Solutions Manual For Fundamentals of Heat and Mass Transfer 8th Edition By Bergman, Lavine, Incropera, DeWitt (All Chapters, 100 Original Verified, A+ Grade)

2-1


Solutions Manual l



for
Heat and Mass Transfer: Fundamentals & Applications
l l l l l l



5th Edition
l



Yunus A. Cengel & Afshin J. Ghajar Mc
l l l l l l l



Graw-Hill, 2015 l




Chapter 2 l




HEAT CONDUCTION EQUATION
l l




PROPRIETARY AND CONFIDENTIAL l l




ThislManuallislthelproprietarylpropertyloflThelMcGraw-HilllCompanies,lInc.l(“McGraw-
Hill”)landlprotectedlbylcopyrightlandlotherlstatelandlfederalllaws.l BylopeninglandlusinglthislManualltheluserl
agreesltolthelfollowinglrestrictions,landliflthelrecipientldoeslnotlagreeltoltheselrestrictions,lthelManuallshouldl
belpromptlylreturnedlunopenedltolMcGraw-
Hill:l ThislManuallislbeinglprovidedlonlyltolauthorizedlprofessorslandlinstructorslforluselinlpreparinglf
orlthelclasseslusinglthelaffiliatedltextbook.l NolotherluselorldistributionloflthislManuallislpermitted.l Th
islManuallmaylnotlbelsoldlandlmaylnotlbeldistributedltolorlusedlbylanylstudentlorlotherlthirdlparty.l Nol
partloflthislManuallmaylbelreproduced,ldisplayedlorldistributedlinlanylformlorlbylanylmeans,lelectroni
clorlotherwise,lwithoutlthelpriorlwrittenlpermissionloflMcGraw-Hill.




PROPRIETARYlMATERIAL.l©l2015lThelMcGraw-
HilllCompanies,lInc.l Limitedldistributionlpermittedlonlyltolteacherslandleducatorslforlcoursel preparation.l IflyoularelalstudentlusinglthislManual,lyoularel
usinglitlwithoutlpermission.
Fulllfilelatlhttp://textbooktestbank.eu/Heat-and-Mass-Transfer-Fundamentals-and-Applications-5th-Edition-Solutions-Cengel

, 2-2
Introduction


2-1 Cl Theltermlsteadylimplieslnolchangelwithltimelatlanylpointlwithinlthelmediumlwhileltransientlimplieslvariationlwithltimel
orltimeldependence.lTherefore,ltheltemperaturelorlheatlfluxlremainslunchangedlwithltimelduringlsteadylheatltransferlthroughla
lmediumlatlanyllocationlalthoughlbothlquantitiesl maylvarylfromlonellocationltolanother.l Duringltransientlheatltransfer,lthelte

mperaturelandlheatlfluxlmaylvarylwithltimelaslwelllasllocation.lHeatltransferlislone-
dimensionalliflitloccurslprimarilylinloneldirection.lItlisltwo-dimensionalliflheatltranferlinlthelthirdldimensionlislnegligible.




2-2 Cl Heatltransferlislalvectorlquantitylsincelitlhasldirectionlaslwelllaslmagnitude.lTherefore,lwelmustlspecifylbothldirectionlandlm
agnitudelinlorderltoldescribelheatltransferlcompletelylatlalpoint.lTemperature,lonlthelotherlhand,lislalscalarlquantity.




2-3 ClYes,lthelheatlfluxlvectorlatlalpointlPlonlanlisothermallsurfaceloflalmediumlhasltolbelperpendicularltolthelsurfacelatlthatlpoint.




2-4 ClIsotropiclmaterialslhavelthelsamelpropertieslinlallldirections,landlweldolnotlneedltolbelconcernedlaboutlthelvariationloflprope
rtieslwithldirectionlforlsuchlmaterials.lThelpropertiesloflanisotropiclmaterialslsuchlaslthelfibrouslorlcompositelmaterials,lhoweve
r,lmaylchangelwithldirection.




2-5 ClInlheatlconductionlanalysis,lthelconversionloflelectrical,lchemical,lorlnuclearlenergylintolheatl(orlthermal)lenergylinlsolid
slislcalledlheatlgeneration.




2-6 ClThelphrasel“thermallenergylgeneration”lislequivalentltol“heatlgeneration,”landltheylarelusedlinterchangeably.lTheylimpl
ylthelconversionloflsomelotherlformloflenergylintolthermallenergy.lThelphrasel“energylgeneration,”lhowever,lislvaguelsincelthelf
ormloflenergylgeneratedlislnotlclear.




2-7 ClThelheatltransferlprocesslfromlthelkitchenlairltolthelrefrigeratedlspacelisltransi
entlinlnaturelsincelthelthermallconditionslinlthelkitchenlandlthelrefrigerator,linlgenera
l,lchangelwithltime.lHowever,lwelwouldlanalyzelthislproblemlaslalsteadylheatltransf
erlproblemlunderlthelworstlanticipatedlconditionslsuchlaslthellowestlthermostatlsetti
nglforlthelrefrigeratedlspace,landlthelanticipatedlhighestltemperaturelinlthelkitchenl(
thelso-
calledldesignlconditions).lIflthelcompressorlisllargelenoughltolkeeplthelrefrigeratedl
spacelatltheldesiredltemperaturelsettinglunderlthelpresumedlworstlconditions,lthenlit
lisllargelenoughltoldolsolunderlalllconditionslbylcyclinglonlandloff.lHeatltransferlinto

lthelrefrigeratedlspacelis

three-
dimensionallinlnaturelsincelheatlwilllbelenteringlthroughlalllsixlsidesloflthelrefrigerator
.lHowever,lheatltransferlthroughlanylwalllorlfloorltakeslplacelinltheldirectionlnormallt
olthelsurface,landlthuslitlcanlbelanalyzedlaslbeinglone-
ldimensional.lTherefore,lthislproblemlcanlbelsimplifiedlgreatlylbylconsideringlthelheatl

transferltolbelonedimensionallatleachloflthelfourlsideslaslwelllasltheltoplandlbottomlsec
tions,landlthenlbyladdinglthelcalculatedlvaluesloflheatltransferlatleach
l surface.

PROPRIETARYlMATERIAL.l©l2015lThelMcGraw-
HilllCompanies,lInc.l Limitedldistributionlpermittedlonlyltolteacherslandleducatorslforlcoursel preparation.l IflyoularelalstudentlusinglthislManual,lyoularel
usinglitlwithoutlpermission.
Fulllfilelatlhttp://textbooktestbank.eu/Heat-and-Mass-Transfer-Fundamentals-and-Applications-5th-Edition-Solutions-Cengel

, 2-3
2-8 ClHeatltransferlthroughlthelwalls,ldoor,landltheltoplandlbottomlsectionsloflanlovenlisltransientlinlnaturelsincelthelthermallcondit
ionslinlthelkitchenlandltheloven,linlgeneral,lchangelwithltime.lHowever,lwelwouldlanalyzelthislproblemlaslalsteadylheatltransferlp
roblemlunderlthelworstlanticipatedlconditionslsuchlaslthelhighestltemperaturelsettinglforltheloven,landlthelanticipatedllowestltem
peraturelinlthelkitchenl(thelsolcalledl“design”lconditions).lIflthelheatinglelementloflthelovenlisllargelenoughltolkeeplthelovenlatlthe
ldesiredltemperaturelsettinglunderlthelpresumedlworstlconditions,lthenlitlisllargelenoughltoldolsolunderlalllconditionslbylcyclinglo

nlandloff.
Heatltransferlfromlthelovenlislthree-
dimensionallinlnaturelsincelheatlwilllbelenteringlthroughlalllsixlsideslofltheloven.lHowever,lheatltransferlthroughlanylwalllorlfloorl
takeslplacelinltheldirectionlnormalltolthelsurface,landlthuslitlcanlbelanalyzedlaslbeinglone-
dimensional.lTherefore,lthislproblemlcanlbelsimplifiedlgreatlylbylconsideringlthelheatltransferlaslbeinglone-
ldimensionallatleachloflthel fourlsideslasl welllasltheltoplandlbottomlsections,landlthenlbyladdinglthelcalculatedlvaluesloflheatltransfe

rslatleachlsurface.




2-9 ClHeatltransferltolalpotatolinlanlovenlcanlbelmodeledlaslone-
dimensionallsinceltemperatureldifferencesl(andlthuslheatltransfer)lwilllexistlinlthelradialldirectionlonlylbecauseloflsymmetrylab
outlthelcenterlpoint.lThislwouldlbelaltransientlheatltransferlprocesslsinceltheltemperaturelatlanylpointlwithinlthelpotatolwilllchan
gelwithltimelduringlcooking.lAlso,lwelwouldluselthelsphericallcoordinatelsystemltolsolvelthislproblemlsincelthelentirelouterlsurf
aceloflalsphericallbodylcanlbeldescribedlbylalconstantlvalueloflthelradiuslinlsphericallcoordinates.lWelwouldlplaceltheloriginlatlt
helcenterloflthelpotato.




2-10 ClAssumingltheleggltolbelround,lheatltransferltolanlegglinlboilinglwaterlcanlbelmodeledlaslone-
dimensionallsinceltemperatureldifferencesl(andlthuslheatltransfer)lwilllprimarilylexistlinlthelradialldirectionlonlylbecauseloflsymm
etrylaboutlthelcenterlpoint.l Thislwouldlbelaltransientlheatltransferlprocesslsinceltheltemperaturelatlanylpointlwithinlthelegglwilllch
angelwithltimelduringlcooking.lAlso,lwelwouldluselthelsphericallcoordinatelsystemltolsolvelthislproblemlsincelthelentirelouterlsur
faceloflalsphericallbodylcanlbeldescribedlbylalconstantlvalueloflthelradiuslinlsphericallcoordinates.lWelwouldlplaceltheloriginlatlth
elcenterloflthelegg.




2-11 ClHeatltransferltolalhotldoglcanlbelmodeledlasltwo-
dimensionallsinceltemperatureldifferencesl(andlthuslheatltransfer)lwilllexistlinlthelradiallandlaxialldirectionsl(butltherelwilllbelsy
mmetrylaboutlthelcenterllinelandlnolheatltransferlinlthelazimuthalldirection.lThislwouldlbelaltransientlheatltransferlprocesslsincelt
heltemperaturelatlanylpointlwithinlthelhotldoglwilllchangelwithltimelduringlcooking.lAlso,lwelwouldluselthelcylindricallcoordinatel
systemltolsolvelthislproblemlsincelalcylinderlislbestldescribedlinlcylindricallcoordinates.lAlso,lwelwouldlplaceltheloriginlsomewh
erelonlthelcenterlline,lpossiblylatlthelcenterloflthelhotldog.lHeatltransferlinlalveryllonglhotldoglcouldlbelconsideredltolbelone-
dimensionallinlpreliminarylcalculations.




2-12 ClHeatltransferltolalroastlbeeflinlanlovenlwouldlbeltransientlsinceltheltemperaturelatlanylpointlwithinlthelroastlwilllchangelw
ithltimelduringlcooking.lAlso,lbylapproximatinglthelroastlaslalsphericallobject,lthislheatltransferlprocesslcanlbelmodeledlaslone-
dimensionallsinceltemperatureldifferencesl(andlthuslheatltransfer)lwilllprimarilylexistlinlthelradialldirectionlbecauseloflsymmetr
ylaboutlthelcenterlpoint.




2-13 ClHeatllosslfromlalhotlwaterltanklinlalhouseltolthelsurroundinglmediumlcanlbelconsideredltolbelalsteadylheatltransferlproble
m.lAlso,litlcanlbelconsideredltolbeltwo-
dimensionallsinceltemperatureldifferencesl(andlthuslheatltransfer)lwilllexistlinlthelradiallandlaxialldirectionsl(butltherelwilllbelsy
mmetrylaboutlthelcenterllinelandlnolheatltransferlinlthelazimuthalldirection.)



PROPRIETARYlMATERIAL.l©l2015lThelMcGraw-
HilllCompanies,lInc.l Limitedldistributionlpermittedlonlyltolteacherslandleducatorslforlcoursel preparation.l IflyoularelalstudentlusinglthislManual,lyoularel
usinglitlwithoutlpermission.
Fulllfilelatlhttp://textbooktestbank.eu/Heat-and-Mass-Transfer-Fundamentals-and-Applications-5th-Edition-Solutions-Cengel

, 2-4
2-14 ClHeatltransferltolalcannedldrinklcanlbelmodeledlasltwo-
dimensionallsinceltemperatureldifferencesl(andlthuslheatltransfer)lwilllexistlinlthelradiallandlaxialldirectionsl(butltherelwilllbelsym
metrylaboutlthelcenterllinelandlnolheatltransferlinlthelazimuthalldirection.lThislwouldlbelaltransientlheatltransferlprocesslsincelthelt
emperaturelatlanylpointlwithinltheldrinklwilllchangelwithltimelduringlheating.lAlso,lwelwouldluselthelcylindricallcoordinatelsyste
mltolsolvelthislproblemlsincelalcylinderlislbestldescribedlinlcylindricallcoordinates.lAlso,lwelwouldlplaceltheloriginlsomewherelon
lthelcenterlline,lpossiblylatlthelcenterloflthelbottomlsurface.




2-15 Alcertainlthermopilelusedlforlheatlfluxlmeterslislconsidered.lThelminimumlheatlfluxlthislmeterlcanldetectlisltolbeldeter
mined.
Assumptionsl1lSteadyloperatinglconditionslexist.
PropertieslThelthermallconductivityloflkaptonlislgivenltolbel0.345lW/mK.
AnalysislThelminimumlheatlfluxlcanlbeldeterminedlfrom
tl 0.1C
q˙l=lkl =l(0.345lW/mC) =l17.3lW/m2
L 0.002lm




2-16 Thelrateloflheatlgenerationlperlunitlvolumelinlalstainlesslsteellplatelislgiven.lThelheatlfluxlonlthelsurfaceloflthelplatelisltolbeld
etermined.
Assumptionsl Heatlislgeneratedluniformlylinlsteellplate.
AnalysislWelconsiderlalunitlsurfacelarealofl1lm2.lTheltotallrateloflheatlgenerationli el
nlthislsectionloflthelplatelis
L
Ė g en =le˙genV plate =le˙gen (AlL)l=l(5106l W/m3l)(1m2l)(0.03lm)l=l1.5105l W

Notinglthatlthislheatlwilllbeldissipatedlfromlbothlsidesloflthelplate,lthelheatlfluxlonleithe
rlsurfaceloflthelplatelbecomes
Ė g en 1.5105l W
q˙l= =l =l75,000lW/m2 =l75lkW/m2l
Aplate 21lml2




PROPRIETARYlMATERIAL.l©l2015lThelMcGraw-
HilllCompanies,lInc.l Limitedldistributionlpermittedlonlyltolteacherslandleducatorslforlcoursel preparation.l IflyoularelalstudentlusinglthislManual,lyoularel
usinglitlwithoutlpermission.
Fulllfilelatlhttp://textbooktestbank.eu/Heat-and-Mass-Transfer-Fundamentals-and-Applications-5th-Edition-Solutions-Cengel