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Chapter 0 The Subject of Transport Phenomena1

Part Ⅰ Momentum TransportChapter 1 Viscosity and the Mechanisms of Momentum Transport11

1.1 Newton's Law of Viscosity（Molecular Momentum Transport）11

Ex.1.1-1 Calculation of Momentum Flux15

1.2 Generalization of Newton's Law of Viscosity16

1.3 Pressure and Temperature Dependence of Viscosity21

Ex.1.3-1 Estimation of Viscosity from Critical Properties23

1.4 Molecular Theory of the Viscosity of Gases at Low Density23

Ex.1.4-1 Computation of the Viscosity of a Gas Mixture at Low Density28

Ex.1.4-2 Prediction of the Viscosity of a Gas Mixture at Low Density28

1.5 Molecular Theory of the Viscosity of Liquids29

Ex.1.5-1 Estimation of the Viscosity of a Pure Liquid31

1.6 Viscosity of Suspensions and Emulsions31

1.7 Convective Momentum Transport34

Questions for Discussion37

Problems37

Chapter 2 Shell Momentum Balances and Velocity Distributions in Laminar Flow40

2.1 Shell Momentum Balances and Boundary Conditions41

2.2 Flow of a Falling Film42

Ex.2.2-1 Calculation of Film Velocity47

Ex.2.2-2 Falling Film with Variable Viscosity47

2.3 Flow Through a Circular Tube48

Ex.2.3-1 Determination of Viscosity from Capillary Flow Data52

Ex.2.3-2 Compressible Flow in a Horizontal Circular Tube53

2.4 Flow through an Annulus53

2.5 Flow of Two Adjacent Immiscible Fluids56

2.6 Creeping Flow around a Sphere58

Ex.2.6-1 Determination of Viscosity from the Terminal Velocity of a Falling Sphere61

Questions for Discussion61

Problems62

Chapter 3 The Equations of Change for Isothermal Systems75

3.1 The Equation of Continuity77

Ex.3.1-1 Normal Stresses at Solid Surfaces for Incompressible Newtonian Fluids78

3.2 The Equation of Motion78

3.3 The Equation of Mechanical Energy81

3.4 The Equation of Angular Momentum82

3.5 The Equations of Change in Terms of the Substantial Derivative83

Ex.3.5-1 The Bernoulli Equation for the Steady Flow of Inviscid Fluids86

3.6 Use of the Equations of Change to Solve Flow Problems86

Ex.3.6-1 Steady Flow in a Long Circular Tube88

Ex.3.6-2 Falling Film with Variable Viscosity89

Ex.3.6-3 Operation ofa Couette Viscometer89

Ex.3.6-4 Shape of the Surface of a Rotating Liquid93

Ex.3.6-5 Flow near a Slowly Rotating Sphere95

3.7 Dimensional Analysis of the Equations of Change97

Ex.3.7-1 Transverse Flow around a Circular Cylinder98

Ex.3.7-2 Steady Flow in an Agitated Tank101

Ex.3.7-3 Pressure Drop for Creeping Flow in a Packed Tube103

Questions for Discussion104

Problems104

Chapter 4 Velocity Distributions with More than One Independent Variable114

4.1 Time-Dependent Flow of Newtonian Fluids114

Ex.4.1-1 Flow near a Wall Suddenly Set in Motion115

Ex.4.1-2 Unsteady Laminar Flow between Two Parallel Plates117

Ex.4.1-3 Unsteady Laminar Flow near an Oscillating Plate120

4.2 Solving Flow Problems Using a Stream Function121

Ex.4.2-1 Creeping Flow around a Sphere122

4.3 Flow of Inviscid Fluids by Use of the Velocity Potential126

Ex.4.3-1 Potential Flow around a Cylinder128

Ex.4.3-2 Flow into a Rectangular Channel130

Ex.4.3-3 Flow near a Corner131

4.4 Flow near Solid Surfaces by Boundary-Layer Theory133

Ex.4.4-1 Laminar Flow along a Flat Plate（Approximate Solution）136

Ex.4.4-2 Laminar Flow along a Flat Plate（Exact Solution）137

Ex.4.4-3 Flow near a Corner139

Questions for Discussion140

Problems141

Chapter 5 Velocity Distributions in Turbulent Flow152

5.1 Comparisons of Laminar and Turbulent Flows154

5.2 Time-Smoothed Equations of Change for Incompressible Fluids156

5.3 The Time-Smoothed Velocity Profile near a Wall159

5.4 Empirical Expressions for the Turbulent Momentum Flux162

Ex.5.4-1 Development of the Reynolds Stress Expression in the Vicinity of the Wall164

5.5 Turbulent Flow in Ducts165

Ex.5.5-1 Estimation of the Average Velocity in a Circular Tube166

Ex.5.5-2 Application of Prandtl's Mixing Length Formula to Turbulent Flow in a Circular Tube167

Ex.5.5-3 Relative Magnitude of Viscosity and Eddy Viscosity167

5.6 Turbulent Flow in Jets168

Ex.5.6-1 Time-Smoothed Velocity Distribution in a Circular Wall Jet168

Questions for Discussion172

Problems172

Chapter 6 Interphase Transport in Isothermal Systems177

6.1 Definition of Friction Factors178

6.2 Friction Factors for Flow in Tubes179

Ex.6.2-1 Pressure Drop Required for a Given Flow Rate183

Ex.6.2-2 Flow Rate for a Given Pressure Drop183

6.3 Friction Factors for Flow around Spheres185

Ex.6.3-1 Determination of the Diameter of a Falling Sphere187

6.4 Friction Factors for Packed Columns188

Questions for Discussion192

Problems193

Chapter 7 Macroscopic Balances for Isothermal Flow Systems197

7.1 The Macroscopic Mass Balance198

Ex.7.1-1 Draining of a Spherical Tank199

7.2 The Macroscopic Momentum Balance200

Ex.7.2-1 Force Exerted by a 1et （Part a）201

7.3 The Macroscopic Angular Momentum Balance202

Ex.7.3-1 Torque on a Mixing Vessel202

7.4 The Macroscopic Mechanical Energy Balance203

Ex.7.4-1 Force Exerted by a Jet（Part b）205

7.5 Estimation of the Viscous Loss205

Ex.7.5-1 Power Requirement for Pipeline Flow207

7.6 Use of the Macroscopic Balances for Steady-State Problems209

Ex.7.6-1 Pressure Rise and Friction Loss in a Sudden Enlargement209

Ex.7.6-2 Performance of a Liquid-Liquid Ejector210

Ex.7.6-3 Thrust on a Pipe Bend212

Ex.7.6-4 The Impinging Jet214

Ex.7.6-5 Isothermal Flow of a Liquid through an Orifice215

7.7 Use of the Macroscopic Balances for Unsteady-State Problems216

Ex.7.7.1 Acceleration Effects in Unsteady Flow from a Cylindrical Tank217

Ex.7.7-2 Manometer Oscillations219

7.8 Derivation of the Macroscopic Mechanical Energy Balance221

Questions for Discussion223

Problems224

Chapter 8 Polymeric Liquids231

8.1 Examples of the Behavior of Polymeric Liquids232

8.2 Rheometry and Material Functions236

8.3 Non-Newtonian Viscosity and the Generalized Newtonian Models240

Ex.8.3-1 Laminar Flow of an Incompressible Power-Law Fluid in a Circular Tube242

Ex.8.3-2 Flow of a Power-Law Fluid in a Narrow Slit243

Ex.8.3-3 Tangential Annular Flow of a Power-Law Fluid244

8.4 Elasticity and the Linear Viscoelastic Models244

Ex.8.4-1 Small-Amplitude Oscillatory Motion247

Ex.8.4-2 Unsteady Viscoelastic Flow near an Oscillating Plate248

8.5 The Corotational Derivatives and the Nonlinear Viscoelastic Models249

Ex.8.5-1 Material Functions for the Oldroyd 6-Constant Model251

8.6 Molecular Theories for Polymeric Liquids253

Ex.8.6-1 Material Functions for the FENE-P Model255

Questions for Discussion258

Problems258

Part Ⅱ Energy Transport263

Chapter 9 Thermal Conductivity and the Mechanisms of Energy Transport263

9.1 Fouriers Law of Heat Conduction（Molecular Energy Transport）266

Ex.9.1-1 Measurement of Thermal Conductivity270

9.2 Temperature and Pressure Dependence of Thermal Conductivity272

Ex.9.2-1 Effect of Pressure on Thermal Conductivity273

9.3Theory of Thermal Conductivity of Gases at Low Density274

Ex.9.3-1 Computation of the Thermal Conductivity of a Monatomic Gas at Low Density277

Ex.9.3-2 Estimation of the Thermal Conductivity of a Polyatomic Gas at Low Density278

Ex.9.3-3 Prediction of the Thermal Conductivity of a Gas Mixture at Low Density278

9.4 Theory of Thermal Conductivity of Liquids279

Ex.9.4-1 Prediction of the Thermal Conductivity of a Liquid280

9.5 Thermal Conductivity of Solids280

9.6 Effective Thermal Conductivity of Composite Solids281

9.7 Convective Transport of Energy283

9.8 Work Associated with Molecular Motions284

Questions for Discussion286

Problems287

Chapter 10 Shell Energy Balances and Temperature Distributions in Solids and Laminar Flow290

10.1 Shell Energy Balances;Boundary Conditions291

10.2 Heat Conduction with an Electrical Heat Source292

Ex.10.2-1 Voltage Required for a Given Temperature Rise in a Wire Heated by an Electric Current295

Ex.10.2-2 Heated Wire with Specified Heat Transfer Coefficient and Ambient Air Temperature295

10.3 Heat Conduction with a Nuclear Heat Source296

10.4 Heat Conduction with a Viscous Heat Source298

10.5 Heat Conduction with a Chemical Heat Source300

10.6 Heat Conduction through Composite Walls303

Ex.10.6-1 Composite Cylindrical Walls305

10.7 Heat Conduction in a Cooling Fin307

Ex.10.7-1 Error in Thermocouple Measurement309

10.8 Forced Convection310

10.9 Free Convection316

Questions for Discussion319

Problems320

Chapter 11 The Equations of Change for Nonisothermal Systems333

11.1 The Energy Equation333

11.2 Special Forms of the Energy Equation336

11.3 The Boussinesq Equation of Motion for Forced and Free Convection338

11.4 Use of the Equations of Change to Solve Steady-State Problems339

Ex.11.4-1 Steady-State Forced-Convection Heat Transfer in Laminar Flow in a Circular Tube342

Ex.11.4-2 Tangential Flow in an Annulus with Viscous Heat Generation342

Ex.11.4-3 Steady Flow in a Nonisothermal Film343

Ex.11.4-4 Transpiration Cooling344

Ex.11.4-5 Free Convection Heat Transfer from a Vertical Plate346

Ex.11.4-6 Adiabatic Frictionless Processes in an Ideal Gas349

Ex.11.4-7 One-Dimensional Compressible Flow：Velocity,Temperature,and Pressure Profiles in a Stationary Shock Wave350

11.5 Dimensional Analysis of the Equations of Change for Nonisothermal Systems353

Ex.11.5-1 Temperature Distribution about a Long Cylinder356

Ex.11.5-2 Free Convection in a Horizontal Fluid Layer;Formation of Bénard Cells358

Ex.11.5-3 Surface Temperature of an Electrical Heating Coil360

Questions for Discussion361

Problems361

Chapter 12 Temperature Distributions with More than One Independent Variable374

12.1 Unsteady Heat Conduction in Solids374

Ex.12.1-1 Heatingofa Semi-Infinite Slab375

Ex.12.1-2 Heatingofa Finite Slab376

Ex.12.1-3 Unsteady Heat Conduction near a Wall with Sinusoidal Heat Flux379

Ex.12.1-4 Coolingofa Sphere in Contact with a Well-Stirred Fluid379

12.2Steady Heat Conduction in Laminar,Incompressible Flow381

Ex.12.2-1 Laminar Tube Flow with Constant Heat Flux at the Wall383

Ex.12.2-2 Laminar Tube Flow with Constant Heat Flux at the Wall：Asymptotic Solution for the Entrance Region384

12.3Steady Potential Flow of Heat in Solids385

Ex.12.3-1 Temperature Distribution in a Wall386

12.4Boundary Layer Theory for Nonisothermal Flow387

Ex.12.4-1 Heat Transfer in Laminar Forced Convection along a Heated Flat Plate（the von Kármán Integral Method）388

Ex.12.4-2 Heat Transfer in Laminar Forced Convection along a Heated Flat Plate（Asymptotic Solution for Large Prandtl Numbers）391

Ex.12.4-3 Foreed Convection in Steady Three-Dimensional Flow at High Prandtl Numbers392

Questions for Discussion394

Problems395

Chapter 13 Temperature Distributions in Turbulent Flow407

13.1 Time-Smoothed Equations of Change for Incompressible Nonisothermal Flow407

13.2 The Time-Smoothed Temperature Profile near a Wall409

13.3 Empirical Expressions for the Turbulent Heat Flux410

Ex.13.3-1 An Approximate Relation for the Wall Heat Flux for Turbulent Flow in a Tube411

13.4 Temperature Distribution for Turbulent Flow in Tubes411

13.5 Temperature Distribution for Turbulent Flow in Jets415

13.6 Fourier Analysis of Energy Transport in Tube Flow at Large Prandtl Numbers416

Questions for Discussion421

Problems421

Chapter 14 Interphase Transport in Nonisothermal Systems422

14.1 Definitions of Heat Transfer Coefficients423

Ex.14.1-1 Calculation of Heat Transfer Coefficients from Experimental Data426

14.2 Analytical Calculations of Heat Transfer Coefficients for Forced Convection through Tubes and Slits428

14.3 Heat Transfer Coefficients for Forced Convection in Tubes433

Ex.14.3-1 Design of a Tubular Heater437

14.4 Heat Transfer Coefficients for Forced Convection around Submerged Objects438

14.5 Heat Transfer Coefficients for Forced Convection through Packed Beds441

14.6 Heat Transfer Coefficients for Free and Mixed Convection442

Ex14.6-1 Heat Loss bu Free Convection from a Horizontal Pipe445

14.7 Heat Transfer Coefficients for Condensation of Pure Vapors on Solid Surfaces446

Ex.14.7-1 Condensation of Steam on a Vertical Surface449

Questions for Discussion449

Problems450

Chapter 15 Macroscopic Balances for Nonisothermal Systems454

15.1 The Macroscopic Energy Balance455

15.2 The Macroscopic Mechanical Energy Balance456

15.3 Use of the Macroscopic Balances to Solve Steady-State Problems with Flat Velocity Profiles458

Ex.15.3-1 The Cooling of an Ideal Gas459

Ex.15.3-2 Mixing of Tuo Ideal Gas Streams460

15.4 The d-Forms of the Macroscopic Balances461

Ex.15.4-1 Parallel-or Counter-Flow Heat Exchangers462

Ex.15.4-2 Power Requirement for Pumping a Compressible Fluid through a Long Pipe464

15.5 Use of the Macroscopic Balances to Solve Unsteady-State Problems and Problems with Nonflat Velocity Profiles465

Ex.15.5-1 Heating ofa Liquid in an Agitated Tank466

Ex.15.5-2 Operation ofa Simple Temperature Controller468

Ex.15.5-3 Flow of Compressible Fluids through Heat Meters471

Ex.15.5-4 Free Batch Expansion of a Compressible Fluid472

Questions for Discussion474

Problems474

Chapter 16 Energy Transport by Radiation487

16.1 The Spectrum of Electromagnetic Radiation488

16.2 Absorption and Emission at Solid Surfaces490

16.3 Planck's Distribution Law,Wien's Displacement Law,and the Stefan-Boltzmann Law493

Ex.16.3-1 Temperature and Radiation-Energy Emission of the Sun496

16.4 Direct Radiation between Black Bodies in Vacuo at Different Temperatures497

Ex.16.4-1 Estimation of the Solar Constant501

Ex.16.4-2 Radiant Heat Transfer between Disks501

16.5 Radiation between Nonblack Bodies at Different Temperatures502

Ex.16.5-1 Radiation Shields503

Ex.16.5-2 Radiation and Free-Convection Heat Losses from a Horizontal Pipe504

Ex.16.5-3 Combined Radiation and Convection505

16.6 Radiant Energy Transport in Absorbing Media506

Ex.16.6-1 Absorption ofa Monochromatic Radiant Beam507

Questions for Discussion508

Problems508

Part Ⅲ Mass Transport513

Chapter 17 Diffusivity and the Mechanisms of Mass Transport513

17.1 Fick's Law of Binary Diffusion（Molecular Mass Transport）514

Ex.17.1-1 Diffusion ofHelium through Pyrex Glass519

Ex.17.1-2 The Equivalence of DAB and DBA520

17.2 Temperature and Pressure Dependence of Diffusivities521

Ex.17.2-1 Estimation of Diffusivity at Low Density523

Ex.17.2-2 Estimation of Self-Diffusivity at High Density523

Ex.17.2-3 Estimation of Binary Diffusivity at High Density524

17.3 Theory of Diffusion in Gases at Low Density525

Ex.17.3-1 Computation of Mass Diffusivity for Low-Density Monatomic Gases528

17.4 Theory of Diffusion in Binary Liquids528

Ex.17.4-1 Estimation of Liquid Diffusivity530

17.5 Theory of Diffusion in Colloidal Suspensions531

17.6 Theory of Diffusion in Polymers532

17.7 Mass and Molar Transport by Convection533

17.8 Summary of Mass and Molar Fluxes536

17.9 The Maxwell-Stefan Equations for Multicomponent Diffusion in Gases at Low Density538

Questions for Discussion538

Problems539

Chapter 18 Concentration Distributions in Solids and Laminar Flow543

18.1 Shell Mass Balances;Boundary Conditions545

18.2 Diffusion through a Stagnant Gas Film545

Ex.18.2-1 Diffusion with a Moving Interface549

Ex.18.2-2 Determination of Diffusivity549

Ex.18.2-3 Diffusion through a Nonisothermal Spherical Film550

18.3 Diffusion with a Heterogeneous Chemical Reaction551

Ex.18.3-1 Diffusion with a Slow Heterogeneous Reaction553

18.4 Diffusion with a Homogeneous Chemical Reaction554

Ex.18.4-1 Gas Absorption with Chemical Reaction in an Agitated Tank555

18.5 Diffusion into a Falling Liquid Film（Gas Absorption）558

Ex.18.5-1 Gas Absorption from Rising Bubbles560

18.6 Diffusion into a Falling Liquid Film（Solid Dissolution）562

18.7 Diffusion and Chemical Reaction inside a Porous Catalyst563

18.8 Diffusion in a Three-Component Gas System567

Questions for Discussion568

Problems568

Chapter 19 Equations of Change for Multicomponent Systems582

19.1 The Equations of Continuity for a Multicomponent Mixture582

Ex.19.1-1 Diffusion,Convection,and Chemical Reaction585

19.2 Summary of the Multicomponent Equations of Change586

19.3 Summary of the Multicomponent Fluxes590

Ex.19.3-1 The Partial Molar Enthalpy591

19.4 Use of the Equations of Change for Mixtures592

Ex.19.4-1 Simultaneous Heat and Mass Transport592

Ex.19.4-2 Concentration Profile in a Tubular Reactor595

Ex.19.4-3 Catalytic Oxidation of Carbon Monoxide596

Ex.19.4-4 Thermal Conductivity of a Polyatomic Gas598

19.5 Dimensional Analysis of the Equations of Change for Nonreacting Binary Mixtures599

Ex.19.5-1 Concentration Distribution about a Long Cylinder601

Ex.19.5-2 Fog Formation during Dehumidification602

Ex.19.5-3 Blending of Miscible Fluids604

Questions for Discussion605

Problems606

Chapter 20 Concentration Distributions with More than One Independent Variable612

20.1 Time-Dependent Diffusion613

Ex.20.1-1 Unsteady-State Evaporation of a Liquid（the“Arnold Problem”）613

Ex.20.1-2 Gas Absorption with Rapid Reaction617

Ex.20.1-3 Unsteady Diffusion with First-Order Homogeneous Reaction619

Ex.20.1-4 Influence of Changing Interfacial Area on Mass Transferat an Interface621

20.2 Steady-State Transport in Binary Boundary Layers623

Ex.20.2-1 Diffusion and Chemical Reaction in Isothermal Laminar Flow along a Soluble Flat Plate625

Ex.20.2-2 Forced Convection from a Flat Plate at High Mass-Transfer Rates627

Ex.20.2-3 Approximate Analogies for the Flat Plate at Low Mass-Transfer Rates632

20.3 Steady-State Boundary-Layer Theory for Flow around Objects633

Ex.20.3-1 Mass Transfer for Creeping Flow around a Gas Bubble636

20.4 Boundary Layer Mass Transport with Complex Interfacial Motion637

Ex.20.4-1 Mass Transfer with Nonuniform Interfacial Deformation641

Ex.20.4-2 Gas Absorption with Rapid Reaction and Interfacial Deformation642

20.5 “Taylor Dispersion”in Laminar Tube Flow643

Questions for Discussion647

Problems648

Chapter 21 Concentration Distributions in Turbulent Flow657

21.1 Concentration Fluctuations and the Time-Smoothed Concentration657

21.2 Time-Smoothing of the Equation of Continuity of A658

21.3 Semi-Empirical Expressions for the Turbulent Mass Flux659

21.4 Enhancement of Mass Transfer by a First-Order Reaction in Turbulent Flow659

21.5 Turbulent Mixing and Turbulent Flow with Second-Order Reaction663

Questions for Discussion667

Problems668

Chapter 22 Interphase Transport in Nonisothermal Mixtures671

22.1 Definition of Transfer Coefficients in One Phase672

22.2 Analytical Expressions for Mass Transfer Coefficients676

22.3 Correlation of Binary Transfer Coefficients in One Phase679

Ex.22.3-1 Evaporation from a Freely Falling Drop682

Ex.22.3-2 The Wet and Dry Bulb Psychrometer683

Ex.22.3-3 Mass Transfer in Creeping Flow through Packed Beds685

Ex.22.3-4 Mass Transfer to Drops and Bubbles687

22.4 Definition of Transfer Coefficients in Two Phases687

Ex.22.4-1 Determination of the Controlling Resistance690

Ex.22.4-2 Interaction of Phase Resistances691

Ex.22.4-3 Area Averaging693

22.5 Mass Transfer and Chemical Reactions694

Ex.22.5-1 Estimation of the Interfacial Area in a Packed Column694

Ex.22.5-2 Estimation of Volumetric Mass Transfer Coefficients695

Ex.22.5-3 Model-Insensitive Correlations for Absorption with Rapid Reaction696

22.6 Combined Heat and Mass Transfer by Free Convection698

Ex.22.6-1 Additivity of Grashof Numbers698

Ex.22.6-2 Free-Convection Heat Transfer as a Source of Forced-Convection Mass Transfer698

22.7 Effects of Interfacial Forces on Heat and Mass Transfer699

Ex.22.7-1 Elimination of Circulation in a Rising Gas Bubble701

Ex.22.7-2 Marangoni Instability in a Falling Film702

22.8 Transfer Coefficients at High Net Mass Transfer Rates703

Ex.22.8-1 Rapid Evaporation of a Liquid from a Plane Surface710

Ex.22.8-2 Correction Factors in Droplet Evaporation711

Ex.22.8-3 Wet-Bulb Performance Corrected for Mass-Transfer Rate711

Ex.22.8-4 Comparison of Film and Penetration Models for Unsteady Evaporation in a Long Tube712

Ex.22.8-5 Concentration Polarization in Ultrafiltration713

22.9 Matrix Approximations for Multicomponent Mass Transport716

Questions for Discussion721

Problems722

Chapter 23 Macroscopic Balances for Multicomponent Systems726

23.1 The Macroscopic Mass Balances727

Ex.23.1-1 Disposal of an Unstable Waste Product728

Ex.23.1-2 Binary Splitters730

Ex.23.1-3 The Macroscopic Balances and Dirac's Separative Capacity”and“Value Function”731

Ex.23.1-4 Compartmental Analysis733

Ex.23.1-5 Time Constants and Model Insensitivity736

23.2 The Macroscopic Momentum and Angular Momentum Balances738

23.3 The Macroscopic Energy Balance738

23.4 The Macroscopic Mechanical Energy Balance739

23.5 Use of the Macroscopic Balances to Solve Steady-State Problems739

Ex.23.5-1 Energy Balances for a Sulfur Dioxide Converter739

Ex.23.5-2 Heighht of a Packed-Tower Absorber742

Ex.23.5-3 Linear Cascades746

Ex.23.5-4 Expansion ofa Reactive Gas Mixture through a Frictionless Adiabatic Nozzle749

23.6 Use of the Macroscopic Balances to Solve Unsteady-State Problems752

Ex.23.6-1 Start-Up of a Chemical Reactor752

Ex.23.6-2 Unsteady Operation of a Packed Column753

Ex.23.6-3 The Utility of Low-Order Moments756

Questions for Discussion758

Problems759

Chapter 24 Other Mechanisms for Mass Transport764

24.1 The Equation of Change for Entropy765

24.2 The Flux Expressions for Heat and Mass767

Ex.24.2-1 Thermal Diffusion and the Clusius-Dickel Column770

Ex.24.2-2 Pressure Diffusion and the Ultra-centrifuge772

24.3 Concentration Diffusion and Driving Forces774

24.4 Applications of the Generalized Maxwell-Stefan Equations775

Ex.24.4-1 Centrifugation of Proteins776

Ex.24.4-2 Proteins as Hydrodynamic Particles779

Ex.24.4-3 Diffusion of Salts in an Aqueous Solution780

Ex.24.4-4 Departures from Local Electroneutrality：Electro-Osmosis782

Ex.24.4-5 Additional Mass-Transfer Driving Forces784

24.5 Mass Transport across Selectively Permeable Membranes785

Ex.24.5-1 Concentration Diffusion between Preexisting Bulk Phases788

Ex.24.5-2 Ultrafiltration and Reverse Osmosis789

Ex.24.5-3 Charged Membranes and Donnan Exclusion791

24.6 Mass Transport in Porous Media793

Ex.24.6-1 Knudsen Diffusion795

Ex.24.6-2 Transport from a Binary External Solution797

Questions for Discussion798

Problems799

Postface805

Appendices807

Appendix A Vector and Tensor Notation807

A.1 Vector Operations from a Geometrical Viewpoint808

A.2 Vector Operations in Terms of Components810

Ex.A.2-1 Proof of a Vector Identity814

A.3 Tensor Operations in Terms of Components815

A.4 Vector and Tensor Differential Operations819

Ex.A.4-1 Proof of a Tensor Identity822

A.5 Vector and Tensor Integral Theorems824

A.6 Vector and Tensor Algebra in Curvilinear Coordinates825

A.7 Differential Operations in Curvilinear Coordinates829

Ex.A.7-1 Differential Operations in Cylindrical Coordinates831

Ex.A.7-2 Differential Operations in Spherical Coordinates838

A.8 Integral Operations in Curvilinear Coordinates839

A.9 Further Comments on Vector-Tensor Notation841

Appendix B Fluxes and the Equations of Change843

B.1 Newton's Law of Viscosity843

B.2 Fourier's Law of Heat Conduction845

B.3 Fick's（First）Law of Binary Diffusion846

B.4 The Equation of Continuity846

B.5 The Equation of Motion in Terms of ？847

B.6 The Equation of Motion for a Newtonian Fluid with Constantρandμ848

B.7 The Dissipation Functionφv for Newtonian Fluids849

B.8 The Equation of Energy in Terms of q849

B.9 The Equation of Energy for Pure Newtonian Fluids with Constantρand k850

B.10 The Equation of Continuity for Speciesαin Terms of jα850

B.11 The Equation of Continuity for Species A in Terms of ωA for ConstantρDAB851

Appendix C Mathematical Topics852

C.1 Some Ordinary Differential Equations and Their Solutions852

C.2 Expansions of Functions in Taylor Series853

C.3 Differentiation of Integrals（the Leibniz Formula）854

C.4 The Gamma Function855

C.5 The Hyperbolic Functions856

C.6 The Error Function857

Appendix D The Kinetic Theory of Gases858

D.1 The Boltzmann Equation858

D.2 The Equations of Change859

D.3 The Molecular Expressions for the Fluxes859

D.4 The Solution to the Boltzmann Equation860

D.5 The Fluxes in Terms of the Transport Properties860

D.6 The Transport Properties in Terms of the Intermolecular Forces861

D.7 Concluding Comments861

Appendix E Tables for Prediction of Transport Properties863

E.1 Intermolecular Force Parameters and Critical Properties864

E.2 Functions for Prediction of Transport Properties of Gases at Low Densities866

Appendix F Constants and Conversion Factors867

F.1 Mathematical Constants867

F.2 Physical Constants867

F.3 Conversion Factors868

Notation872

Author Index877

Subject Index885