Heat Chap13111.docx
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Heat Chap13111.docx
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HeatChap13111
ReviewProblems
13-111Hotoiliscooledbywaterinamulti-passshell-and-tubeheatexchanger.Theoverallheattransfercoefficientbasedontheinnersurfaceistobedetermined.
Assumptions1Waterflowisfullydeveloped.2Propertiesofthewaterareconstant.
PropertiesThepropertiesofwaterat300K25Care(TableA-9)
AnalysisTheReynoldsnumberis
whichisgreaterthan10,000.Therefore,weassumefullydevelopedturbulentflow,anddetermineNusseltnumberfrom
and
Theinnerandtheoutersurfaceareasofthetubeare
Thetotalthermalresistanceofthisheatexchangerperunitlengthis
Thentheoverallheattransfercoefficientofthisheatexchangerbasedontheinnersurfacebecomes
13-112Hotoiliscooledbywaterinamulti-passshell-and-tubeheatexchanger.Theoverallheattransfercoefficientbasedontheinnersurfaceistobedetermined.
Assumptions1Waterflowisfullydeveloped.2Propertiesofthewaterareconstant.
PropertiesThepropertiesofwaterat300K25Care(TableA-9)
AnalysisTheReynoldsnumberis
whichisgreaterthan10,000.Therefore,weassumefullydevelopedturbulentflow,anddetermineNusseltnumberfrom
and
Theinnerandtheoutersurfaceareasofthetubeare
Thetotalthermalresistanceofthisheatexchangerperunitlengthofitwithafoulingfactoris
Thentheoverallheattransfercoefficientofthisheatexchangerbasedontheinnersurfacebecomes
13-113Waterisheatedbyhotoilinamulti-passshell-and-tubeheatexchanger.Therateofheattransferandtheheattransfersurfaceareaontheoutersideofthetubearetobedetermined.
Assumptions1Steadyoperatingconditionsexist.2Theheatexchangeriswell-insulatedsothatheatlosstothesurroundingsisnegligibleandthusheattransferfromthehotfluidisequaltotheheattransfertothecoldfluid.3Changesinthekineticandpotentialenergiesoffluidstreamsarenegligible.4Theoverallheattransfercoefficientisconstantanduniform.
PropertiesThespecificheatsofthewaterandoilaregiventobe4.18and2.2kJ/kg.C,respectively.
Analysis(a)Therateofheattransferinthisheatexchangeris
(b)Theoutlettemperatureofthecoldwateris
Thetemperaturedifferencesatthetwoendsare
Thelogarithmicmeantemperaturedifferenceis
and
Theheattransfersurfaceareaontheoutersideofthetubeisthendeterminedfrom
13-114EWaterisheatedbysolar-heatedhotairinadouble-pipecounter-flowheatexchanger.Therequiredlengthofthetubeistobedetermined.
Assumptions1Steadyoperatingconditionsexist.2Theheatexchangeriswell-insulatedsothatheatlosstothesurroundingsisnegligibleandthusheattransferfromthehotfluidisequaltotheheattransfertothecoldfluid.3Changesinthekineticandpotentialenergiesoffluidstreamsarenegligible.4Theoverallheattransfercoefficientisconstantanduniform.
PropertiesThespecificheatsofthewaterandairaregiventobe1.0and0.24Btu/lbm.F,respectively.
AnalysisTherateofheattransferinthisheatexchangeris
Theoutlettemperatureofthecoldwateris
Thetemperaturedifferencesatthetwoendsare
Thelogarithmicmeantemperaturedifferenceis
Theheattransfersurfaceareaontheoutersideofthetubeisdeterminedfrom
Thenthelengthofthetuberequiredbecomes
13-115ItistobeshownthatwhenT1=T2foraheatexchanger,theTlmrelationreducestoTlm=T1=T2.
AnalysisWhenT1=T2,weobtain
ThiscasecanbehandledbyapplyingL'Hospital'srule(takingderivativesofnominatoranddenominatorseparatelywithrespectto
).Thatis,
13-116Refrigerant-134aiscondensedbyairinthecondenserofaroomairconditioner.Theheattransferareaontherefrigerantsideistobedetermined.
Assumptions1Steadyoperatingconditionsexist.2Theheatexchangeriswell-insulatedsothatheatlosstothesurroundingsisnegligibleandthusheattransferfromthehotfluidisequaltotheheattransfertothecoldfluid.3Changesinthekineticandpotentialenergiesoffluidstreamsarenegligible.4Theoverallheattransfercoefficientisconstantanduniform.
PropertiesThespecificheatofairisgiventobe1.005kJ/kg.C.
AnalysisThetemperaturedifferencesatthetwoendsare
Thelogarithmicmeantemperaturedifferenceis
Theheattransfersurfaceareaontheoutersideofthetubeisdeterminedfrom
13-117Airispreheatedbyhotexhaustgasesinacross-flowheatexchanger.Therateofheattransferistobedetermined.
Assumptions1Steadyoperatingconditionsexist.2Theheatexchangeriswell-insulatedsothatheatlosstothesurroundingsisnegligibleandthusheattransferfromthehotfluidisequaltotheheattransfertothecoldfluid.3Changesinthekineticandpotentialenergiesoffluidstreamsarenegligible.4Theoverallheattransfercoefficientisconstantanduniform.
PropertiesThespecificheatsofairandcombustiongasesaregiventobe1.005and1.1kJ/kg.C,respectively.
AnalysisTherateofheattransferissimply
13-118Awater-to-waterheatexchangerisproposedtopreheattheincomingcoldwaterbythedrainedhotwaterinaplanttosaveenergy.Theheattransferratingoftheheatexchangerandtheamountofmoneythisheatexchangerwillsavearetobedetermined.
Assumptions1Steadyoperatingconditionsexist.2Theheatexchangeriswell-insulatedsothatheatlosstothesurroundingsisnegligibleandthusheattransferfromthehotfluidisequaltotheheattransfertothecoldfluid.3Changesinthekineticandpotentialenergiesoffluidstreamsarenegligible.
PropertiesThespecificheatofthehotwaterisgiventobe4.18kJ/kg.C.
AnalysisThemaximumrateofheattransferis
Notingthattheheatexchangerwillrecover72%ofit,theactualheattransferratebecomes
whichistheheattransferrating.Theoperatinghoursperyearare
Theannualoperatinghours=(8h/day)(5days/week)(52week/year)=2080h/year
Theenergysavedduringtheentireyearwillbe
Energysaved=(heattransferrate)(operatingtime)
=(18.43kJ/s)(2080h/year)(3600s/h)
=1.38x108kJ/year
Thenamountoffuelandmoneysavedwillbe
Moneysaved=(fuelsaved)(thepriceoffuel)
=(1677therms/year)($0.54/therm)=$906/year
13-119Ashell-and-tubeheatexchangerisusedtoheatwaterwithgeothermalsteamcondensing.Therateofheattransfer,therateofcondensationofsteam,andtheoverallheattransfercoefficientaretobedetermined.
Assumptions1Steadyoperatingconditionsexist.2Theheatexchangeriswell-insulatedsothatheatlosstothesurroundingsisnegligibleandthusheattransferfromthehotfluidisequaltotheheattransfertothecoldfluid.3Changesinthekineticandpotentialenergiesoffluidstreamsarenegligible.4Fluidpropertiesareconstant.
PropertiesTheheatofvaporizationofgeothermalwaterat120Cisgiventobehfg=2203kJ/kgandspecificheatofwaterisgiventobeCp=4180J/kg.C.
Analysis(a)Theoutlettemperatureofthewateris
Thentherateofheattransferbecomes
(b)Therateofcondensationofsteamisdeterminedfrom
(c)Theheattransferareais
Thelogarithmicmeantemperaturedifferenceforcounter-flowarrangementandthecorrectionfactorFare
Thentheoverallheattransfercoefficientisdeterminedtobe
13-120Waterisheatedbygeothermalwaterinadouble-pipecounter-flowheatexchanger.Themassflowrateofthegeothermalwaterandtheoutlettemperaturesofbothfluidsaretobedetermined.
Assumptions1Steadyoperatingconditionsexist.2Theheatexchangeriswell-insulatedsothatheatlosstothesurroundingsisnegligibleandthusheattransferfromthehotfluidisequaltotheheattransfertothecoldfluid.3Changesinthekineticandpotentialenergiesoffluidstreamsarenegligible.4Theoverallheattransfercoefficientisconstantanduniform.
PropertiesThespecificheatsofthegeothermalwaterandthecoldwateraregiventobe4.25and4.18kJ/kg.C,respectively.
AnalysisTheheatcapacityratesofthehotandcoldfluidsare
and
TheNTUofthisheatexchangeris
Usingtheeffectivenessrelation,wefindthecapacityratio
Thenthemassflowrateofgeothermalwaterisdeterminedfrom
Themaximumheattransferrateis
Thentheactualrateofheattransferratebecomes
Theoutlettemperaturesofthegeothermalandcoldwatersaredeterminedtobe
13-121Airistobeheatedbyhotoilinacross-flowheatexchangerwithbothfluidsunmixed.Theeffectivenessoftheheatexchanger,themassflowrateofthecoldfluid,andtherateofheattransferaretobedetermined.
.Assumptions1Steadyoperatingconditionsexist.2Theheatexchangeriswell-insulatedsothatheatlosstothesurroundingsisnegligibleandthusheattransferfromthehotfluidisequaltotheheattransfertothecoldfluid.3Changesinthekineticandpotentialenergiesoffluidstreamsarenegligible.4Theoverallheattransfercoefficientisconstantanduniform.
PropertiesThespecificheatsoftheairandtheoilaregiventobe1.006and2.15kJ/kg.C,respectively.
Analysis(a)Theheatcapacityratesofthehotandcoldfluidsare
Therefore,
and
Theeffectivenessoftheheatexchangerisdeterminedfrom
(b)TheNTUofthisheatexchangerisexpressedas
TheNTUofthisheatexchangercanalsobedeterminedfrom
Thenthemassflowrateoftheairisdeterminedtobe
(c)Therateofheattransferisdeterminedfrom
13-122Awater-to-watercounter-flowheatexchangerisconsidered.Theoutlettemperatureo
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