Transport and Surface Phenomena PDF
Preview Transport and Surface Phenomena
TRANSPORT AND SURFACE PHENOMENA From the Czech original translated by J. J. ULBRECHT TRANSPORT AND SURFACE PHENOMENA KAMIL WICHTERLE MAREK VEČEŘ Elsevier Radarweg29,POBox211,1000AEAmsterdam,Netherlands TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates ©2020ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronic ormechanical,includingphotocopying,recording,oranyinformationstorageandretrievalsystem, withoutpermissioninwritingfromthepublisher.Detailsonhowtoseekpermission,further informationaboutthePublisher’spermissionspoliciesandourarrangementswithorganizationssuch astheCopyrightClearanceCenterandtheCopyrightLicensingAgency,canbefoundatourwebsite: www.elsevier.com/permissions. Thisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythe Publisher(otherthanasmaybenotedherein). 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LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN:978-0-12-818994-8 ForinformationonallElsevierpublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:SusanDennis AcquisitionsEditor:AnnekaHess EditorialProjectManager:SaraValentino ProductionProjectManager:R.VijayBharath CoverDesigner:MarkRogers TypesetbySPiGlobal,India Foreword The three basic engineering tasks Thefundamentaltaskofanengineeringassignmentistofindqualita- tively possible solutions to a given problem and to answer the quantitative question about its technical feasibility and economic advantage. Thequalitativesolutionusuallyleansonthesearchofthescientific,com- mercial,andpatentliteraturebut,inthefirstplace,onone’sownexperience combined with one’s own capability of combinations and fantasy. When a quantitative solution is required then the engineer is asked to apply the three basic engineering tasks, often using simple, but more often sophisticated mathematical methods. Thefirsttaskisbasedonsimple,andinthesimplifiedworldofreallife, undisputed principlesofnatural sciences, suchas thelaw of conservation ofmass,thelawofconservationofvariouskindsofenergy,andthestoichio- metriclawsofchemistry;alsoincludedaresimplerulesfortheconversionof quantities such as the mass and volumes. Using these rules one can reliably perform mass and energy balances of a particular process. Thesecondtaskfollowsaquestionhowfarcanacertainprocesspro- ceed,orunderwhatcircumstanceswilltheprocesschangequalitatively.In thiscase,onecanmakeuseofknownprocessequilibrium.Thequantities thatenterintothecalculationsherearemorecomplexparametersfromthe domain of statics and thermodynamics that can have the form of con- stants,functions,orcomplexmathematicalobjects,thevaluesofwhichmust bedeterminedexperimentally.Alternatively,thevaluesofsome(suchasthe meltingpoints,vaportensions,solubilities,interfacialtensions,andbonding enthalpies) can be found with sufficient accuracy in a tabular form in the appropriateliterature.Insomecases,onecanuserelativelyreliableformulas for the estimation of these quantities into which one needs to substitute quantities that are easier to obtain. Thethirdtaskdealswiththekineticsofaprocess,i.e.,whatisitsrate. Inthecaseofchemicalandphysicalprocessesthatproceedoutsidetheequi- librium,therateisdeterminedbythesetofdrivingforcesopposedbyasetof resistancesthatactagainsttheequalizationofthepropertiesindifferentparts ofthesystem.Thethreemostsignificantresistancesarethosethatopposethe transferofmomentum,thetransferofheat,andthetransferofmass. These resistances have, to a certain degree, a linear character so it is xi xii Foreword advantageous to study them together under a common title of transport phenomena. A separate task is the study of the chemical kinetics that, as a rule, is not linear and, therefore, must be studied independently. Transport phenomena: The continuum and the interfaces Under ordinary circumstances we perceive through our senses any mass as beingacontinuumorasasetofcontinuaseparatedbysimplegeometrical interfaces. In reality (unless one wants to immerse deeper into nuclear physics), the mass is rather a set of moving particles (vibrating, sometimes rotating, and even mutually exchanging their positions). Despite of that, it is useful to consider a large set of particles (be they molecules, nanoparticles, or even particles visible by bare eye) to be a continuum to which one can assign averaged quantities to every point of the system. Intensive quantities are ratios of directly measurable extensive quantities (e.g., the density is the ratio of mass and volume at a given point). Amongthestatistically averaged quantities,the local velocityisthe statisticalaverageofparticlepathscuttingtheimaginaryplaneinthevicinity of the point in question per unit of time) or the temperature (expressing mean energy of the oscillating molecules). Todescribesuchanapproach,theclassicalphysicsdevelopedmathe- matical tools; the analysis of continuous functions (Newton, Leibnitz) lead to usual differential and integral calculus. Theequilibriumstatesinhomogeneousphasesarecharacterizedbyinvari- abilityofquantitiesthatcanbecalledthemeasuresofequilibrium,forexam- ple,thetemperature.Whenthetemperatureisconstant,thereisnolocalheat transport, when the concentration (activities, fugacities) are constant, there is nomasstransport,etc.Thedisciplineofphysicsthatdealswiththeusualequilib- riumprocessesiscalledstatics;inphysicalchemistryitiscalledthermodynamics. When the system is not in equilibrium then the variability of those quantities that measure the equilibrium lead to position changing, regrouping, and transformations of both mass and energy. To evaluate theratewithwhichthesystemmovestowardtheequilibrium,theso-called transportprocesses,itisusefultointroducequantitiesthatcharacterizethe basic transport phenomena: momentum transfer, heat transfer, and mass transfer. The relevant transfer coefficients are viscosity, thermal conductivity, and diffusivity. Foreword xiii Inthepast,theindividualphenomenawerestudiedinseparatescientific disciplines, such as the fluid mechanics, hydrodynamics, and the science of heat and mass transfer. Later, it turned out, however that these three processes are analogous and that they can be treated with the same mathematical tools. As a rule, the individual steps of an engineering solution usually are as follows: (cid:129) The definition of a spatial and temporal region in which the process in question takes place. (cid:129) The application of a mathematical model to the transport in question including boundary and initial conditions. (cid:129) An analysis of possible solutions of themodel, firstin a simplified form. (cid:129) The evaluation of all possible solutions, in simple cases, is carried out. (cid:129) The presentation of the results in a useful form. The transport across a phase boundary is a special case. The difference betweenthetransportcoefficientsin differentmediumsresultsin adiscon- tinuity that modifies velocity fields, velocity gradients, temperature gradi- ents, concentration gradients, etc. The opposing limits at the phase boundaryareusuallyrelatedbyasimplemathematicalformulathatisfortu- natelynotmodifiedbythetransportitself.Therefore,thecommonrulesof physicsandphysicalchemistrydescribingtheequilibriumsatphasebound- aryremainvalid.Thus,theknowledgeofsurfacephenomenaisessentialfor the study of complex transport phenomena. The history of this discipline Aperfunctoryopeningofanymonographtitled“TransportPhenom- ena” (possibly expanded in “Transport of momentum, heat, and mass”) mightleadthereadertoerroneousconclusions.Thosewhoarenottoofond ofmathematicsarefrightenedbythemassofformulasandrelationshipsfrom thedomainofdifferentialequationsandthosefromthevectorcount.Onthe other hand, mathematical geeks see a fascinating playing field. This should not be very surprising since this discipline grew out of the work of such physicists (Newton, Bernoulli, Euler, Cauchy, Stokes, and others)whoareknownbytheirdiscoveriesinmathematicsneededforsolu- tionstospecificphysicalproblems.Itisevenpossibletoclaimwithacertain degree of exaggeration that mathematics in its time owed its progress more to the study of transport phenomena than the science of transport xiv Foreword phenomena to mathematics. Up to the end of the 19th century, these dis- ciplines formed relatively special and not too emphasized part of physics. Next came the period characterized by the progress in ship transporta- tion,upswingofaviation,steamenergygeneration,andchemicalengineer- ing,whenthisdisciplinebecomesthesubjectofinterestofexperimentalists andmathematicallytrainedengineerssuchasNusselt,Kirchhoff,Reynolds, Grashof,Zhoukovsky,Prandtl,Karman,Luikov,Kolmogoroff,andothers. In 1956, Professor Hans Kramers from the Technical University, Delft (The Netherlands) for the first time connected and organized the existing knowledge about the transports of momentum, heat, and mass in a series oflectures“FysischeTransportverschijnselen”sothatmethodshithertoused only in particular cases could now be used generally. This idea was further expandedbyhisdiscipleR.B.Bird,laterprofessorofchemicalengineering at the University of Wisconsin, USA, and his colleagues Professors W.E. StewartandE.N.Lightfootintheseminalmonograph“TransportPhenom- ena” published in 1960. In the next two decades, the discipline became a domain of theoreti- cians from universities who gradually filled any remaining gaps in already solvedtasks.Inmostcases,theseweretheoreticalcomputationalworkseven thoughsomeofthemwerejustinsignificantproblems.Still,theappearance ofnewadvancedexperimentalmethodsmadeitpossibletocarryoutaseries of new measurement techniques. The inclusion of transport phenomena courses in engineering curricula at universities became common. With the exponential growth of the performance of the computational techniques,withtheexpansionofpersonalcomputers,andwiththeappear- anceofuser-friendlysoftwarehasdiminishedthepressureonthemathemat- icalskills ofthesubmitter.Transport phenomenabecome again availableto engineersandgenerallyforchemicalengineerswhoneedtounderstandthe processes taking place under more complex conditions since they have to design these processes. The tempting availability of ready-made solutions should not, however, distract from a sensible definition of the problem and from the rational specification of the main goal of the calculations. The structure of this book ThisbookoriginatedfromthelecturesgivenattheTechnicalUniver- sity Ostrava (Czech Republic) in 1995 for graduate students of chemical engineering. The lectures were also attended by graduate students of Foreword xv material engineering, environmental engineering, safety engineering, and nanotechnology. Therefore, the book is divided into three parts: In the first part named “Fundamentals of Transport Phenomena” the focusisongeometricallysimplesetupsinwhichthetransportoccurs.Some more common problems that are often encountered by physical chemists, material engineers and technologists (metallurgists, plastics engineers, ceramicists,foodprocessingengineers,etc.)areexpanded.Toalargeextent, thispartisonlyqualitativebutitdefinescertainfundamentalconceptsofthis discipline that are later used in more complex situations. Thesecondpartnamed“BalancesofTransportPhenomena”isintended forpracticinghydrodynamicists,heattechnologists,andgenerallytochem- ical engineers who need to understand the processes under more complex conditions and design such processes. The solution to these tasks usually requires more complex mathematical apparatus. Therefore, it is the basic priority of this work to get the student formulate a specific task to such anextentthattheactualsolutioncanbeperformedwiththehelpofthecom- putationalmethodsbyaspecialistwhodoesnotneedtoknowmuchabout thephysicalnatureoftheproblem.Acompletesolutionusuallyleadstothe description of the velocity, temperature, or concentration fields but the engineerneedstoobtainoutoftheseonlyrelativelysimpleresults,forexam- ple,onlysomelocalvaluesorthosesuitablyaveraged.Thefinalaimisthusis to suitably specify the task and suitably interpret the results. The third part termed “Mathematical Methods for Solving the Trans- ports”conciselyelucidatesthemathematicalmeansusedtosolvethetrans- ports:vectorandtensorcountandtheselectedapproachestosolvingpartial and ordinary differential equations that do not belong to the common widely trained gear of college students of technical and science faculties. Theaimofthistextwasnotthecreationofanencyclopedictreatmentof the subject neither to stay with a simple manual for the solution of a few standard tasks. The aim is to demonstrate how the necessary concepts and methods of the discipline were created and to show what are they useful for.Thestudentshouldbecomecompetentinunderstandingoriginalworks dealingwiththetransferofmomentum,heat,andmassandorienthim/her- selfinnumerousmonographsthatsystematicallydealwiththesubjectinvar- ious depths and extent andwith miscellaneous orientation and application. Forthepriceofacertaininconsistencyitwillbeattemptednottoover- whelmthestudentwithanexcessofformalisms.Rightfromthebeginning the text is sandwiched between notes referring to practical problems in which the discussed theoretical concepts are applied.
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