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1、HeatConductionLiqiuWang·XueshengZhou·XiaohaoWeiHeatConductionMathematicalModelsandAnalyticalSolutions123LiqiuWangXueshengZhouXiaohaoWeiDepartmentofMechanicalEngineeringTheUniversityofHongKongPokfulamRoadHongKongP.R.Chinalqwang@hku.hkISBN-13978-3-540-74028-5e-ISBN-13978-3
2、-540-74303-3DOI10.1007/978-3-540-74303-3LibraryofCongressControlNumber:2007932886©2008Springer-VerlagBerlinHeidelbergThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillust
3、rations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfrom
4、Springer.ViolationsareliabletoprosecutionundertheGermanCopyrightLaw.Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandtheref
5、orefreeforgeneraluse.Coverdesign:ErichKirchner,HeidelbergTypesettingandProduction:LE-TEXJelonek,Schmidt&VöcklerGbR,LeipzigPrintedonacid-freepaper987654321springer.comPrefaceAsanimportanttransportprocess,heatconductionisgovernedbythefirstlawofthermodynamics,ortheconservati
6、onofenergy.Theheat-conductionequationisitsmathematicalrepresentationforheatconductionprocesses.However,wecanhavedifferenttypesofheat-conductionequationsdependingonwhichconstitutivere-lationsofheatfluxdensity,therelationsbetweentheheatfluxdensityvectorandthetemperaturegradi
7、ent,areused.Thedual-phase-laggingconstitutiverelationwasfirstproposedbyProfessorD.Y.Tzouin1995andisusedfordescribingheatcon-ductioninvolvinghighheatfluxandstrongunsteadiness,whereheatconductionismicrobothintimeandinspace.ItstwoimportantspecialcasesaretheCattaneoVernottecon
8、stitutiverelationandtheFourierlawofheatconduction.Theformerisappropriatefordescribingheatconductionthat
