Heat Chap12041.docx
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Heat Chap12041.docx
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HeatChap12041
12-41Acirculargrillisconsidered.Thebottomofthegrilliscoveredwithhotcoalbricks,whilethewiremeshontopofthegrilliscoveredwithsteaks.Theinitialrateofradiationheattransferfromcoalbrickstothesteaksistobedeterminedfortwocases.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareopaque,diffuse,andgray.3Convectionheattransferisnotconsidered.
PropertiesTheemissivitiesare=1forallsurfacessincetheyareblackorreradiating.
AnalysisWeconsiderthecoalbrickstobesurface1,thesteakstobesurface2andthesidesurfacestobesurface3.Firstwedeterminetheviewfactorbetweenthebricksandthesteaks(Table12-1),
(ItcanalsobedeterminedfromFig.12-7).
Thentheinitialrateofradiationheattransferfromthecoalbrickstothestakesbecomes
Whenthesideopeningisclosedwithaluminumfoil,theentireheatlostbythecoalbricksmustbegainedbythestakessincetherewillbenoheattransferthroughareradiatingsurface.Thegrillcanbeconsideredtobethree-surfaceenclosure.Thentherateofheatlossfromtheroomcanbedeterminedfrom
where
and
Substituting,
12-42EAroomisheatedbylectricresistanceheatersplacedontheceilingwhichismaintainedatauniformtemperature.Therateofheatlossfromtheroomthroughtheflooristobedetermined.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareopaque,diffuse,andgray.3Convectionheattransferisnotconsidered.4Thereisnoheatlossthroughthesidesurfaces.
PropertiesTheemissivitiesare=1fortheceilingand=0.8forthefloor.Theemissivityofinsulated(orreradiating)surfacesisalso1.
AnalysisTheroomcanbeconsideredtobethree-surfaceenclosurewiththeceilingsurface1,thefloorsurface2andthesidesurfacessurface3.Weassumesteady-stateconditionsexist.Sincethesidesurfacesarereradiating,thereisnoheattransferthroughthem,andtheentireheatlostbytheceilingmustbegainedbythefloor.Thentherateofheatlossfromtheroomthroughitsfloorcanbedeterminedfrom
where
and
Theviewfactorfromthefloortotheceilingoftheroomis
(FromFigure12-42).Theviewfactorfromtheceilingorthefloortothesidesurfacesisdeterminedbyapplyingthesummationruletobe
sincetheceilingisflatandthus
.Thentheradiationresistanceswhichappearintheequationabovebecome
Substituting,
12-43Twoperpendicularrectangularsurfaceswithacommonedgearemaintainedatspecifiedtemperatures.Thenetrateofradiationheattransfersbetweenthetwosurfacesandbetweenthehorizontalsurfaceandthesurroundingsaretobedetermined.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareopaque,diffuse,andgray.3Convectionheattransferisnotconsidered.
PropertiesTheemissivitiesofthehorizontalrectangleandthesurroundingsare=0.75and=0.85,respectively.
AnalysisWeconsiderthehorizontalrectangletobesurface1,theverticalrectangletobesurface2andthesurroundingstobesurface3.Thissystemcanbeconsideredtobeathree-surfaceenclosure.Theviewfactorfromsurface1tosurface2isdeterminedfrom
(Fig.12-6)
Thesurfaceareasare
Notethatthesurfaceareaofthesurroundingsisdeterminedassumingthatsurroundingsformsflatsurfacesatallopeningstoformanenclosure.Thenotherviewfactorsaredeterminedtobe
(reciprocityrule)
(summationrule)
(summationrule)
(reciprocityrule)
(reciprocityrule)
WenowapplyEq.9-52btoeachsurfacetodeterminetheradiosities.
Surface1:
Surface2:
Surface3:
Solvingtheaboveequations,wefind
Thenthenetrateofradiationheattransfersbetweenthetwosurfacesandbetweenthehorizontalsurfaceandthesurroundingsaredeterminedtobe
12-44Twolongparallelcylindersaremaintainedatspecifiedtemperatures.Theratesofradiationheattransferbetweenthecylindersandbetweenthehotcylinderandthesurroundingsaretobedetermined.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareblack.3Convectionheattransferisnotconsidered.
AnalysisWeconsiderthehotcylindertobesurface1,coldcylindertobesurface2,andthesurroundingstobesurface3.Usingthecrossed-stringsmethod,theviewfactorbetweentwocylindersfacingeachotherisdeterminedtobe
or
Theviewfactorbetweenthehotcylinderandthesurroundingsis
(summationrule)
Therateofradiationheattransferbetweenthecylinderspermeterlengthis
Notethathalfofthesurfaceareaofthecylinderisused,whichistheonlyareathatfacestheothercylinder.Therateofradiationheattransferbetweenthehotcylinderandthesurroundingspermeterlengthofthecylinderis
12-45Alongsemi-cylindricalductwithspecifiedtemperatureonthesidesurfaceisconsidered.Thetemperatureofthebasesurfaceforaspecifiedheattransferrateistobedetermined.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareopaque,diffuse,andgray.3Convectionheattransferisnotconsidered.
PropertiesTheemissivityofthesidesurfaceis=0.4.
AnalysisWeconsiderthebasesurfacetobesurface1,thesidesurfacetobesurface2.Thissystemisatwo-surfaceenclosure,andweconsideraunitlengthoftheduct.Thesurfaceareasandtheviewfactoraredeterminedas
(summationrule)
Thetemperatureofthebasesurfaceisdeterminedfrom
12-46Ahemispherewithspecifiedbaseanddometemperaturesandheattransferrateisconsidered.Theemissivityofthedomeistobedetermined.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareopaque,diffuse,andgray.3Convectionheattransferisnotconsidered.
PropertiesTheemissivityofthebasesurfaceis=0.55.
AnalysisWeconsiderthebasesurfacetobesurface1,thedomesurfacetobesurface2.Thissystemisatwo-surfaceenclosure.Thesurfaceareasandtheviewfactoraredeterminedas
(summationrule)
Theemissivityofthedomeisdeterminedfrom
RadiationShieldsandTheRadiationEffect
12-47CRadiationheattransferbetweentwosurfacescanbereducedgreatlybyinsertingathin,highreflectivity(lowemissivity)sheetofmaterialbetweenthetwosurfaces.Suchhighlyreflectivethinplatesorshellsareknownasradiationshields.Multilayerradiationshieldsconstructedofabout20shieldspercm.thicknessseparatedbyevacuatedspacearecommonlyusedincryogenicandspaceapplicationstominimizeheattransfer.Radiationshieldsarealsousedintemperaturemeasurementsoffluidstoreducetheerrorcausedbytheradiationeffect.
12-48CTheinfluenceofradiationonheattransferortemperatureofasurfaceiscalledtheradiationeffect.Theradiationexchangebetweenthesensorandthesurroundingsmaycausethethermometertoindicateadifferentreadingforthemediumtemperature.Tominimizetheradiationeffect,thesensorshouldbecoatedwithamaterialofhighreflectivity(lowemissivity).
12-49CApersonwhofeelsfineinaroomataspecifiedtemperaturemayfeelchillyinanotherroomatthesametemperatureasaresultofradiationeffectifthewallsofsecondroomareataconsiderablylowertemperature.Forexamplemostpeoplefeelcomfortableinaroomat22Cifthewallsoftheroomarealsoroughlyatthattemperature.Whenthewalltemperaturedropsto5Cforsomereason,theinteriortemperatureoftheroommustberaisedtoatleast27Ctomaintainthesamelevelofcomfort.Also,peoplesittingnearthewindowsofaroominwinterwillfeelcolderbecauseoftheradiationexchangebetweenthepersonandthecoldwindows.
12-50Therateofheatlossfromapersonbyradiationinalargeroomwhosewallsaremaintainedatauniformtemperatureistobedeterminedfortwocases.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareopaque,diffuse,andgray.3Convectionheattransferisnotconsidered.
PropertiesTheemissivityofthepersonisgiventobe1=0.7.
Analysis(a)Notingthattheviewfactorfromthepersontothewalls
therateofheatlossfromthatpersontothewallsatalargeroomwhichareatatemperatureof300Kis
(b)Whenthewallsareatatemperatureof280K,
12-51Athinaluminumsheetisplacedbetweentwoverylargeparallelplatesthataremaintainedatuniformtemperatures.Thenetrateofradiationheattransferbetweenthetwoplatesistobedeterminedforthecasesofwithandwithouttheshield.
Assumptions1Steadyoperatingconditionsexist2Thesurfacesareopaque,diffuse,andgray.3Convectionheattransferisnotconsidered.
PropertiesTheemissivitiesofsurfacesaregiventobe1=0.5,2=0.8,and3=0.15.
AnalysisThenetrateofradiationheattransferwithathinaluminumshieldperunitareaoftheplatesis
Thenetrateofradiationheattransferbetweentheplatesinthecaseofnoshieldis
Thentheratioofradiationheattransferforthetwocasesbecomes
12-52"!
PROBLEM12-52"
"GIVEN"
"epsilon_3=0.15parametertobevaried"
T_1=900"[K]"
T_2=650"[K]"
epsilon_1=0.5
epsilon_2=0.8
sigma=5.67E-8"[W/m^2-K^4],Stefan-Boltzmannconstant"
"ANALYSIS"
Q_dot_12_1shield=(sigma*(T_1^4-T_2^4))/((1/epsilon_1+1/epsilon_2-1)+(1/epsilon_3+1/epsilon_3-1))
3
Q12,1shield[W/m2]
0.05
656.5
0.06
783
0.07
908.1
0.08
1032
0.09
1154
0.1
1274
0.11
1394
0.12
1511
0.13
1628
0.14
1743
0.15
1857
0.16
1969
0.17
2081
0.18
2191
0.19
2299
0.2
2407
0.21
2513
0.22
2619
0.23
2723
0.24
2826
0.25
2928
12-53Twoverylargeplatesaremaintainedatuniformtemperatures.Thenumberof
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