Heat Chap03001.docx
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Heat Chap03001.docx
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HeatChap03001
Chapter3
STEADYHEATCONDUCTION
SteadyHeatConductionInPlaneWalls
3-1C(a)Ifthelateralsurfacesoftherodareinsulated,theheattransfersurfaceareaofthecylindricalrodisthebottomorthetopsurfaceareaoftherod,
.(b)Ifthetopandthebottomsurfacesoftherodareinsulated,theheattransferareaoftherodisthelateralsurfaceareaoftherod,
.
3-2CInsteadyheatconduction,therateofheattransferintothewallisequaltotherateofheattransferoutofit.Also,thetemperatureatanypointinthewallremainsconstant.Therefore,theenergycontentofthewalldoesnotchangeduringsteadyheatconduction.However,thetemperaturealongthewallandthustheenergycontentofthewallwillchangeduringtransientconduction.
3-3CThetemperaturedistributioninaplanewallwillbeastraightlineduringsteadyandonedimensionalheattransferwithconstantwallthermalconductivity.
3-4CThethermalresistanceofamediumrepresentstheresistanceofthatmediumagainstheattransfer.
3-5CThecombinedheattransfercoefficientrepresentsthecombinedeffectsofradiationandconvectionheattransfersonasurface,andisdefinedashcombined=hconvection+hradiation.Itofferstheconvenienceofincorporatingtheeffectsofradiationintheconvectionheattransfercoefficient,andtoignoreradiationinheattransfercalculations.
3-6CYes.Theconvectionresistancecanbedefinedastheinverseoftheconvectionheattransfercoefficientperunitsurfaceareasinceitisdefinedas
.
3-7CTheconvectionandtheradiationresistancesatasurfaceareparallelsinceboththeconvectionandradiationheattransfersoccursimultaneously.
3-8CForasurfaceofAatwhichtheconvectionandradiationheattransfercoefficientsare
thesingleequivalentheattransfercoefficientis
whenthemediumandthesurroundingsurfacesareatthesametemperature.Thentheequivalentthermalresistancewillbe
.
3-9CThethermalresistancenetworkassociatedwithafive-layercompositewallinvolvesfivesingle-layerresistancesconnectedinseries.
3-10COncetherateofheattransfer
isknown,thetemperaturedropacrossanylayercanbedeterminedbymultiplyingheattransferratebythethermalresistanceacrossthatlayer,
3-11CThetemperatureofeachsurfaceinthiscasecanbedeterminedfrom
where
isthethermalresistancebetweentheenvironment
andsurfacei.
3-12CYes,itis.
3-13CThewindowglasswhichconsistsoftwo4mmthickglasssheetspressedtightlyagainsteachotherwillprobablyhavethermalcontactresistancewhichservesasanadditionalthermalresistancetoheattransferthroughwindow,andthustheheattransferratewillbesmallerrelativetotheonewhichconsistsofasingle8mmthickglasssheet.
3-14CConvectionheattransferthroughthewallisexpressedas
.Insteadyheattransfer,heattransferratetothewallandfromthewallareequal.Thereforeattheoutersurfacewhichhasconvectionheattransfercoefficientthreetimesthatoftheinnersurfacewillexperiencethreetimessmallertemperaturedropcomparedtotheinnersurface.Therefore,attheoutersurface,thetemperaturewillbeclosertothesurroundingairtemperature.
3-15CThenewdesignintroducesthethermalresistanceofthecopperlayerinadditiontothethermalresistanceofthealuminumwhichhasthesamevalueforbothdesigns.Therefore,thenewdesignwillbeapoorerconductorofheat.
3-16CTheblanketwillintroduceadditionalresistancetoheattransferandslowdowntheheatgainofthedrinkwrappedinablanket.Therefore,thedrinkleftonatablewillwarmupfaster.
3-17Thetwosurfacesofawallaremaintainedatspecifiedtemperatures.Therateofheatlossthroughthewallistobedetermined.
Assumptions1Heattransferthroughthewallissteadysincethesurfacetemperaturesremainconstantatthespecifiedvalues.2Heattransferisone-dimensionalsinceanysignificanttemperaturegradientswillexistinthedirectionfromtheindoorstotheoutdoors.3Thermalconductivityisconstant.
PropertiesThethermalconductivityisgiventobek=0.8W/m°C.
AnalysisThesurfaceareaofthewallandtherateofheatlossthroughthewallare
3-18Thetwosurfacesofawindowaremaintainedatspecifiedtemperatures.Therateofheatlossthroughthewindowandtheinnersurfacetemperaturearetobedetermined.
Assumptions1Heattransferthroughthewindowissteadysincethesurfacetemperaturesremainconstantatthespecifiedvalues.2Heattransferisone-dimensionalsinceanysignificanttemperaturegradientswillexistinthedirectionfromtheindoorstotheoutdoors.3Thermalconductivityisconstant.4Heattransferbyradiationisnegligible.
PropertiesThethermalconductivityoftheglassisgiventobek=0.78W/m°C.
AnalysisTheareaofthewindowandtheindividualresistancesare
Thesteadyrateofheattransferthroughwindowglassisthen
Theinnersurfacetemperatureofthewindowglasscanbedeterminedfrom
3-19Adouble-panewindowconsistsoftwo3-mmthicklayersofglassseparatedbya12-mmwidestagnantairspace.Forspecifiedindoorsandoutdoorstemperatures,therateofheatlossthroughthewindowandtheinnersurfacetemperatureofthewindowaretobedetermined.
Assumptions1Heattransferthroughthewindowissteadysincetheindoorandoutdoortemperaturesremainconstantatthespecifiedvalues.2Heattransferisone-dimensionalsinceanysignificanttemperaturegradientswillexistinthedirectionfromtheindoorstotheoutdoors.3Thermalconductivitiesoftheglassandairareconstant.4Heattransferbyradiationisnegligible.
PropertiesThethermalconductivityoftheglassandairaregiventobekglass=0.78W/m°Candkair=0.026W/m°C.
AnalysisTheareaofthewindowandtheindividualresistancesare
Thesteadyrateofheattransferthroughwindowglassthenbecomes
Theinnersurfacetemperatureofthewindowglasscanbedeterminedfrom
3-20Adouble-panewindowconsistsoftwo3-mmthicklayersofglassseparatedbyanevacuatedspace.Forspecifiedindoorsandoutdoorstemperatures,therateofheatlossthroughthewindowandtheinnersurfacetemperatureofthewindowaretobedetermined.
Assumptions1Heattransferthroughthewindowissteadysincetheindoorandoutdoortemperaturesremainconstantatthespecifiedvalues.2Heattransferisone-dimensionalsinceanysignificanttemperaturegradientswillexistinthedirectionfromtheindoorstotheoutdoors.3Thermalconductivitiesoftheglassandairareconstant.4Heattransferbyradiationisnegligible.
PropertiesThethermalconductivityoftheglassisgiventobekglass=0.78W/m°C.
AnalysisHeatcannotbeconductedthroughanevacuatedspacesincethethermalconductivityofvacuumiszero(nomediumtoconductheat)andthusitsthermalresistanceiszero.Therefore,ifradiationisdisregarded,theheattransferthroughthewindowwillbezero.Thentheanswerofthisproblemiszerosincetheproblemstatestodisregardradiation.
DiscussionInreality,heatwillbetransferredbetweentheglassesbyradiation.Wedonotknowtheinnersurfacetemperaturesofwindows.Inordertodetermineradiationheatresistanceweassumethemtobe5°Cand15°C,respectively,andtaketheemissivitytobe1.Thenindividualresistancesare
Thesteadyrateofheattransferthroughwindowglassthenbecomes
Theinnersurfacetemperatureofthewindowglasscanbedeterminedfrom
Similarly,theinnersurfacetemperaturesoftheglassesarecalculatedtobe15.2and-1.2C(wehadassumedthemtobe15and5Cwhendeterminingtheradiationresistance).Wecanimprovetheresultobtainedbyreevaluatingtheradiationresistanceandrepeatingthecalculations.
3-21
"GIVEN"
A=1.2*2"[m^2]"
L_glass=3"[mm]"
k_glass=0.78"[W/m-C]"
"L_air=12[mm],parametertobevaried"
T_infinity_1=24"[C]"
T_infinity_2=-5"[C]"
h_1=10"[W/m^2-C]"
h_2=25"[W/m^2-C]"
"PROPERTIES"
k_air=conductivity(Air,T=25)
"ANALYSIS"
R_conv_1=1/(h_1*A)
R_glass=(L_glass*Convert(mm,m))/(k_glass*A)
R_air=(L_air*Convert(mm,m))/(k_air*A)
R_conv_2=1/(h_2*A)
R_total=R_conv_1+2*R_glass+R_air+R_conv_2
Q_dot=(T_infinity_1-T_infinity_2)/R_total
Lair[mm]
Q[W]
2
307.8
4
228.6
6
181.8
8
150.9
10
129
12
112.6
14
99.93
16
89.82
18
81.57
20
74.7
3-22ETheinnerandoutersurfacesofthewallsofanelectricallyheatedhouseremainatspecifiedtemperaturesduringawinterday.Theamountofheatlostfromthehousethatdayanditsitscostaretobedetermined.
Assumptions1Heattransferthroughthewallsissteadysincethesurfacetemperaturesofthewallsremainconstantatthespecifiedvaluesduringthetimeperiodconsidered.2Heattransferisone-dimensionalsinceanysignificanttemperaturegradientswillexistinthedirectionfromtheindoorstotheoutdoors.3Thermalconductivityofthewallsisconstant.
PropertiesThethermalconductivityofthebrickwallisgiventobek=0.40Btu/hft°F.
AnalysisWeconsiderheatlossthroughthewallsonly.Thetotalheattransferareais
Therateofheatlossduringthedaytimeis
Therateofheatlossduringnighttimeis
Theamountofheatlossfromthehousethatnightwillbe
Thenthecostofthisheatlossforthatdaybecomes
3-23Acylindricalresistoronacircuitboarddissipates0.15Wofpowersteadilyinaspecifiedenvironment.Theamountofheatdissipatedin24h,thesurfaceheatflux,andthesurfacetemperatureoftheresistoraretobedetermined.
Assumptions1Steadyoperatingconditionsexist.2Heatistransferreduniformlyfromallsurfacesoftheresist
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