Heat Chap12088.docx
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Heat Chap12088.docx
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HeatChap12088
ReviewProblems
12-88Thetemperatureofairinaductismeasuredbyathermocouple.Theradiationeffectonthetemperaturemeasurementistobequantified,andtheactualairtemperatureistobedetermined.
AssumptionsThesurfacesareopaque,diffuse,andgray.
PropertiesTheemissivityofthermocoupleisgiventobe=0.6.
AnalysisTheactualtemperatureoftheaircanbedeterminedfrom
12-89Thetemperatureofhotgasesinaductismeasuredbyathermocouple.Theactualtemperatureofthegasistobedetermined,andcomparedwiththatwithoutaradiationshield.
AssumptionsThesurfacesareopaque,diffuse,andgray.
PropertiesTheemissivityofthethermocoupleisgiventobe=0.7.
AnalysisAssumingtheareaoftheshieldtobeveryclosetothesensorofthethermometer,theradiationheattransferfromthesensorisdeterminedfrom
Thentheactualtemperatureofthegascanbedeterminedfromaheattransferbalancetobe
Withouttheshieldthetemperatureofthegaswouldbe
12-90EAsealedelectronicboxisplacedinavacuumchamber.Thehighesttemperatureatwhichthesurroundingsurfacesmustbekeptifthisboxiscooledbyradiationaloneistobedetermined.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareopaque,diffuse,andgray.3Convectionheattransferisnotconsidered.4Heattransferfromthebottomsurfaceoftheboxisnegligible.
PropertiesTheemissivityoftheoutersurfaceoftheboxis=0.95.
AnalysisThetotalsurfaceareais
Thenthetemperatureofthesurroundingsurfacesisdeterminedtobe
12-91Adouble-walledsphericaltankisusedtostoreicedwater.Theairspacebetweenthetwowallsisevacuated.Therateofheattransfertotheicedwaterandtheamountoficethatmeltsa24-hperiodaretobedetermined.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareopaque,diffuse,andgray.
PropertiesTheemissivitiesofbothsurfacesaregiventobe1=2=0.15.
Analysis(a)Assumingtheconductionresistancesofthewallstobenegligible,therateofheattransfertotheicedwaterinthetankisdeterminedtobe
(b)Theamountofheattransferduringa24-hourperiodis
Theamountoficethatmeltsduringthisperiodthenbecomes
12-92Twoconcentricsphereswhicharemaintainedatuniformtemperaturesareseparatedbyairat1atmpressure.Therateofheattransferbetweenthetwospheresbynaturalconvectionandradiationistobedetermined.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareopaque,diffuse,andgray.3Airisanidealgaswithconstantproperties.
PropertiesTheemissivitiesofthesurfacesaregiventobe1=2=0.5.Thepropertiesofairat1atmandtheaveragetemperatureof(T1+T2)/2=(350+275)/2=312.5K=39.5Care(TableA-15)
Analysis(a)NotingthatDi=D1andDo=D2,thecharacteristiclengthis
Then
Theeffectivethermalconductivityis
Thentherateofheattransferbetweenthespheresbecomes
(b)Therateofheattransferbyradiationisdeterminedfrom
12-93Asolarcollectorisconsidered.Theabsorberplateandtheglasscoveraremaintainedatuniformtemperatures,andareseparatedbyair.Therateofheatlossfromtheabsorberplatebynaturalconvectionandradiationistobedetermined.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareopaque,diffuse,andgray.3Airisanidealgaswithconstantproperties.
PropertiesTheemissivitiesofsurfacesaregiventobe1=0.9forglassand2=0.8fortheabsorberplate.Thepropertiesofairat1atmandtheaveragetemperatureof(T1+T2)/2=(80+32)/2=56Care(TableA-15)
AnalysisFor
wehavehorizontalrectangularenclosure.ThecharacteristiclengthinthiscaseisthedistancebetweenthetwoglassesLc=L=0.03mThen,
Neglectingtheendeffects,therateofheattransferbyradiationisdeterminedfrom
DiscussionTheratesofheatlossbynaturalconvectionforthehorizontalandverticalcaseswouldbeasfollows(NotethattheRanumberremainsthesame):
Horizontal:
Vertical:
12-94EThecirculatingpumpofasolarcollectorthatconsistsofahorizontaltubeanditsglasscoverfails.Theequilibriumtemperatureofthetubeistobedetermined.
Assumptions1Steadyoperatingconditionsexist.2Thetubeanditscoverareisothermal.3Airisanidealgas.4Thesurfacesareopaque,diffuse,andgrayforinfraredradiation.5Theglasscoveristransparenttosolarradiation.
PropertiesThepropertiesofairshouldbeevaluatedattheaveragetemperature.Butwedonotknowtheexittemperatureoftheairintheduct,andthuswecannotdeterminethebulkfluidandglasscovertemperaturesatthispoint,andthuswecannotevaluatetheaveragetemperatures.Therefore,wewillassumetheglasstemperaturetobe85F,andusepropertiesatananticipatedaveragetemperatureof(75+85)/2=80°F(TableA-15E),
AnalysisWehaveahorizontalcylindricalenclosurefilledwithairat0.5atmpressure.Theprobleminvolvesheattransferfromthealuminumtubetotheglasscoverandfromtheoutersurfaceoftheglasscovertothesurroundingambientair.Whensteadyoperationisreached,thesetwoheattransferratesmustequaltherateofheatgain.Thatis,
(perfootoftube)
Theheattransfersurfaceareaoftheglasscoveris
(perfootoftube)
TodeterminetheRayleighnumber,weneedtoknowthesurfacetemperatureoftheglass,whichisnotavailable.Therefore,solutionwillrequireatrial-and-errorapproach.Assumingtheglasscovertemperaturetobe85°F,theRayleighnumber,theNusseltnumber,theconvectionheattransfercoefficient,andtherateofnaturalconvectionheattransferfromtheglasscovertotheambientairaredeterminedtobe
Also,
Thenthetotalrateofheatlossfromtheglasscoverbecomes
whichismorethan30Btu/h.Therefore,theassumedtemperatureof85°Ffortheglasscoverishigh.Repeatingthecalculationswithlowertemperatures(includingtheevaluationofproperties),theglasscovertemperaturecorrespondingto30Btu/hisdeterminedtobe81.5°F.
Thetemperatureofthealuminumtubeisdeterminedinasimilarmannerusingthenaturalconvectionandradiationrelationsfortwohorizontalconcentriccylinders.Thecharacteristiclengthinthiscaseisthedistancebetweenthetwocylinders,whichis
Also,
(perfootoftube)
Westartthecalculationsbyassumingthetubetemperaturetobe118.5°F,andthusanaveragetemperatureof(81.5+118.5)/2=100F=640R.Usingpropertiesat100F,
Theeffectivethermalconductivityis
Thentherateofheattransferbetweenthecylindersbyconvectionbecomes
Also,
Thenthetotalrateofheatlossfromtheglasscoverbecomes
whichismorethan30Btu/h.Therefore,theassumedtemperatureof118.5°Fforthetubeishigh.Bytryingothervalues,thetubetemperaturecorrespondingto30Btu/hisdeterminedtobe113.2°F.Therefore,thetubewillreachanequilibriumtemperatureof113.2°Fwhenthepumpfails.
12-95Adouble-panewindowconsistsoftwosheetsofglassseparatedbyanairspace.Theratesofheattransferthroughthewindowbynaturalconvectionandradiationaretobedetermined.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareopaque,diffuse,andgray.3Airisanidealgaswithconstantspecificheats.4Heattransferthroughthewindowisone-dimensionalandtheedgeeffectsarenegligible.
PropertiesTheemissivitiesofglasssurfacesaregiventobe1=2=0.9.Thepropertiesofairat0.3atmandtheaveragetemperatureof(T1+T2)/2=(15+5)/2=10Care(TableA-15)
AnalysisThecharacteristiclengthinthiscaseisthedistancebetweentheglasses,
Thentherateofheattransferbynaturalconvectionbecomes
Therateofheattransferbyradiationisdeterminedfrom
Thentherateoftotalheattransferbecomes
DiscussionNotethatheattransferthroughthewindowismostlybyradiation.
12-96Asimplesolarcollectorisbuiltbyplacingaclearplastictubearoundagardenhose.Therateofheatlossfromthewaterinthehosebynaturalconvectionandradiationistobedetermined.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareopaque,diffuse,andgray.3Airisanidealgaswithconstantspecificheats.
PropertiesTheemissivitiesofsurfacesaregiventobe1=2=0.9.Thepropertiesofairareat1atmandthefilmtemperatureof(Ts+T)/2=(40+25)/2=32.5Care(TableA-15)
AnalysisUndersteadyconditions,theheattransferratefromthewaterinthehoseequalstotherateofheatlossfromtheclearplastictubetothesurroundingsbynaturalconvectionandradiation.Thecharacteristiclengthinthiscaseisthediameteroftheplastictube,
.
Thentherateofheattransferfromtheoutersurfacebynaturalconvectionbecomes
Therateofheattransferbyradiationfromtheoutersurfaceisdeterminedfrom
Finally,
DiscussionNotethatheattransferismostlybyradiation.
12-97Asolarcollectorconsistsofahorizontalcoppertubeenclosedinaconcentricthinglasstube.Theannularspacebetweenthecopperandtheglasstubesisfilledwithairat1atm.Therateofheatlossfromthecollectorbynaturalconvectionandradiationistobedetermined.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareopaque,diffuse,andgray.3Airisanidealgaswithconstantspecificheats.
PropertiesTheemissivitiesofsurfacesaregiventobe1=0.85forthetubesurfaceand2=0.9forglasscover.Thepropertiesofairat1atmandtheaveragetemperatureof(T1+T2)/2=(60+40)/2=50Care(TableA-15)
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