Transport Phenomena: An Introduction to Advanced Topics

281 Pages·2010·7.873 MB·English

by  Larry A. Glasgow

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TRANSPORTPHENOMENA
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TRANSPORT PHENOMENA
An Introduction to Advanced Topics
LARRYA.GLASGOW
ProfessorofChemicalEngineering
KansasStateUniversity
Manhattan,Kansas
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LibraryofCongressCataloging-in-PublicationData
Glasgow,LarryA.,1950-
Transportphenomena:anintroductiontoadvancedtopics/LarryA.Glasgow.
p.cm.
Includesindex.
ISBN978-0-470-38174-8(cloth)
1.Transporttheory–Mathematics. I.Title.
TP156.T7G552010
530.4’75–dc22
2009052127
PrintedintheUnitedStatesofAmerica
10987654321
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CONTENTS
Preface ix 3.13 FlowsinOpenChannels, 41
3.14 PulsatileFlowsinCylindricalDucts, 42
3.15 SomeConcludingRemarksforIncompressible
1. IntroductionandSomeUsefulReview 1
ViscousFlows, 43
1.1 AMessagefortheStudent, 1
References, 44
1.2 DifferentialEquations, 3
1.3 ClassificationofPartialDifferentialEquationsand
BoundaryConditions, 7 4. ExternalLaminarFlowsandBoundary-Layer
1.4 NumericalSolutionsforPartialDifferential Theory 46
Equations, 8 4.1 Introduction, 46
1.5 Vectors,Tensors,andtheEquationofMotion, 8 4.2 TheFlatPlate, 47
1.6 TheMenforWhomtheNavier-StokesEquations 4.3 FlowSeparationPhenomenaAboutBluff
areNamed, 12 Bodies, 50
1.7 SirIsaacNewton, 13 4.4 BoundaryLayeronaWedge:TheFalkner–Skan
References, 14 Problem, 52
4.5 TheFreeJet, 53
2. InviscidFlow:SimplifiedFluidMotion 15 4.6 IntegralMomentumEquations, 54
2.1 Introduction, 15 4.7 HiemenzStagnationFlow, 55
2.2 Two-DimensionalPotentialFlow, 16 4.8 FlowintheWakeofaFlatPlateatZero
2.3 NumericalSolutionofPotentialFlowProblems, 20 Incidence, 56
2.4 Conclusion, 22 4.9 Conclusion, 57
References, 23 References, 58
3. LaminarFlowsinDuctsandEnclosures 24 5. Instability,Transition,andTurbulence 59
3.1 Introduction, 24 5.1 Introduction, 59
3.2 Hagen–PoiseuilleFlow, 24 5.2 LinearizedHydrodynamicStabilityTheory, 60
3.3 TransientHagen–PoiseuilleFlow, 25 5.3 InviscidStability:TheRayleighEquation, 63
3.4 PoiseuilleFlowinanAnnulus, 26 5.4 StabilityofFlowBetweenConcentric
3.5 DuctswithOtherCrossSections, 27 Cylinders, 64
3.6 CombinedCouetteandPoiseuilleFlows, 28 5.5 Transition, 66
3.7 CouetteFlowsinEnclosures, 29 5.5.1 TransitioninHagen–Poiseuille
3.8 GeneralizedTwo-DimensionalFluidMotionin Flow, 66
Ducts, 32 5.5.2 TransitionfortheBlasiusCase, 67
3.9 SomeConcernsinComputationalFluid 5.6 Turbulence, 67
Mechanics, 35 5.7 HigherOrderClosureSchemes, 71
3.10 FlowintheEntranceofDucts, 36 5.7.1 Variations, 74
3.11 CreepingFluidMotionsinDuctsandCavities, 38 5.8 IntroductiontotheStatisticalTheoryof
3.12 Microfluidics:FlowinVerySmallChannels, 38 Turbulence, 74
3.12.1 ElectrokineticPhenomena, 39 5.9 Conclusion, 79
3.12.2 GasesinMicrofluidics, 40 References, 81
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vi CONTENTS
6. HeatTransferbyConduction 83 8.2 UnsteadyEvaporationofVolatileLiquids:The
6.1 Introduction, 83 ArnoldProblem, 120
6.2 Steady-StateConductionProblemsin 8.3 DiffusioninRectangularGeometries, 122
RectangularCoordinates, 84 8.3.1 DiffusionintoQuiescentLiquids:
6.3 TransientConductionProblemsinRectangular Absorption, 122
Coordinates, 86 8.3.2 AbsorptionwithChemicalReaction, 123
6.4 Steady-StateConductionProblemsinCylindrical 8.3.3 Concentration-DependentDiffusivity, 124
Coordinates, 88 8.3.4 DiffusionThroughaMembrane, 125
6.5 TransientConductionProblemsinCylindrical 8.3.5 DiffusionThroughaMembranewith
Coordinates, 89 VariableD, 125
6.6 Steady-StateConductionProblemsinSpherical 8.4 DiffusioninCylindricalSystems, 126
Coordinates, 92 8.4.1 ThePorousCylinderinSolution, 126
6.7 TransientConductionProblemsinSpherical 8.4.2 TheIsothermalCylindricalCatalyst
Coordinates, 93 Pellet, 127
6.8 Kelvin’sEstimateoftheAgeoftheEarth, 95 8.4.3 DiffusioninSquat(SmallL/d)
6.9 SomeSpecializedTopicsinConduction, 95 Cylinders, 128
6.9.1 ConductioninExtendedSurfaceHeat 8.4.4 DiffusionThroughaMembranewithEdge
Transfer, 95 Effects, 128
6.9.2 AnisotropicMaterials, 97 8.4.5 DiffusionwithAutocatalyticReactionina
6.9.3 CompositeSpheres, 99 Cylinder, 129
6.10 Conclusion, 100 8.5 DiffusioninSphericalSystems, 130
References, 100 8.5.1 TheSphericalCatalystPelletwith
ExothermicReaction, 132
8.5.2 SorptionintoaSpherefromaSolutionof
7. HeatTransferwithLaminarFluidMotion 101
LimitedVolume, 133
7.1 Introduction, 101
8.6 SomeSpecializedTopicsinDiffusion, 133
7.2 ProblemsinRectangularCoordinates, 102
8.6.1 DiffusionwithMovingBoundaries, 133
7.2.1 CouetteFlowwithThermalEnergy
8.6.2 DiffusionwithImpermeable
Production, 103
Obstructions, 135
7.2.2 ViscousHeatingwith
8.6.3 DiffusioninBiologicalSystems, 135
Temperature-DependentViscosity, 104
8.6.4 ControlledRelease, 136
7.2.3 TheThermalEntranceRegioninRectangular
8.7 Conclusion, 137
Coordinates, 104
References, 137
7.2.4 HeatTransfertoFluidMovingPastaFlat
Plate, 106
7.3 ProblemsinCylindricalCoordinates, 107 9. MassTransferinWell-CharacterizedFlows 139
7.3.1 ThermalEntranceLengthinaTube:The 9.1 Introduction, 139
GraetzProblem, 108 9.2 ConvectiveMassTransferinRectangular
7.4 NaturalConvection:Buoyancy-InducedFluid Coordinates, 140
Motion, 110 9.2.1 ThinFilmonaVerticalWall, 140
7.4.1 VerticalHeatedPlate:ThePohlhausen 9.2.2 ConvectiveTransportwithReactionatthe
Problem, 110 Wall, 141
7.4.2 TheHeatedHorizontalCylinder, 111 9.2.3 MassTransferBetweenaFlowingFluidand
7.4.3 NaturalConvectioninEnclosures, 112 aFlatPlate, 142
7.4.4 Two-DimensionalRayleigh–Benard 9.3 MassTransferwithLaminarFlowinCylindrical
Problem, 114 Systems, 143
7.5 Conclusion, 115 9.3.1 FullyDevelopedFlowinaTube, 143
References, 116 9.3.2 VariationsforMassTransferinaCylindrical
Tube, 144
8. DiffusionalMassTransfer 117 9.3.3 MassTransferinanAnnuluswithLaminar
8.1 Introduction, 117 Flow, 145
8.1.1 DiffusivitiesinGases, 118 9.3.4 HomogeneousReactioninFully-Developed
8.1.2 DiffusivitiesinLiquids, 119 LaminarFlow, 146
CONTENTS vii
9.4 MassTransferBetweenaSphereandaMoving 11.2 Liquid–LiquidSystems, 180
Fluid, 146 11.2.1 DropletBreakage, 180
9.5 SomeSpecializedTopicsinConvectiveMass 11.3 Particle–FluidSystems, 183
Transfer, 147 11.3.1 IntroductiontoCoagulation, 183
9.5.1 UsingOscillatoryFlowstoEnhance 11.3.2 CollisionMechanisms, 183
InterphaseTransport, 147 11.3.3 Self-PreservingSizeDistributions, 186
9.5.2 ChemicalVaporDepositioninHorizontal 11.3.4 DynamicBehavioroftheParticleSize
Reactors, 149 Distribution, 186
9.5.3 DispersionEffectsinChemical 11.3.5 OtherAspectsofParticleSizeDistribution
Reactors, 150 Modeling, 187
9.5.4 TransientOperationofaTubular 11.3.6 AHighlySimplifiedExample, 188
Reactor, 151 11.4 MulticomponentDiffusioninGases, 189
9.6 Conclusion, 153 11.4.1 TheStefan–MaxwellEquations, 189
References, 153 11.5 Conclusion, 191
References, 192
10. HeatandMassTransferinTurbulence 155
ProblemstoAccompanyTransportPhenomena:An
10.1 Introduction, 155
IntroductiontoAdvancedTopics 195
10.2 SolutionThroughAnalogy, 156
10.3 ElementaryClosureProcesses, 158
AppendixA:FiniteDifferenceApproximationsfor
10.4 ScalarTransportwithTwo-EquationModelsof
Derivatives 238
Turbulence, 161
10.5 TurbulentFlowswithChemicalReactions, 162
AppendixB:AdditionalNotesonBessel’sEquationand
10.5.1 SimpleClosureSchemes, 164
BesselFunctions 241
10.6AnIntroductiontopdfModeling, 165
10.6.1 TheFokker–PlanckEquationandpdf
AppendixC:SolvingLaplaceandPoisson(Elliptic)
ModelingofTurbulentReactive
PartialDifferentialEquations 245
Flows, 165
10.6.2 TransportedpdfModeling, 167
AppendixD:SolvingElementaryParabolicPartial
10.7 TheLagrangianViewofTurbulent
DifferentialEquations 249
Transport, 168
10.8 Conclusions, 171
AppendixE:ErrorFunction 253
References, 172
AppendixF:GammaFunction 255
11. TopicsinMultiphaseandMulticomponent
Systems 174 AppendixG:RegularPerturbation 257
11.1 Gas–LiquidSystems, 174
11.1.1 GasBubblesinLiquids, 174 AppendixH:SolutionofDifferentialEquationsby
11.1.2 BubbleFormationatOrifices, 176 Collocation 260
11.1.3 BubbleOscillationsandMass
Transfer, 177 Index 265
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