Heat Chap03164Word文档格式.docx
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Heat Chap03164Word文档格式.docx
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Thensurfacetemperaturesonthetwosidesofthecircuitboardbecomes
(b)Notingthatthecross-sectionalareasofthefinsareconstant,theefficiencyoftheserectangularfinsisdeterminedtobe
Thefinnedandunfinnedsurfaceareasare
Then,
Substituting,thebasetemperatureofthefinnedsurfacesisdeterminedtobe
Thenthetemperaturesonbothsidesoftheboardaredeterminedusingthethermalresistancenetworktobe
3-165Acircuitboardhouseselectroniccomponentsononeside,dissipatingatotalof15Wthroughthebacksideoftheboardtothesurroundingmedium.Thetemperaturesonthetwosidesofthecircuitboardaretobedeterminedforthecasesofnofinsand20copperfinsofrectangularprofileonthebackside.
Cforthecircuitboard,k=386W/m°
Cforthecopperplateandfins,andk=1.8W/m°
(b)Notingthatthecross-sectionalareasofthefinsareconstant,theefficiencyoftheserectangularfinsisdeterminedtobe
Substituting,thebasetemperatureofthefinnedsurfacesdeterminetobe
3-166Steampassesthrougharowof10parallelpipesplacedhorizontallyinaconcretefloorexposedtoroomairat25
withaheattransfercoefficientof12W/m2.C.Ifthesurfacetemperatureoftheconcretefloorisnottoexceed40
theminimumburialdepthofthesteampipesbelowthefloorsurfaceistobedetermined.
Assumptions1Steadyoperatingconditionsexist.2Heattransferistwo-dimensional(nochangeintheaxialdirection).3Thermalconductivityoftheconcreteisconstant.
PropertiesThethermalconductivityofconcreteisgiventobek=0.75W/m°
C.
AnalysisInsteadyoperation,therateofheatlossfromthesteamthroughtheconcretefloorbyconductionmustbeequaltotherateofheattransferfromtheconcretefloortotheroombycombinedconvectionandradiation,whichisdeterminedtobe
ThenthedepththesteampipesshouldbeburiedcanbedeterminedwiththeaidofshapefactorforthisconfigurationfromTable3-5tobe
3-167Twopersonsarewearingdifferentclothesmadeofdifferentmaterialswithdifferentsurfaceareas.Thefractionsofheatlostfromeachperson’sbodybyrespirationaretobedetermined.
Assumptions1Heattransferissteady.2Heattransferisone-dimensional.3Thermalconductivitiesareconstant.4Heattransferbyradiationisaccountedforintheheattransfercoefficient.5Thehumanbodyisassumedtobecylindricalinshapeforheattransferpurposes.
PropertiesThethermalconductivitiesoftheleatherandsyntheticfabricaregiventobek=0.159W/m°
Candk=0.13W/m°
C,respectively.
AnalysisThesurfaceareaofeachbodyisfirstdeterminedfrom
Thesensibleheatlostfromthefirstperson’sbodyis
Thetotalsensibleheattransferisthesumofheattransferredthroughtheclothesandtheskin
Thenthefractionofheatlostbyrespirationbecomes
Repeatingsimilarcalculationsforthesecondperson’sbody
T1
3-168Awallconstructedofthreelayersisconsidered.Therateofhattransferthroughthewallandtemperaturedropsacrosstheplaster,brick,covering,andsurface-ambientairaretobedetermined.
Assumptions1Heattransferissteady.2Heattransferisone-dimensional.3Thermalconductivitiesareconstant.4Heattransferbyradiationisaccountedforintheheattransfercoefficient.
PropertiesThethermalconductivitiesoftheplaster,brick,andcoveringaregiventobek=0.72W/m°
C,k=0.36W/m°
C,k=1.40W/m°
AnalysisThesurfaceareaofthewallandtheindividualresistancesare
Thesteadyrateofheattransferthroughthewallthenbecomes
Thetemperaturedropsare
3-169Aninsulationistobeaddedtoawalltodecreasetheheatlossby85%.Thethicknessofinsulationandtheoutersurfacetemperatureofthewallaretobedeterminedfortwodifferentinsulatingmaterials.
PropertiesThethermalconductivitiesoftheplaster,brick,covering,polyurethanefoam,andglassfiberaregiventobe0.72W/m°
C,0.36W/m°
C,1.40W/m°
C,0.025W/m°
C,0.036W/m°
Therateofheatlosswithouttheinsulationis
(a)Therateofheattransferafterinsulationis
Thetotalthermalresistancewiththefoaminsulationis
Thethicknessofinsulationisdeterminedfrom
Theoutersurfacetemperatureofthewallisdeterminedfrom
(b)Thetotalthermalresistancewiththefiberglassinsulationis
DiscussionTheoutersurfacetemperatureissameforbothcasessincetherateofheattransferdoesnotchange.
3-170Coldconditionedairisflowinginsideaductofsquarecross-section.Themaximumlengthoftheductforaspecifiedtemperatureincreaseintheductistobedetermined.
Assumptions1Heattransferissteady.2Heattransferisone-dimensional.3Thermalconductivitiesareconstant.4Steadyone-dimensionalheatconductionrelationscanbeusedduetosmallthicknessoftheductwall.5Whencalculatingtheconductionthermalresistanceofaluminum,theaverageofinnerandoutersurfaceareaswillbeused.
PropertiesThethermalconductivityofaluminumisgiventobe237W/m°
C.ThespecificheatofairatthegiventemperatureisCp=1006J/kg°
C(TableA-15).
AnalysisTheinnerandtheoutersurfaceareasoftheductperunitlengthandtheindividualthermalresistancesare
Therateofheatlossfromtheairinsidetheductis
Foratemperatureriseof1°
C,theairinsidetheductshouldgainheatatarateof
Thenthemaximumlengthoftheductbecomes
3-171Heattransferthroughawindowisconsidered.Thepercenterrorinvolvedinthecalculationofheatgainthroughthewindowassumingthewindowconsistofglassonlyistobedetermined.
Assumptions1Heattransferissteady.2Heattransferisone-dimensional.3Thermalconductivitiesareconstant.4Radiationisaccountedforinheattransfercoefficients.
PropertiesThethermalconductivitiesaregiventobe0.7W/m°
Cforglassand0.12W/m°
Cforpinewood.
AnalysisThesurfaceareasoftheglassandthewoodandtheindividualthermalresistancesare
Therateofheatgainthroughtheglassandthewoodandtheirtotalare
Ifthewindowconsistsofglassonlytheheatgainthroughthewindowis
Thenthepercentageerrorinvolvedinheatgainthroughthewindowassumingthewindowconsistofglassonlybecomes
3-172Steamisflowinginsideasteelpipe.Thethicknessoftheinsulationneededtoreducetheheatlossby95percentandthethicknessoftheinsulationneededtoreduceoutersurfacetemperatureto40Caretobedetermined.
Assumptions1Heattransferissteadysincethereisnoindicationofanychangewithtime.2Heattransferisone-dimensionalsincethereisthermalsymmetryaboutthecenterlineandnovariationintheaxialdirection.3Thermalconductivitiesareconstant.4Thethermalcontactresistanceattheinterfaceisnegligible.
PropertiesThethermalconductivitiesaregiventobek=61W/m°
Cforsteelandk=0.038W/m°
Cforinsulation.
Analysis(a)Consideringaunitlengthofthepipe,theinnerandtheoutersurfaceareasofthepipeandtheinsulationare
Theindividualthermalresistancesare
Thenthes
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