisvthevelectricvpotentialvdifferencev(voltage).v(a)vThevdrivingvforcevforvfluidvflowvisvthevpressurev
difference.

1-3 CvThevcaloricvtheoryvisvbasedvonvthevassumptionvthatvheatvisvavfluid-
likevsubstancevcalledvthev"caloric"vwhichvisvavmassless,vcolorless,vodorlessvsubstance.vvvItvwasvabandonedvinvt
hevmiddlevofvthevnineteenthvcenturyvaftervitvwasvshownvthatvtherevisvnovsuchvthingvasvthevcaloric.

1-4 CvThevratingvproblemsvdealvwithvthevdeterminationvofvthevheatvtransfervratevforvanvexistingvsystemvatvavs
pecifiedvtemperaturevdifference.vThevsizingvproblemsvdealvwithvthevdeterminationvofvthevsizevofvavsystemvinvo
rdervtovtransfervheatvatvavspecifiedvratevforvavspecifiedvtemperaturevdifference.

1-5 CvThevexperimentalvapproachv(testingvandvtakingvmeasurements)vhasvthevadvantagevofvdealingvwithvtheva
ctualvphysicalvsystem,vandvgettingvavphysicalvvaluevwithinvthevlimitsvofvexperimentalverror.vHowever,vthisvap
proachvisvexpensive,vtimevconsuming,vandvoftenvimpractical.vThevanalyticalvapproachv(analysisvorvcalculatio
ns)vhasvthevadvantagevthatvitvisvfastvandvinexpensive,vbutvthevresultsvobtainedvarevsubjectvtovthevaccuracyvofvth
evassumptionsvandvidealizationsvmadevinvthevanalysis.

1-6 CvModelingvmakesvitvpossiblevtovpredictvthevcoursevofvanveventvbeforevitvactuallyvoccurs,vorvtovstudyvvari
ousvaspectsvofvanveventvmathematicallyvwithoutvactuallyvrunningvexpensivevandvtime-
consumingvexperiments.vWhenvpreparingvavmathematicalvmodel,vallvthevvariablesvthatvaffectvthevphenomena
varevidentified, vreasonable vassumptions vand vapproximations varevmade, vand vthevinterdependence vofv thesevvari

ablesvarevstudied.vThevrelevantvphysicalvlawsvandvprinciplesvarevinvoked,vandvthevproblemvisvformulatedvmat
hematically.vFinally,vthevproblemvisvsolvedvusingvanvappropriatevapproach,vandvthevresultsvarevinterpreted.
1-7 CvThevrightvchoicevbetweenvavcrudevandvcomplexvmodelvisvusuallyvthevsimplestvmodelvwhichvyieldsvadeq
uatevresults.vPreparingvveryvaccuratevbutvcomplexvmodelsvisvnotvnecessarilyvavbettervchoicevsincevsuchvmode
lsvarevnotvmuchvusevtovanvanalystvifvtheyvarevveryvdifficultvandvtimevconsumingvtovsolve.vAtvthevminimum,vth
evmodelvshouldvreflectvthevessentialvfeaturesvofvthevphysicalvproblemvitvrepresents.




1-1

, Chapterv1vBasicsvofvHeatvTransfer

HeatvandvOthervFormsvofvEnergy


1-8 CvvvThev ratev ofv heatv transferv perv unitv surfacev areav isv calledv heatv fluxvvq&v.v Itv isv relatedv tov thev ratev ofv heatv
transfervbyvvQ&v v  q&dAv.
Av


1-9 Cv Energyvcanvbevtransferredvbyvheat,vwork,vandvmass.vAnvenergyvtransfervisvheatvtransfervwhenvitsvdrivin
gvforcevisvtemperaturevdifference.

1-10 CvThermalvenergyvisvthevsensiblevandvlatentvformsvofvinternalvenergy,vandvitvisvreferredvtovasvheatvinvdail
yvlife.

1-11 CvForvthevconstantvpressurevcase.vThisvisvbecausevthevheatvtransfervtovanvidealvgasvisvmCpTvatvconstantv
pressurevandvmCpTvatvconstantvvolume,vandvCpvisvalwaysvgreatervthanvCv.

1-12 Av cylindricalv resistorv onv av circuitv boardv dissipatesv 0.6v Wv ofv power.v Thev amountv ofv heatv dissipatedv inv
24vh,vthevheatvflux,vandvthevfractionvofvheatvdissipatedvfromvthevtopvandvbottomvsurfacesvarevtov bevdetermine
d.
AssumptionsvHeatvisvtransferredvuniformlyvfromvallvsurfaces.
Analysisv(a)vThevamountvofvheatvthisvresistorvdissipatesvduringvav24-hourvperiodvis
QvvQ& tv v(0.6vvW)(24vvh)vv14.4vvWhv=v51.84v kJ (sincev1vWhv=v3600vWsv=v3.6vkJ)
Q&
(b) Thevheatvfluxvonvthevsurfacevofvthevresistorvis
Resistor
Dv2 v(0.4vcm)v2
Asv v2 vDLv v2 vv(0.4vcm)(1.5vcm)v v 0.251v1.885v v 2.136v cmv2 0.6vW
4 4
Q&vv
q&vvvvv  0.60vW v 0.2809v W/cmv2





s As 2.136vcmv2
(c) Assumingvthevheatvtransfervcoefficientvtovbevuniform,vheatvtransfervisvproportionalvtovthev
surfacevarea.vThenvthevfractionvofvheatvdissipatedvfromvthevtopvandvbottomvsurfacesvofvthevr
esistorvbecomes
Qtopbasev v Atopbasev 0.251v
 v v0.11 orv (11.8%)
8
Qtotal Atotal 2.136
DiscussionvHeatvtransfervfromvthevtopvandvbottomvsurfacesvisvsmallvrelativevtovthatvtransferredvfromvthevsidev
surface.




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