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1、VISCOUSFLUIDFLOWVISCOUSFLUIDFLOWbyTasosC.PapanastasiouGeorgiosC.GeorgiouDepartmentofMathematicsandStatisticsUniversityofCyprusNicosia,CyprusAndreasN.AlexandrouDepartmentofMechanicalEngineeringWorcesterPolytechnicInstituteWorcester,MACRCPressBocaRatonLondonNewYorkWa
2、shington,D.C.ToAndroula,CharisandYiangosPapanastasiouandtoDimitra,NadiaandLisaContentsPREFACE1VECTORANDTENSORCALCULUS1.1SystemsofCoordinates1.2Vectors1.2.1VectorsinFluidMechanics1.2.2UnitTangentandNormalVectors1.3Tensors1.3.1PrincipalDirectionsandInvariants1.3.2Ind
3、exNotationandSummationConvention1.3.3TensorsinFluidMechanics1.4Di?erentialOperators1.4.1TheSubstantialDerivative1.5IntegralTheorems1.6Problems1.7References2INTRODUCTIONTOTHECONTINUUMFLUID2.1PropertiesoftheContinuumFluid2.2MacroscopicandMicroscopicBalances2.3LocalFl
4、uidKinematics2.4ElementaryFluidMotions2.5Problems2.6References3CONSERVATIONLAWS3.1ControlVolumeandSurroundings3.2TheGeneralEquationsofConservation3.3TheDi?erentialFormsoftheConservationEquations3.4Problems3.5References4STATICEQUILIBRIUMOFFLUIDSANDINTERFACES4.1Mecha
5、nicsofStaticEquilibrium4.2MechanicsofFluidInterfaces4.2.1InterfacesinStaticEquilibrium4.3Problems4.4References5THENAVIER-STOKESEQUATIONS5.1TheNewtonianLiquid5.2AlternativeFormsoftheNavier-StokesEquations5.3BoundaryConditions5.4Problems5.5References6UNIDIRECTIONALFL
6、OWS6.1Steady,One-DimensionalRectilinearFlows6.2Steady,AxisymmetricRectilinearFlows6.3Steady,AxisymmetricTorsionalFlows6.4Steady,AxisymmetricRadialFlows6.5Steady,SphericallySymmetricRadialFlows6.6TransientOne-DimensionalUnidirectionalFlows6.7SteadyTwo-DimensionalRec
7、tilinearFlows6.8Problems6.9References7APPROXIMATEMETHODS7.1DimensionalAnalysis7.1.1Non-dimensionalizationoftheGoverningEquations7.2PerturbationMethods7.2.1RegularPerturbations7.2.2SingularPerturbations7.3PerturbationMethodsinFluidMechanics7.4Problems7.5References8L
8、AMINARBOUNDARYLAYERFLOWS8.1BoundaryLayerFlow8.2BoundaryLayerEquations8.3ApproximateMomentumIntegralTheory8.4BoundaryLayerswithinAcceleratingPoten
