Electromagnetic Processing of Materials FLUID MECHANICS AND ITS APPLICATIONS Volume99 SeriesEditor: R.MOREAU MADYLAM EcoleNationaleSupe´rieured’HydrauliquedeGrenoble BoˆıtePostale95 38402SaintMartind’He´resCedex,France AimsandScopeoftheSeries Thepurposeofthisseriesistofocusonsubjectsinwhichfluidmechanicsplaysa fundamentalrole. As well as the more traditional applications of aeronautics, hydraulics, heat and masstransferetc.,bookswillbepublisheddealingwithtopicswhicharecurrently in a state of rapid development, such as turbulence, suspensions and multiphase fluids,superandhypersonicflowsandnumericalmodelingtechniques. It is a widely held view that it is the interdisciplinary subjects that will receive intensescientificattention,bringingthemtotheforefrontoftechnologicaladvance- ment. Fluids have the ability to transport matter and its properties as well as to transmit force, therefore fluid mechanics is a subject that is particularly open to crossfertilizationwithothersciencesanddisciplinesofengineering.Thesubjectof fluidmechanicswillbehighlyrelevantindomainssuchaschemical,metallurgical, biologicalandecologicalengineering.Thisseriesisparticularlyopentosuchnew multidisciplinarydomains. The medianlevelof presentationis the first year graduatestudent. Some textsare monographsdefiningthecurrentstate ofafield;othersareaccessibleto finalyear undergraduates;butessentiallytheemphasisisonreadabilityandclarity. Forfurthervolumes: http://www.springer.com/series/5980 Shigeo Asai Electromagnetic Processing of Materials Materials Processing by Using Electric and Magnetic Functions 123 ShigeoAsai JapanScienceandTechnologyAgency Ahara-cho23-1 457-0063Nagoya Minami-ku Japan [email protected] ThisworkispartlybasedonanupdatedtranslationfromtheoriginalJapaneseworkentitled: “ZairyouDenziPurossesingu”,byShigeoAsai,2000,UchidaRokakuho,Japan. ISSN0926-5112 ISBN978-94-007-2644-4 e-ISBN978-94-007-2645-1 DOI10.1007/978-94-007-2645-1 SpringerDordrechtHeidelbergLondonNewYork LibraryofCongressControlNumber:2011945107 ©SpringerScience+BusinessMediaB.V.2012 Nopartofthisworkmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorby anymeans,electronic,mechanical,photocopying,microfilming,recordingorotherwise,withoutwritten permissionfromthePublisher,withtheexceptionofanymaterialsuppliedspecificallyforthepurpose ofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthework. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Most people who choose to read this book are likely to begin with the question “WhatisElectromagneticProcessingofMaterials?”Thisquestionisareasonable one since Electromagnetic Processing of Materials, so called EPM, will find its future development in concert with Materials Science and Engineering, a conjoiningofareasofresearchthathasnotyetbeenfullyconsummated. Inthemetalsindustry,utilizationoftheLorentzforcestartedinveryearlytimes; for example, machines to effect electromagnetic levitation and electromagnetic mixingwereinventedin1923and1932,respectively,butwithlittleunderstanding of the science behind them. To bridge the gap between technology and sci- ence, the term Magnetohydrodynamics, which had been established by Alfve´n in 1942, was first introduced at the IUTAM (InternationalUnion of Theoretical and Applied Mechanics) symposium entitled “Metallurgical Applications of Magne- tohydrodynamics”, held in 1982 in Cambridge, England. Thus, we can say that Electromagnetic Processing of Materials started from this symposium where the twochannelsofMetallurgyandMagnetohydrodynamicswerecombined.Theterm ElectromagneticProcessingofMaterialsfirstappearedatTheSixthInternational IronandSteelCongressheldin1990inNagoya,JapanandthenthefirstSymposium ofEPM washeld in1994,also in Nagoya.Thatis, EPM startedin the1980sand grewinthe1990sasanintimatecollaborationbetweenFranceandJapan.Thefirst fruits of EPM progress were found in utilization of the Lorentz force, mainly for developmentofsteelmakingprocesses,especiallyofcontinuouscastingprocesses. By the2000stheactivityof EPM hadspreadinto theutilizationofmagnetization force,enabledbythefortuitousfactthatahighmagneticfield,uptoaround15Tesla, becameeasilyavailablethroughthedevelopmentofsuper-conductingtechnologies. Briefly speaking, EPM is now located in one branch of Materials Science and Engineering andaimstocreatenew materialsand/ortodesignefficientprocesses bymakinguseofvariousfunctionswhichappearwhenelectricandmagneticfields areappliedtoknownmaterials. ThisbookcontainsnotonlyanEnglishtranslationofmy bookonElectromag- netic Processingof Materialsfirst publishedin 2000by UchidaRokakuho,Japan, thecontentofwhichisbasedonthelecturesgivenforadvancedundergraduateand v vi Preface graduatestudentsintheDepartmentofMaterialsScienceandEngineering,Nagoya Universityovertwodecades,butalsotheintroductionoftransportphenomena.Fur- thermore,tablesandappendixareaddedforhelpingthedesignofelectromagnetic processes, and better understanding of the contents of the book. In Chap. 1, the birth, characteristics and prospects of EPM are described to give readers a brief summary of what EPM is. In Chap. 2, the concept of Transport Phenomena, which is indispensable in materials processing, is given a concise introduction in order to establish that the transportphenomenaof mass, heat and momentumcan all be described by the same diffusion type equation. In Chap. 3, I describe the essentialsofMagnetohydrodynamicsthatarerequiredforunderstandingEPMand I show that the governing equation of a magnetic field can also be expressed by thesamediffusiontypeequationasintroducedinChap.2.Thatis,itisunderstood that the concept of transport phenomena holds not only in relation to heat, mass andmomentum,butalsoinmagneticfields.Thoughmanymathematicalequations appearin this chapter,for the sake of developinga stricter analysis, I recommend that the beginner in EPM read until Chap. 5 by skipping derivation of equations. Afterthat,readersshouldagainreadtheskippedChapters.InChap.4,thevarious functions that appear when applying electric and magnetic fields to materials are enumeratedandtheirutilizationinmaterialsprocessingis explored.Recently,due toadvancesinsuperconductingmagnets,ahighmagneticfieldhasbecomereadily available and is being applied in various fields of science. In this trend many interestingphenomenarelatingtohighmagneticfieldshavebeenfoundandanew academicareacalledMagneto-Sciencehasbeguntoopenagatetofurtherresearch. Inordertoconnecttheseedssproutingfromthenewacademicfieldwiththeneeds of Materials Science and Engineering, a new branch of EPM is growing. Thus, in Chap. 5, materials science and engineering utilizing a high magnetic field is introduced and the functions that appear when applying a high magnetic field to materialsprocessingareexplained. EPM has only recently been recognized as a cutting edge technology. If publication of this textbook leads to opening a new academic field in Materials Science and Engineering, and becomes universally known as Electromagnetic Processing of Materials, it will deepen my great pleasure as one of the persons who have participated in this field from the beginning. Especially, I would like to dedicate this book to the late Dr. Marcel Garnier of the EPM-MADYRAM in Grenoble,France,whofirstinitiatedanddevelopedthisfieldtogetherwithme. I am indebted to many people for help of one kind or another in the making of this book.I am especially gratefulto the late Professor Iwao Muchiat Nagoya UniversityandthelateProfessorJulianSzekelyatMIT,whotaughtmethebasisof MetallurgicalReactionEngineeringandMagnetohydrodynamics,respectively. Thoseacademicbackgroundspromptedmeto writethisbook.ProfessorEmeritus Tsuyoshi Masumoto of Tohoku University, Japan always has encouraged us in developingthisfield bynominatingthe EPM subjecttoa placein the science and technology program in The Ministry of Education, Culture, Sports, Science and Technology,Japan.ProfessorEmeritusRene´ MoreauofSIMAP/EPMinGrenoble, notonlygaveusefulacademicadviceregardingtheproblemsofMagnetohydrody- Preface vii namics,butalsokindlyarrangedacontactwithSpringertopublishthisbook.The ProfessorYvesFautrelleofSIMAP/EPMinGrenobleandProfessorShojiTaniguchi ofTohokuUniversityhavedevotedalotofeffortfordevelopingEPMwithmefora longtime.Aboveall,theauthorwouldliketothankProfessorKen-ichiMiyazawa ofNagoyaUniversitywhopainstakinglyreadeachdraft,queryingeveryambiguity andexposingthemanyinconsistenciesintheoriginalmanuscript.Carefulreviews ofthefinalmanuscriptscontributedcrucialdescriptionsoftheacademicviewpoints of Profs.NoboruYoshikawaand KazuyukiUenoof TohokoUniversity,Kazuhiko IwaiofNagoyaUniversityandHideyukiYasudaofOsakaUniversity.Inthissense Iamnottheonlyauthorofthisbook,butsharethatrolewithallofmycolleagues inworldEPMcommunity. Despite this help, errors and obscurities undoubtedlyremain. I would be most gratefultoanyonewhobringsthemtomyattentionatoneoftheaddressesbelow. Postaladdress:Yakushiyama112,Narumi-cho, Midori-ku,Nagoya,458-0846,Japan e-mailaddress:[email protected] [email protected] Japan ShigeoAsai Contents 1 DevelopmentofElectromagneticProcessingofMaterials............... 1 1 TheBirthofElectromagneticProcessingofMaterials.................. 1 2 TheComparisonofVariousEnergies.................................... 2 3 IndustrialBackgroundandEngineeringAspects........................ 4 3.1 IncreaseofElectricEnergyConsumption........................ 4 3.2 DevelopmentofRelatedTechnologies........................... 4 3.3 High Density, Cleanliness and Controllability ofElectricEnergy ................................................. 4 3.4 EffectiveUseofElectricEnergy.................................. 5 3.5 ApplicationofMagnetohydrodynamicstoMaterialsProcessing 5 4 TreeofElectromagneticProcessingofMaterials........................ 6 References..................................................................... 7 2 TransportPhenomenainMaterialsProcessing........................... 9 1 Formulation................................................................ 9 1.1 Flux ................................................................ 9 1.2 ConservationLaw ................................................. 11 1.3 MathematicalFormulationandSolution ......................... 11 2 DerivationofGoverningEquations ...................................... 12 2.1 TheEquationofContinuity....................................... 13 2.2 EnergyEquationforaFluidwithConstantDensity............. 15 2.3 TheEquationofMotion........................................... 17 3 DimensionlessNumbersAppearinginTransportPhenomena.......... 21 4 TheProcedureforSolvingProblemsbyUseofGoverningEquations. 23 4.1 The Mass Diffusion Model in the Infinite One-DimensionalField............................................ 23 4.2 TheDiffusionModelintheFiniteOne-DimensionalField ..... 27 4.3 TheLaminarFlowinaCylindricalTube......................... 32 4.4 TheLaminarFlowBetweenParallelWalls ...................... 34 4.5 AnalysisofSurfaceWaveMotion................................ 35 ix x Contents AppendixesA–E .............................................................. 36 AppendixA:MethodsforSolvingEq.2.37............................. 36 AppendixB:DerivationofEq.2.54...................................... 39 AppendixC:DerivationofEq.2.57...................................... 41 AppendixD:DerivationofEq.2.65 ..................................... 43 AppendixE:DerivationofEq.2.72...................................... 45 References..................................................................... 47 3 MagnetohydrodynamicsinMaterialsProcessing ........................ 49 1 FundamentalEquation.................................................... 50 1.1 TransportEquationofVorticity................................... 50 1.2 TheEquationofEnergy........................................... 52 1.3 TheDiffusionEquationoftheMagneticField................... 52 2 ElectromagneticForceandMaxwellStressTensor ..................... 54 3 TheEffectofaStaticMagneticField(DirectMagnetic Field)onaFlow........................................................... 55 4 DiffusionofaMagneticField ............................................ 62 4.1 SimplifiedModel.................................................. 62 4.2 Diffusion Model of a Magnetic Field in One-DimensionalSemi-infiniteSpace ........................... 63 4.3 MagneticPressureandJouleHeat................................ 64 4.4 DiffusionModelofaMagneticFieldinLimited One-Dimension.................................................... 67 4.5 TravelingMagneticField ......................................... 70 5 BoundaryConditions ..................................................... 74 6 DimensionlessNumbersRelatingtoMagnetohydrodynamics.......... 77 7 SolutionsofProblems3.1–3.12.......................................... 80 References..................................................................... 86 4 ElectromagneticProcessingofMaterials.................................. 87 1 FunctionsofElectricandMagneticFieldsPerforming onElectricallyConductiveFluids........................................ 87 1.1 ShapeControllingFunction....................................... 87 1.2 FlowSuppressingFunction....................................... 90 1.3 WaveSuppressingFunction....................................... 91 1.4 SeparatingandAgglomeratingFunctions........................ 91 1.5 Driving(Mixing)Function........................................ 92 1.6 Oscillating(Vibrating)Function.................................. 94 1.7 SplashingFunction................................................ 94 1.8 Levitating(GravityChanging)Function ......................... 94 1.9 TemperatureRaisingFunction.................................... 95 1.10 FlowVelocityDetectingFunction................................ 95 1.11 CompoundFunction............................................... 96 2 ProcessesUsingElectromagneticForce ................................. 96 2.1 ShapeControllingFunction....................................... 96 2.2 FlowSuppressingFunction....................................... 101