喜欢热与传质基本原理答案分章节版

PROBLEMKNOWN:Cylindrical-shapedmeatroastweighing2.25kg,initiallyat6C,iscedinanovenandsubjectedtoconvectionheatingwithprescribed(T,h).FIND:Timerequiredforthecentertoreacha emperatureofASSUMPTIONS:(1)Two-dimensionalconductioninxandrdirections,(2)Uniformandconstantproperties,(3)Propertiesapproximatedasthoseofwater.PROPERTIES:TableA-6,Water,liquidT806C/2 =1/vf=1/1.009-3 107m

/kg=991.1kg/m,cp,f=4179J/kgK,k=0.634W/mK,=k/c=1.531YSIS:Thedimensionsoftheroastaredeterminedfromtherequirementro=LknowledgeofitsweightandMV2L rLM1/3 2.25 1/3 TheroastcorrespondstoCase(i),Figure5S.11,andthetemperaturedistributionmayexpressedastheproductofone-dimensionalsolutions,Tx,r,tTi

Px,twhereP(x,t)andC(r,t)aredefinedbyEquations5S.2and5S.3,respectively.FortheoftheT0,0,t

T 0.56. 6175CIntermsoftheproductsolutions,T0,0,tT0.56T0,tT T0,tT

Foreachoftheseshapes,weneedtofindvaluesofo/isuchthattheirproductsatisfiesEquation(3).Forbothshapes,BihrohL15W/m2K0.0712m1.68 0.634W/mKoFot/r2t/L21.53107m2/st/0.0712m23.020105o…..PROBLEM5S.12Atrial-and-errorsolutionisnecessary.BeginbyassumingavalueofFo;obtainrespectiveo/ivaluesfromFigures5S.1and5S.4;testwhethertheirproductsatisfiesEquation(3).Twotrialsareshownasfollows: o/i

o/i

o o

ii

12ForTrial2,theproductof0.53agreescloselywiththevalueof0.56fromEquation(2).Hence,itwilltakeapproximay2¾hourstoroastthemeat.2.256°C(T∞,h)流加热。FIND：中心达到80°C完成温度所需的时间。原理图：假设：(1)xr，(2)，(3)特性：表A-6，水，液体(T=(80+6)C/2≈315K)：ρ=1/vf=1/1.009×3310m/kg=991.1kg/m,cp,f=4179J/kg.K,k=0.634W/m.K,α=k/ρc=1.531×roL131/32.25kgM=ρVρ.2L.πr2rL0.0712m2πρ..2π991.1kg/m3(i5S.11T(x,r,tP(x,t)×TTiP(x,t)C(r,t)5S.25S.3T(0,0,t(80.175)=0.56TTi6.175)C，T(0,0,tTT(0,t)TT0,t)T。0.56TTTTTTiihrohL15W/m2.×K0.0712m1Bi====1.68或Bi≈0.6kk0.634KFoαt/r2=αt/L21.53×10.7m2/st/(