Introductory Transport Phenomena PDF
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Page1 SUMMARY OF FLUX EXPRESSIONS CONVECTIVEFLUXEXPRESSIONS Convectivemomentumfluxtensor: 0(c) =ivv or 0(c) =ivv ij i j Convectiveenergyfluxvector: ( ) ( ) q(c) = iÛ + 1iv2 v or q(c) = iÛ + 1iv2 v 2 i 2 i Convectivemassandmolarfluxvectors: j(c) =ia v or j(c) =ia v A A Ai A i J*(c) =cx v* or J*(c) =cx v* A A Ai A i MOLECULARFLUXEXPRESSIONS Molecularmomentumfluxtensor(i=constant,Newtonianfluid): 0=pt−4(∇v+(∇v)†) or 0 =pt −4((𝜕v∕𝜕x)+(𝜕v∕𝜕x)) ij ij j i i j Conductiveheatfluxvector+workfluxvector(purefluidsonly;seeEqs.19.3-3and 24.1-10): ∑3 q+w=−k∇T+[0⋅v] or q +w =−k(𝜕T∕𝜕x)+ 0 v i i i ij j j=1 Diffusivemassandmolarfluxvectors(ordinarydiffusiononly;seeEq.24.1-9): j =−i𝒟 ∇a or j =−i𝒟 (𝜕a ∕𝜕x) A AB A Ai AB A i J* =−c𝒟 ∇x or J* =−c𝒟 (𝜕x ∕𝜕x) A AB A Ai AB A i TOTAL(CONVECTIVE+MOLECULAR)FLUXEXPRESSIONS Totalmomentumfluxtensor: d=ivv+0 or d=ivv+pt+f Totalenergyfluxvector(purefluidsonly): ( ) ( ) e= iÛ + 1iv2 v+q+w or e= iĤ + 1iv2 v+q+[f⋅v] 2 2 Totalmassandmolarfluxvectors(ordinarydiffusiononly): n =ia v+j or n =a (n +n )+j A A A A A A B A N =cx v*+J* or N =x (N +N )+J* A A A A A A B A Allfluxesdefinedabovehavethesamesignconvention;theyarepositivewhenthe quantitybeingtransportedismovingfromthenegativesideofasurfacetotheposi- tiveside.Derivatives𝜕∕𝜕x appearingincomponentformsofequationsareforCarte- i siancomponentsonly. TrimSize:8inx10in Bird1e b03.tex V1-October21,2014 4:39P.M. Page2 EQUATIONSOFCHANGEINTERMSOFTHETOTALFLUXES Theseequationsarevalidonlyforsystemsinwhichgravityisthesoleexternalforce. Moreinformationcanbefoundin§19.2. Momentum: 𝜕 iv=−[∇⋅d]+ig 𝜕t Energy: ( ) 𝜕 iÛ + 1iv2 =−(∇⋅e)+i(v⋅g) 𝜕t 2 Mass: 𝜕 ia =−(∇⋅n )+r 𝜕t A A A EQUATIONSOFCHANGE(RESTRICTEDFORMS) Momentum(forNewtonianfluidswithconstantiand4): ( ) Dv 𝜕v i ≡i +[v⋅∇v] =−∇p+4∇2v+ig Dt 𝜕t Energy(forNewtonianfluidswithconstantiandk): ( ) iĈ DT ≡iĈ 𝜕T +(v⋅∇T) =k∇2T+4C p Dt p 𝜕t v Mass(forbinarymixturesofAandBwithconstanti𝒟 andnocrosseffects): AB ( ) Da 𝜕a ( ) i A ≡i A + v⋅∇a =i𝒟 ∇2a +r Dt 𝜕t A AB A A DIMENSIONLESSGROUPS (l andv areacharacteristiclengthandvelocity,respectively) 0 0 Re=l v i∕4 Pr=Ĉ 4∕k Sc=4∕i𝒟 0 0 p AB Ra=GrPr Gr=gvl32T∕l2 Gr =grl32a ∕l2 0 a 0 A Nu=hl ∕k Pé=RePr Pé =ReSc 0 AB Sh=k l ∕𝒟 j =Nu∕RePr1∕3 j =Sh∕ReSc1∕3 c 0 AB H D TrimSize:8inx10in Bird1e r01.tex V1-October30,2014 1:49P.M. Pagei Introductory Transport Phenomena R. Byron Bird Warren E. Stewart Edwin N. Lightfoot Daniel J. Klingenberg TrimSize:8inx10in Bird1e r01.tex V1-October30,2014 1:49P.M. Pageii VP&ExecutivePublisher: DonFowley ExecutiveEditor: DanSayre ProductDesigner: JennyWelter MarketingManager: ChristopherRuel OperationsManager: YanaMermel EditorialAssistant: FrancescaBaratta AssociateProductionManager: JoycePoh Designer: KenjiNgieng ThisbookwassetinPalatinobyLaserwordsPrivateLimited. 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Returninstructionsandafreeofchargereturnmailing labelareavailableatwww.wiley.com/go/returnlabel. Ifyouhavechosentoadoptthis textbookforuseinyourcourse,pleaseacceptthisbookasyourcomplimentarydeskcopy. OutsideoftheUnitedStates,pleasecontactyourlocalsalesrepresentative. ISBN978-1-118-77552-3(cloth) PrintedintheUnitedStatesofAmerica 10987654321 TrimSize:8inx10in Bird1e f02.tex V1-October21,2014 9:21P.M. Pageiii Preface Transportphenomenaisnowgenerallyrecognizedasakeyscientificsubjectsupporting studyof several branchesof engineering,agriculture,meteorology, medicine,and envi- ronmental studies. Historically, the subject had its origins in Europe, and some of the keyoriginalpapersandbookswerewritteninGermanandFrench,aswellasinEnglish. IntheyearsfollowingWorldWarII,interestintheteachingoftransportphenomenain U.S.universitiesledtotherapiddevelopmentofcoursesandtextbooksinthisarea,first forbackgroundinengineeringcurricula,withlatertextbooksinvariousspecializedareas withinengineeringaswellasoutside. So what exactly is meant by the term “transport phenomena”? Very simply put, it includes the transport of momentum (or “fluid mechanics”), the transport of energy (or “heat transfer”), and the transport of chemical species (or “mass transfer”). Of particular importancearethenthetransportcoefficients—theviscosity(describingthetransportof momentum),thethermalconductivity(describingthetransportofenergy),andthediffusiv- ity(describingthetransportofchemicalspecies).Luckilythereare“conservationlaws” thatapplytothethreeentitiesbeingtransported,andwewillpayconsiderableattention totheseconservationlawsthroughoutthistextbook. Understandably,thebookdividesitselfquitenaturallyintothreeparts,oneforeach oftheentitiesbeingtransported.Muchemphasiswillbeplacedonthesimilarities—and differences—betweenthedevelopmentofthethreetypesofconservationequationsand theirassociatedtransportcoefficients.Eachofthethreeareasjustdescribedmaybestud- ied at one of three different levels: the molecular level (where we try to understand the transportcoefficientsintermsofthemolecularinteractions);themicroscopiclevel(where weregardthematerialsascontinua);andthemacroscopiclevel(whereweexaminelarge systems—suchaspiecesofequipmentorbiologicalorgans).Itisimportant,wefeel,for thosefirstmakingacquaintancewiththesubjectoftransportphenomenatounderstand theconnectionbetweenthethreelevelsofthesubject,aswellasthatbetweenthethree quantitiesthataretransported.Sincetherearethesevariousconnections,wecanlayout thegeneralplanofthistextbookasinthetableshowninChapter0—thesubjectmaterial justorganizesitself!Despitethisapparentlyobviousself-organization,thereareineach ofthethreemainpartsofthebooksometopicsthatdonotfitintothistidyscheme.Each ofthethreeparts,therefore,hasan“eighthchapter,”inwhichtheseoddballtopics—but veryimportanttopics—arediscussed. Duetothearrangementofthetopicstobediscussed,itispossibleforteachingpur- posestoconsidertwowaysofproceeding.Inthefirstway,wecanteachthematerial“by columns”—that is, by teaching the chapters in the order 1, 2, 3, and so on. Clearly this isthebestcourseofactionforinstructionofundergraduates.Asforgraduatestudents, teaching“byrows”—thatis,byteachingthechaptersinthesequence1,9,17,2,10,18, andsoon—maybepreferable. Thechaptersareprovidedwithasummarysectionaswellasquestionsfordiscus- sion, and these may be helpful in suggesting ways to organize “problems sessions” or “quizsections.”Eachchapteralsohas,attheend,anumberofproblems,whichhavebeen groupedintovariousclasses:ClassA,illustratingdirectnumericalapplicationsofmate- rialinthetext;ClassB,involvingelementaryanalysisofphysicalsituations;andClassC, requiringmorematureanalysisormaterialfromseveralchapters. Dependingonthenumberofcredithoursallottedtothissubject,itmaynotbepossi- bleforallthematerialinthebooktobecovered.Therefore,inthechapteroutlinesatthe beginningsofthechapters,asanaidtoinstructors,wedesignateoptionalsectionsby(o). iii TrimSize:8inx10in Bird1e f02.tex V1-October21,2014 9:21P.M. Pageiv iv Preface Omissionofthetopicssodesignated,willstillleaveenoughmaterialforawell-balanced introductorycourse. Thesubjectoftransportphenomenahaslongbeenregardedasarathermathematical subject.However,itshouldbetaughtasatopicinappliedphysics.Emphasisshouldbe placedonthevisualizationofphysicalsystems,thephysicalinterpretationoftheresultsof problemsolving,and,ofcourse,thechoiceofthephysicallawsneeded.Mathematicswill inevitablyhavetobeusedinordertosolvetheproblems,butthemathematicsissecondary inimportancetothephysics.Everyeffortismadeinthisintroductorytexttoexplainhow themathematicsisused,andtoincludesufficientintermediatestepsinderivationssothat the text will be useful for self-study. Much emphasis should be placed on checking the mathematicsateachstepinadevelopmentandlearningtoaskwhethertheequationsare givingresultsinagreementwithphysicalintuition. OfimportancetoteacherswillbethedifferencebetweenBSL(TransportPhenomena, by Bird, Stewart, and Lightfoot) and the present textbook, which we will designate by BSLK.Readersfamiliarwiththeformerbookwillrecognizethattheoverallorganization ofthecontentsissimilar,andthatthereisconsiderableoverlapinthecontentsofthetwo books.Youwillfind,however,thatconsiderablemorespacehasbeendevotedtofilling inmissingstepsinmathematicalderivationsandtofullerexplanationsofmathematical developments,includinganenlargementoftheappendixdevotedtomathematicaltopics; inaddition,muchmaterialhasbeenremovedthatwefeltwasbeyondthelevelofmathe- maticalpreparationofmostundergraduates.Ourintentionwastomakethisbookreflect thetopicscoveredinourundergraduatecourse,withtheexceptionofafewadvancedtop- icsincludedforthebrighteststudents.Finally,weremovedthechaptersdealingwithtwo independentvariablesandreplacedthemwithchaptersondimensionalanalysis,includ- ingthemuch-usedBuckinghampitheorem. Wewishtothankthepeoplewhohaveinfluencedthefinalformofthistextbook,and atthetopofthelistwemustputOlafAndreasHougen,whoguidedourdepartmentand emphasizedthescientificbackgroundofchemicalengineering.Also,hefeltverystrongly thatnotopicshouldbetaughttoengineeringstudentsunlessthereareclearindications thatitcanbeusedinapplications.Rarelydidaweekgobythatwedidnotgetquestions fromstudentsorprofessorsatotherinstitutionsaboutunclearportionsofthetextinthe predecessorsofthisvolume.Respondingtothesequerieshasbeenaveryhelpfulexercise forthecoauthorsinplanningfutureprintingsofthebookandforbetterunderstanding thepedagogicalproblemsthatthereadershavehadtocopewith.Everyoneshouldfeel freetocontactusinconnectionwiththepresentvolume,andweencourageyoutopoint outerrorsandinconsistenciesinthetext.Nextwewouldliketoacknowledgeourown studentsandcolleaguesfromwhomwehavelearnedsomuch;conversationswithPro- fessorsEdwinN.Lightfoot,MichaelD.Graham,EricV.Shusta,A.JeffreyGiacomin,and RossE.Swaneyhavebeenparticularlyhelpful.Eachandeveryoneofthemhasinsome waycontributedtoourknowledgeofthesubjectandthesolvingofpedagogicalproblems encountered.SpecialthanksgotoProfessorCarlosRamirezoftheUniversityofPuerto Ricoforthetimeandtroublethathetookinsupplyinguswithcopiouscorrigendaforthe secondeditionofBSL,andtoDr.M.I.HillofColumbiaUniversityforofferingcritiques ofseveralchaptersforBSLK. Transportphenomenaisanevolvingsubject.Eachmonth,newapplicationsappear inthetechnicaljournals,andnewtechniquesforproblemsolvingarepresented.Weare acutelyawarethatwecannotpossiblycoverallthenewestoftheoreticalandexperimental developmentsinabeginningtextbook,butwehopethatwehaveprovidedaspringboard fromwhichthereaderscanlaunchthemselvesintothenewareas. Andnow,wepointoutthatthechiefcoauthorsofthisBSLKbookareRBBandDJK, whohavetriedtocarrythetorchforward;DJKhastaughttheundergraduateandgraduate transportphenomenacoursesforabouttwentyyears,andhisunderstandingofstudents’ challengeshasbeenveryhelpful.RegretfullyENLwasnotabletoparticipatefullyinthis TrimSize:8inx10in Bird1e f02.tex V1-October21,2014 9:21P.M. Pagev Preface v rewriteoftheTransportPhenomenatextbook,althoughhiscontributionstotheearlierBSL editions—particularlysomeofthemorechallengingexamplesandproblems—havebeen retained.TheuntimelypassingofWEShasbeenkeenlyfeltbyour“team,”andtohimwe alsoowegenerousthanksforhisorganizationalskills,hispassionforaccuracy,andhis wonderfulsenseofhumor. RBB ENL WES DJK Madison,Wisconsin Summer2013 TrimSize:8inx10in Bird1e f02.tex V1-October21,2014 9:21P.M. Pagevi
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