The Theory Of Laser Materials Processing
Heat And Mass Transfer In Modern Technology (Springer Series In Materials Science)
Theuseoflasersinmaterialsprocessinghasbecomewidespreadinrecent years, sothatanunderstandingofthenatureofheatandmasstransferin thisbranchofmoderntechnologyisofincreasingimportance. Theaimofthe authorsofthisbookistoconcentrateonthephysicalprocesses;thesecanbe developedfromamathematicalpointofview, orfromdirectexperimental- derivedobservation. Thetwoapproachesarecomplementary;eachcanprovide insightsandthesynthesisofthetwocanleadtoaverypowerfulunderstanding oftheprocessesinvolved. Mathematicalmodellingofphysicalprocesseshas hadanimportantroletoplayinthedevelopmentoftechnologyoverthe centuriesandparticularlysointhelastonehundredand?ftyyearsorso. Itcanbearguedthatitismoreimportanttodaythaneverbeforesincethe availabilityofhigh-speedcomputersallowsaccuratenumericalsimulationof industrialprocessesatafractionofthecostofthecorrespondingexperiments. Thisisoneaspectofmathematicalmodelling, highpro?leandmuchvalued, butitisnottheonlyone. Inthepastmathematicalmodellinghadtorelyonqualitativeinves- gation, veryspecialanalyticalsolutions, orinaccurateandtime-consuming calculationsperformedwithlittleinthewayoftabulatedormechanical assistance. Logtablesandsliderulesarestillrememberedbypeopleworking today, thoughtherearesurelyfewwhoregrettheirdisappearance. Thevalueanddistinctivefunctionofmethodsbasedontheanalytical approachisnowbecomingmuchclearer, nowthattheyarenolongerexpected toproducedetailedimitationsofwhathappensinrealexperimentsofind- trialprocesses, afunctionnowful?lledmostlybynumericalmethods, c- sideredbelow. Theemphasistodayisontheirabilitytocon?rmandextend ourunderstandingofthebasicphysicalmechanismsinvolvedintheprocesses of interest. These are essential for any intelligent use of numerical simulation. Theargumentaboutthevalueofteachingpeoplehowtodoarithmetic themselveswithouttheaidofacalculatorseemstobepassingintohistory, vi Preface butitisanimportantoneandprovidesasimpleanalogy. Ifsomeonedoes nothaveafeelingfornumbersandthewayarithmeticworks, theywillalltoo easilyfailtospotanerrorproducedbyamachine. Computersarenotinfallible andneitherarethosewhobuildorprogramthem. Computersarenow takingonlessmundanemathematicaltasksandthesamecontroversiesare appearinginconnectionwithalgebraicmanipulation. Equally, andwitheven greaterpenaltiesintermsofcostintheeventoferrors, thesameconsiderations applytonumericalsimulationofmajorindustrialprocesses. Awarenessofthe analyticalsolutionscanbeinvaluableindistinguishingtherightfromthe wrong, i. e. forthepractitionertounderstandthebasisofthework, andto haveanideaofthekindsofoutcomesthatareplausible andtorecognise thosewhicharenot. Thephrase mathematicalmodelling is, however, ambiguous, perhaps morenowthanithaseverbeen. Thereisanenormousamountofworkdone todayonsimulationbasedontheuseofverypowerfulcomputerprograms, anditisquitecorrectlyreferredtoasmathematicalmodelling. Theprograms aresometimesconstructedin-housebutareusuallycommercialpackages. This isanentirelyvalidapproachwithspeci?c(generallycommercial)objectives. Ingeneraltherearetwouses. Thedominantobjectiveisnumericalagreement withaparticularexperimentinthe?rstinstance, leadingtopredictivec- mercialuseinthesecondinstance. Thesecondobjectiveistheclari?cation ofphysicalmechanisms, aimedatthegenerationofunderstandingofcomplex interconnectedprocesses, ratherthantheexactreproductionofaparticular experiment. Itissometimesoverlookedthat, withsu?cientcare, anum- icalapproachisequallyvalidintheinvestigationofphysicalfundamentals. Numericalsimulationisnotacentraltopicofthisbook, butbecauseofits crucialimportancetoeachofthetwousestowhichnumericalmodellingcan beput, itisvitalthatthecomputationalbasisoftheworkshouldbec- pletelysound. Inaddition, thelevelofprocessdetailwhichcanbeconsidered bythenumericalapproachusuallyexceedswhatispossiblewiththeanaly- calapproachsigni?cantly, leavinglittlechoicebuttoreverttothenumerical treatmentwheninvestigatingtheinterconnectionsbetweenprocesses. Itis forthesereasonsthatthebookconcludeswithachapteroncomprehensive numericalsimulation. Inmanyways, theapproachadoptedhereiscomplementarytothemore phenomenologicalapproach. Itisalwaysimportantina?eldwhichhasvery directindustrialapplicationstobearinmindhowtechniquessuchasthose describedherewillbeused, butitisessentialnottolosesightofthef- damentals. Thereareserioussafetyimplications;therearecostimplications; therearemoralimplications;thereareconsiderationsoftheappropriateness ofthetechnologytotheapplicationunderconsideration. Aproperrespectfor alltheserequiresanunderstandingofthefundamentals. Wearealltoowellawarethatthisbookdoeslittlemorethanscratch thesurfaceoftheproblemsinvolvedinafundamentalunderstandingofthese phenomena. Ifwehaveprovidedideasandinformationthatcauseothersto Preface vii testthemexperimentallyorintellectually, agreewiththemordisputethem vigorously, anddevelopthemfurther, wewillconsiderthatwehaveachieved ouraim. Colchester April,2008 JohnDowden Contents 1MathematicsinLaserProcessing JohnDowden. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1 MathematicsanditsApplication. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2 FormulationinTermsofPartialDi?erentialEquations. . . . . . . . . 3 1. 2. 1 LengthScales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 2. 2 ConservationEquationsandtheirGeneralisations. . . . . . 4 1. 2. 3 GoverningEquationsofGeneralised ConservationType. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1. 2. 4 Gauss sLaw. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1. 3 BoundaryandInterfaceConditions. . . . . . . . . . . . . . . . . . . . . . . . . . 11 1. 3. 1 GeneralisedConservationConditions. . . . . . . . . . . . . . . . . 11 1. 3. 2 TheKinematicConditioninFluidDynamics. . . . . . . . . . 13 1. 4 Fick sLaws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1. 5 Electromagnetism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1. 5. 1 Maxwell sEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1. 5. 2 Ohm sLaw. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2SimulationofLaserCutting WolfgangSchulz, MarkusNiessen, UrsEppelt, KerstinKowalick. . . . . . . . 21 2. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2. 1. 1 PhysicalPhenomenaandExperimentalObservation. . . . 23 2. 2 MathematicalFormulationandAnalysis. . . . . . . . . . . . . . . . . . . . . . 26 2. 2. 1 TheOne-PhaseProblem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2. 2. 2 TheTwo-PhaseProblem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2. 2. 3 Three-PhaseProblem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2. 3 Outlook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2. 4 Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 x Contents 3KeyholeWelding: TheSolidandLiquidPhases AlexanderKaplan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3. 1 HeatGenerationandHeatTransfer. . . . . . . . . . . . . . . . . . . . . . . . . . 71 3. 1. 1 Absorption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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ذخیره و ثبت ترجمه
گزارش تخلف
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