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Chapter 0 The Subject of Transport Phenomena 1

Part Ⅰ Momentum TransportChapter 1 Viscosity and the Mechanisms of Momentum Transport 11

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

Ex.1.1-1 Calculation of Momentum Flux 15

1.2 Generalization of Newton's Law of Viscosity 16

1.3 Pressure and Temperature Dependence of Viscosity 21

Ex.1.3-1 Estimation of Viscosity from Critical Properties 23

1.4 Molecular Theory of the Viscosity of Gases at Low Density 23

Ex.1.4-1 Computation of the Viscosity of a Gas Mixture at Low Density 28

Ex.1.4-2 Prediction of the Viscosity of a Gas Mixture at Low Density 28

1.5 Molecular Theory of the Viscosity of Liquids 29

Ex.1.5-1 Estimation of the Viscosity of a Pure Liquid 31

1.6 Viscosity of Suspensions and Emulsions 31

1.7 Convective Momentum Transport 34

Questions for Discussion 37

Problems 37

Chapter 2 Shell Momentum Balances and Velocity Distributions in Laminar Flow 40

2.1 Shell Momentum Balances and Boundary Conditions 41

2.2 Flow of a Falling Film 42

Ex.2.2-1 Calculation of Film Velocity 47

Ex.2.2-2 Falling Film with Variable Viscosity 47

2.3 Flow Through a Circular Tube 48

Ex.2.3-1 Determination of Viscosity from Capillary Flow Data 52

Ex.2.3-2 Compressible Flow in a Horizontal Circular Tube 53

2.4 Flow through an Annulus 53

2.5 Flow of Two Adjacent Immiscible Fluids 56

2.6 Creeping Flow around a Sphere 58

Ex.2.6-1 Determination of Viscosity from the Terminal Velocity of a Falling Sphere 61

Questions for Discussion 61

Problems 62

Chapter 3 The Equations of Change for Isothermal Systems 75

3.1 The Equation of Continuity 77

Ex.3.1-1 Normal Stresses at Solid Surfaces for Incompressible Newtonian Fluids 78

3.2 The Equation of Motion 78

3.3 The Equation of Mechanical Energy 81

3.4 The Equation of Angular Momentum 82

3.5 The Equations of Change in Terms of the Substantial Derivative 83

Ex.3.5-1 The Bernoulli Equation for the Steady Flow of Inviscid Fluids 86

3.6 Use of the Equations of Change to Solve Flow Problems 86

Ex.3.6-1 Steady Flow in a Long Circular Tube 88

Ex.3.6-2 Falling Film with Variable Viscosity 89

Ex.3.6-3 Operation ofa Couette Viscometer 89

Ex.3.6-4 Shape of the Surface of a Rotating Liquid 93

Ex.3.6-5 Flow near a Slowly Rotating Sphere 95

3.7 Dimensional Analysis of the Equations of Change 97

Ex.3.7-1 Transverse Flow around a Circular Cylinder 98

Ex.3.7-2 Steady Flow in an Agitated Tank 101

Ex.3.7-3 Pressure Drop for Creeping Flow in a Packed Tube 103

Questions for Discussion 104

Problems 104

Chapter 4 Velocity Distributions with More than One Independent Variable 114

4.1 Time-Dependent Flow of Newtonian Fluids 114

Ex.4.1-1 Flow near a Wall Suddenly Set in Motion 115

Ex.4.1-2 Unsteady Laminar Flow between Two Parallel Plates 117

Ex.4.1-3 Unsteady Laminar Flow near an Oscillating Plate 120

4.2 Solving Flow Problems Using a Stream Function 121

Ex.4.2-1 Creeping Flow around a Sphere 122

4.3 Flow of Inviscid Fluids by Use of the Velocity Potential 126

Ex.4.3-1 Potential Flow around a Cylinder 128

Ex.4.3-2 Flow into a Rectangular Channel 130

Ex.4.3-3 Flow near a Corner 131

4.4 Flow near Solid Surfaces by Boundary-Layer Theory 133

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 Corner 139

Questions for Discussion 140

Problems 141

Chapter 5 Velocity Distributions in Turbulent Flow 152

5.1 Comparisons of Laminar and Turbulent Flows 154

5.2 Time-Smoothed Equations of Change for Incompressible Fluids 156

5.3 The Time-Smoothed Velocity Profile near a Wall 159

5.4 Empirical Expressions for the Turbulent Momentum Flux 162

Ex.5.4-1 Development of the Reynolds Stress Expression in the Vicinity of the Wall 164

5.5 Turbulent Flow in Ducts 165

Ex.5.5-1 Estimation of the Average Velocity in a Circular Tube 166

Ex.5.5-2 Application of Prandtl's Mixing Length Formula to Turbulent Flow in a Circular Tube 167

Ex.5.5-3 Relative Magnitude of Viscosity and Eddy Viscosity 167

5.6 Turbulent Flow in Jets 168

Ex.5.6-1 Time-Smoothed Velocity Distribution in a Circular Wall Jet 168

Questions for Discussion 172

Problems 172

Chapter 6 Interphase Transport in Isothermal Systems 177

6.1 Definition of Friction Factors 178

6.2 Friction Factors for Flow in Tubes 179

Ex.6.2-1 Pressure Drop Required for a Given Flow Rate 183

Ex.6.2-2 Flow Rate for a Given Pressure Drop 183

6.3 Friction Factors for Flow around Spheres 185

Ex.6.3-1 Determination of the Diameter of a Falling Sphere 187

6.4 Friction Factors for Packed Columns 188

Questions for Discussion 192

Problems 193

Chapter 7 Macroscopic Balances for Isothermal Flow Systems 197

7.1 The Macroscopic Mass Balance 198

Ex.7.1-1 Draining of a Spherical Tank 199

7.2 The Macroscopic Momentum Balance 200

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

7.3 The Macroscopic Angular Momentum Balance 202

Ex.7.3-1 Torque on a Mixing Vessel 202

7.4 The Macroscopic Mechanical Energy Balance 203

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

7.5 Estimation of the Viscous Loss 205

Ex.7.5-1 Power Requirement for Pipeline Flow 207

7.6 Use of the Macroscopic Balances for Steady-State Problems 209

Ex.7.6-1 Pressure Rise and Friction Loss in a Sudden Enlargement 209

Ex.7.6-2 Performance of a Liquid-Liquid Ejector 210

Ex.7.6-3 Thrust on a Pipe Bend 212

Ex.7.6-4 The Impinging Jet 214

Ex.7.6-5 Isothermal Flow of a Liquid through an Orifice 215

7.7 Use of the Macroscopic Balances for Unsteady-State Problems 216

Ex.7.7.1 Acceleration Effects in Unsteady Flow from a Cylindrical Tank 217

Ex.7.7-2 Manometer Oscillations 219

7.8 Derivation of the Macroscopic Mechanical Energy Balance 221

Questions for Discussion 223

Problems 224

Chapter 8 Polymeric Liquids 231

8.1 Examples of the Behavior of Polymeric Liquids 232

8.2 Rheometry and Material Functions 236

8.3 Non-Newtonian Viscosity and the Generalized Newtonian Models 240

Ex.8.3-1 Laminar Flow of an Incompressible Power-Law Fluid in a Circular Tube 242

Ex.8.3-2 Flow of a Power-Law Fluid in a Narrow Slit 243

Ex.8.3-3 Tangential Annular Flow of a Power-Law Fluid 244

8.4 Elasticity and the Linear Viscoelastic Models 244

Ex.8.4-1 Small-Amplitude Oscillatory Motion 247

Ex.8.4-2 Unsteady Viscoelastic Flow near an Oscillating Plate 248

8.5 The Corotational Derivatives and the Nonlinear Viscoelastic Models 249

Ex.8.5-1 Material Functions for the Oldroyd 6-Constant Model 251

8.6 Molecular Theories for Polymeric Liquids 253

Ex.8.6-1 Material Functions for the FENE-P Model 255

Questions for Discussion 258

Problems 258

Part Ⅱ Energy Transport 263

Chapter 9 Thermal Conductivity and the Mechanisms of Energy Transport 263

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

Ex.9.1-1 Measurement of Thermal Conductivity 270

9.2 Temperature and Pressure Dependence of Thermal Conductivity 272

Ex.9.2-1 Effect of Pressure on Thermal Conductivity 273

9.3Theory of Thermal Conductivity of Gases at Low Density 274

Ex.9.3-1 Computation of the Thermal Conductivity of a Monatomic Gas at Low Density 277

Ex.9.3-2 Estimation of the Thermal Conductivity of a Polyatomic Gas at Low Density 278

Ex.9.3-3 Prediction of the Thermal Conductivity of a Gas Mixture at Low Density 278

9.4 Theory of Thermal Conductivity of Liquids 279

Ex.9.4-1 Prediction of the Thermal Conductivity of a Liquid 280

9.5 Thermal Conductivity of Solids 280

9.6 Effective Thermal Conductivity of Composite Solids 281

9.7 Convective Transport of Energy 283

9.8 Work Associated with Molecular Motions 284

Questions for Discussion 286

Problems 287

Chapter 10 Shell Energy Balances and Temperature Distributions in Solids and Laminar Flow 290

10.1 Shell Energy Balances;Boundary Conditions 291

10.2 Heat Conduction with an Electrical Heat Source 292

Ex.10.2-1 Voltage Required for a Given Temperature Rise in a Wire Heated by an Electric Current 295

Ex.10.2-2 Heated Wire with Specified Heat Transfer Coefficient and Ambient Air Temperature 295

10.3 Heat Conduction with a Nuclear Heat Source 296

10.4 Heat Conduction with a Viscous Heat Source 298

10.5 Heat Conduction with a Chemical Heat Source 300

10.6 Heat Conduction through Composite Walls 303

Ex.10.6-1 Composite Cylindrical Walls 305

10.7 Heat Conduction in a Cooling Fin 307

Ex.10.7-1 Error in Thermocouple Measurement 309

10.8 Forced Convection 310

10.9 Free Convection 316

Questions for Discussion 319

Problems 320

Chapter 11 The Equations of Change for Nonisothermal Systems 333

11.1 The Energy Equation 333

11.2 Special Forms of the Energy Equation 336

11.3 The Boussinesq Equation of Motion for Forced and Free Convection 338

11.4 Use of the Equations of Change to Solve Steady-State Problems 339

Ex.11.4-1 Steady-State Forced-Convection Heat Transfer in Laminar Flow in a Circular Tube 342

Ex.11.4-2 Tangential Flow in an Annulus with Viscous Heat Generation 342

Ex.11.4-3 Steady Flow in a Nonisothermal Film 343

Ex.11.4-4 Transpiration Cooling 344

Ex.11.4-5 Free Convection Heat Transfer from a Vertical Plate 346

Ex.11.4-6 Adiabatic Frictionless Processes in an Ideal Gas 349

Ex.11.4-7 One-Dimensional Compressible Flow：Velocity,Temperature,and Pressure Profiles in a Stationary Shock Wave 350

11.5 Dimensional Analysis of the Equations of Change for Nonisothermal Systems 353

Ex.11.5-1 Temperature Distribution about a Long Cylinder 356

Ex.11.5-2 Free Convection in a Horizontal Fluid Layer;Formation of Bénard Cells 358

Ex.11.5-3 Surface Temperature of an Electrical Heating Coil 360

Questions for Discussion 361

Problems 361

Chapter 12 Temperature Distributions with More than One Independent Variable 374

12.1 Unsteady Heat Conduction in Solids 374

Ex.12.1-1 Heatingofa Semi-Infinite Slab 375

Ex.12.1-2 Heatingofa Finite Slab 376

Ex.12.1-3 Unsteady Heat Conduction near a Wall with Sinusoidal Heat Flux 379

Ex.12.1-4 Coolingofa Sphere in Contact with a Well-Stirred Fluid 379

12.2Steady Heat Conduction in Laminar,Incompressible Flow 381

Ex.12.2-1 Laminar Tube Flow with Constant Heat Flux at the Wall 383

Ex.12.2-2 Laminar Tube Flow with Constant Heat Flux at the Wall：Asymptotic Solution for the Entrance Region 384

12.3Steady Potential Flow of Heat in Solids 385

Ex.12.3-1 Temperature Distribution in a Wall 386

12.4Boundary Layer Theory for Nonisothermal Flow 387

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 Numbers 392

Questions for Discussion 394

Problems 395

Chapter 13 Temperature Distributions in Turbulent Flow 407

13.1 Time-Smoothed Equations of Change for Incompressible Nonisothermal Flow 407

13.2 The Time-Smoothed Temperature Profile near a Wall 409

13.3 Empirical Expressions for the Turbulent Heat Flux 410

Ex.13.3-1 An Approximate Relation for the Wall Heat Flux for Turbulent Flow in a Tube 411

13.4 Temperature Distribution for Turbulent Flow in Tubes 411

13.5 Temperature Distribution for Turbulent Flow in Jets 415

13.6 Fourier Analysis of Energy Transport in Tube Flow at Large Prandtl Numbers 416

Questions for Discussion 421

Problems 421

Chapter 14 Interphase Transport in Nonisothermal Systems 422

14.1 Definitions of Heat Transfer Coefficients 423

Ex.14.1-1 Calculation of Heat Transfer Coefficients from Experimental Data 426

14.2 Analytical Calculations of Heat Transfer Coefficients for Forced Convection through Tubes and Slits 428

14.3 Heat Transfer Coefficients for Forced Convection in Tubes 433

Ex.14.3-1 Design of a Tubular Heater 437

14.4 Heat Transfer Coefficients for Forced Convection around Submerged Objects 438

14.5 Heat Transfer Coefficients for Forced Convection through Packed Beds 441

14.6 Heat Transfer Coefficients for Free and Mixed Convection 442

Ex14.6-1 Heat Loss bu Free Convection from a Horizontal Pipe 445

14.7 Heat Transfer Coefficients for Condensation of Pure Vapors on Solid Surfaces 446

Ex.14.7-1 Condensation of Steam on a Vertical Surface 449

Questions for Discussion 449

Problems 450

Chapter 15 Macroscopic Balances for Nonisothermal Systems 454

15.1 The Macroscopic Energy Balance 455

15.2 The Macroscopic Mechanical Energy Balance 456

15.3 Use of the Macroscopic Balances to Solve Steady-State Problems with Flat Velocity Profiles 458

Ex.15.3-1 The Cooling of an Ideal Gas 459

Ex.15.3-2 Mixing of Tuo Ideal Gas Streams 460

15.4 The d-Forms of the Macroscopic Balances 461

Ex.15.4-1 Parallel-or Counter-Flow Heat Exchangers 462

Ex.15.4-2 Power Requirement for Pumping a Compressible Fluid through a Long Pipe 464

15.5 Use of the Macroscopic Balances to Solve Unsteady-State Problems and Problems with Nonflat Velocity Profiles 465

Ex.15.5-1 Heating ofa Liquid in an Agitated Tank 466

Ex.15.5-2 Operation ofa Simple Temperature Controller 468

Ex.15.5-3 Flow of Compressible Fluids through Heat Meters 471

Ex.15.5-4 Free Batch Expansion of a Compressible Fluid 472

Questions for Discussion 474

Problems 474

Chapter 16 Energy Transport by Radiation 487

16.1 The Spectrum of Electromagnetic Radiation 488

16.2 Absorption and Emission at Solid Surfaces 490

16.3 Planck's Distribution Law,Wien's Displacement Law,and the Stefan-Boltzmann Law 493

Ex.16.3-1 Temperature and Radiation-Energy Emission of the Sun 496

16.4 Direct Radiation between Black Bodies in Vacuo at Different Temperatures 497

Ex.16.4-1 Estimation of the Solar Constant 501

Ex.16.4-2 Radiant Heat Transfer between Disks 501

16.5 Radiation between Nonblack Bodies at Different Temperatures 502

Ex.16.5-1 Radiation Shields 503

Ex.16.5-2 Radiation and Free-Convection Heat Losses from a Horizontal Pipe 504

Ex.16.5-3 Combined Radiation and Convection 505

16.6 Radiant Energy Transport in Absorbing Media 506

Ex.16.6-1 Absorption ofa Monochromatic Radiant Beam 507

Questions for Discussion 508

Problems 508

Part Ⅲ Mass Transport 513

Chapter 17 Diffusivity and the Mechanisms of Mass Transport 513

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

Ex.17.1-1 Diffusion ofHelium through Pyrex Glass 519

Ex.17.1-2 The Equivalence of DAB and DBA 520

17.2 Temperature and Pressure Dependence of Diffusivities 521

Ex.17.2-1 Estimation of Diffusivity at Low Density 523

Ex.17.2-2 Estimation of Self-Diffusivity at High Density 523

Ex.17.2-3 Estimation of Binary Diffusivity at High Density 524

17.3 Theory of Diffusion in Gases at Low Density 525

Ex.17.3-1 Computation of Mass Diffusivity for Low-Density Monatomic Gases 528

17.4 Theory of Diffusion in Binary Liquids 528

Ex.17.4-1 Estimation of Liquid Diffusivity 530

17.5 Theory of Diffusion in Colloidal Suspensions 531

17.6 Theory of Diffusion in Polymers 532

17.7 Mass and Molar Transport by Convection 533

17.8 Summary of Mass and Molar Fluxes 536

17.9 The Maxwell-Stefan Equations for Multicomponent Diffusion in Gases at Low Density 538

Questions for Discussion 538

Problems 539

Chapter 18 Concentration Distributions in Solids and Laminar Flow 543

18.1 Shell Mass Balances;Boundary Conditions 545

18.2 Diffusion through a Stagnant Gas Film 545

Ex.18.2-1 Diffusion with a Moving Interface 549

Ex.18.2-2 Determination of Diffusivity 549

Ex.18.2-3 Diffusion through a Nonisothermal Spherical Film 550

18.3 Diffusion with a Heterogeneous Chemical Reaction 551

Ex.18.3-1 Diffusion with a Slow Heterogeneous Reaction 553

18.4 Diffusion with a Homogeneous Chemical Reaction 554

Ex.18.4-1 Gas Absorption with Chemical Reaction in an Agitated Tank 555

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

Ex.18.5-1 Gas Absorption from Rising Bubbles 560

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

18.7 Diffusion and Chemical Reaction inside a Porous Catalyst 563

18.8 Diffusion in a Three-Component Gas System 567

Questions for Discussion 568

Problems 568

Chapter 19 Equations of Change for Multicomponent Systems 582

19.1 The Equations of Continuity for a Multicomponent Mixture 582

Ex.19.1-1 Diffusion,Convection,and Chemical Reaction 585

19.2 Summary of the Multicomponent Equations of Change 586

19.3 Summary of the Multicomponent Fluxes 590

Ex.19.3-1 The Partial Molar Enthalpy 591

19.4 Use of the Equations of Change for Mixtures 592

Ex.19.4-1 Simultaneous Heat and Mass Transport 592

Ex.19.4-2 Concentration Profile in a Tubular Reactor 595

Ex.19.4-3 Catalytic Oxidation of Carbon Monoxide 596

Ex.19.4-4 Thermal Conductivity of a Polyatomic Gas 598

19.5 Dimensional Analysis of the Equations of Change for Nonreacting Binary Mixtures 599

Ex.19.5-1 Concentration Distribution about a Long Cylinder 601

Ex.19.5-2 Fog Formation during Dehumidification 602

Ex.19.5-3 Blending of Miscible Fluids 604

Questions for Discussion 605

Problems 606

Chapter 20 Concentration Distributions with More than One Independent Variable 612

20.1 Time-Dependent Diffusion 613

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

Ex.20.1-2 Gas Absorption with Rapid Reaction 617

Ex.20.1-3 Unsteady Diffusion with First-Order Homogeneous Reaction 619

Ex.20.1-4 Influence of Changing Interfacial Area on Mass Transferat an Interface 621

20.2 Steady-State Transport in Binary Boundary Layers 623

Ex.20.2-1 Diffusion and Chemical Reaction in Isothermal Laminar Flow along a Soluble Flat Plate 625

Ex.20.2-2 Forced Convection from a Flat Plate at High Mass-Transfer Rates 627

Ex.20.2-3 Approximate Analogies for the Flat Plate at Low Mass-Transfer Rates 632

20.3 Steady-State Boundary-Layer Theory for Flow around Objects 633

Ex.20.3-1 Mass Transfer for Creeping Flow around a Gas Bubble 636

20.4 Boundary Layer Mass Transport with Complex Interfacial Motion 637

Ex.20.4-1 Mass Transfer with Nonuniform Interfacial Deformation 641

Ex.20.4-2 Gas Absorption with Rapid Reaction and Interfacial Deformation 642

20.5 “Taylor Dispersion”in Laminar Tube Flow 643

Questions for Discussion 647

Problems 648

Chapter 21 Concentration Distributions in Turbulent Flow 657

21.1 Concentration Fluctuations and the Time-Smoothed Concentration 657

21.2 Time-Smoothing of the Equation of Continuity of A 658

21.3 Semi-Empirical Expressions for the Turbulent Mass Flux 659

21.4 Enhancement of Mass Transfer by a First-Order Reaction in Turbulent Flow 659

21.5 Turbulent Mixing and Turbulent Flow with Second-Order Reaction 663

Questions for Discussion 667

Problems 668

Chapter 22 Interphase Transport in Nonisothermal Mixtures 671

22.1 Definition of Transfer Coefficients in One Phase 672

22.2 Analytical Expressions for Mass Transfer Coefficients 676

22.3 Correlation of Binary Transfer Coefficients in One Phase 679

Ex.22.3-1 Evaporation from a Freely Falling Drop 682

Ex.22.3-2 The Wet and Dry Bulb Psychrometer 683

Ex.22.3-3 Mass Transfer in Creeping Flow through Packed Beds 685

Ex.22.3-4 Mass Transfer to Drops and Bubbles 687

22.4 Definition of Transfer Coefficients in Two Phases 687

Ex.22.4-1 Determination of the Controlling Resistance 690

Ex.22.4-2 Interaction of Phase Resistances 691

Ex.22.4-3 Area Averaging 693

22.5 Mass Transfer and Chemical Reactions 694

Ex.22.5-1 Estimation of the Interfacial Area in a Packed Column 694

Ex.22.5-2 Estimation of Volumetric Mass Transfer Coefficients 695

Ex.22.5-3 Model-Insensitive Correlations for Absorption with Rapid Reaction 696

22.6 Combined Heat and Mass Transfer by Free Convection 698

Ex.22.6-1 Additivity of Grashof Numbers 698

Ex.22.6-2 Free-Convection Heat Transfer as a Source of Forced-Convection Mass Transfer 698

22.7 Effects of Interfacial Forces on Heat and Mass Transfer 699

Ex.22.7-1 Elimination of Circulation in a Rising Gas Bubble 701

Ex.22.7-2 Marangoni Instability in a Falling Film 702

22.8 Transfer Coefficients at High Net Mass Transfer Rates 703

Ex.22.8-1 Rapid Evaporation of a Liquid from a Plane Surface 710

Ex.22.8-2 Correction Factors in Droplet Evaporation 711

Ex.22.8-3 Wet-Bulb Performance Corrected for Mass-Transfer Rate 711

Ex.22.8-4 Comparison of Film and Penetration Models for Unsteady Evaporation in a Long Tube 712

Ex.22.8-5 Concentration Polarization in Ultrafiltration 713

22.9 Matrix Approximations for Multicomponent Mass Transport 716

Questions for Discussion 721

Problems 722

Chapter 23 Macroscopic Balances for Multicomponent Systems 726

23.1 The Macroscopic Mass Balances 727

Ex.23.1-1 Disposal of an Unstable Waste Product 728

Ex.23.1-2 Binary Splitters 730

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

Ex.23.1-4 Compartmental Analysis 733

Ex.23.1-5 Time Constants and Model Insensitivity 736

23.2 The Macroscopic Momentum and Angular Momentum Balances 738

23.3 The Macroscopic Energy Balance 738

23.4 The Macroscopic Mechanical Energy Balance 739

23.5 Use of the Macroscopic Balances to Solve Steady-State Problems 739

Ex.23.5-1 Energy Balances for a Sulfur Dioxide Converter 739

Ex.23.5-2 Heighht of a Packed-Tower Absorber 742

Ex.23.5-3 Linear Cascades 746

Ex.23.5-4 Expansion ofa Reactive Gas Mixture through a Frictionless Adiabatic Nozzle 749

23.6 Use of the Macroscopic Balances to Solve Unsteady-State Problems 752

Ex.23.6-1 Start-Up of a Chemical Reactor 752

Ex.23.6-2 Unsteady Operation of a Packed Column 753

Ex.23.6-3 The Utility of Low-Order Moments 756

Questions for Discussion 758

Problems 759

Chapter 24 Other Mechanisms for Mass Transport 764

24.1 The Equation of Change for Entropy 765

24.2 The Flux Expressions for Heat and Mass 767

Ex.24.2-1 Thermal Diffusion and the Clusius-Dickel Column 770

Ex.24.2-2 Pressure Diffusion and the Ultra-centrifuge 772

24.3 Concentration Diffusion and Driving Forces 774

24.4 Applications of the Generalized Maxwell-Stefan Equations 775

Ex.24.4-1 Centrifugation of Proteins 776

Ex.24.4-2 Proteins as Hydrodynamic Particles 779

Ex.24.4-3 Diffusion of Salts in an Aqueous Solution 780

Ex.24.4-4 Departures from Local Electroneutrality：Electro-Osmosis 782

Ex.24.4-5 Additional Mass-Transfer Driving Forces 784

24.5 Mass Transport across Selectively Permeable Membranes 785

Ex.24.5-1 Concentration Diffusion between Preexisting Bulk Phases 788

Ex.24.5-2 Ultrafiltration and Reverse Osmosis 789

Ex.24.5-3 Charged Membranes and Donnan Exclusion 791

24.6 Mass Transport in Porous Media 793

Ex.24.6-1 Knudsen Diffusion 795

Ex.24.6-2 Transport from a Binary External Solution 797

Questions for Discussion 798

Problems 799

Postface 805

Appendices 807

Appendix A Vector and Tensor Notation 807

A.1 Vector Operations from a Geometrical Viewpoint 808

A.2 Vector Operations in Terms of Components 810

Ex.A.2-1 Proof of a Vector Identity 814

A.3 Tensor Operations in Terms of Components 815

A.4 Vector and Tensor Differential Operations 819

Ex.A.4-1 Proof of a Tensor Identity 822

A.5 Vector and Tensor Integral Theorems 824

A.6 Vector and Tensor Algebra in Curvilinear Coordinates 825

A.7 Differential Operations in Curvilinear Coordinates 829

Ex.A.7-1 Differential Operations in Cylindrical Coordinates 831

Ex.A.7-2 Differential Operations in Spherical Coordinates 838

A.8 Integral Operations in Curvilinear Coordinates 839

A.9 Further Comments on Vector-Tensor Notation 841

Appendix B Fluxes and the Equations of Change 843

B.1 Newton's Law of Viscosity 843

B.2 Fourier's Law of Heat Conduction 845

B.3 Fick's（First）Law of Binary Diffusion 846

B.4 The Equation of Continuity 846

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

B.6 The Equation of Motion for a Newtonian Fluid with Constantρandμ 848

B.7 The Dissipation Functionφv for Newtonian Fluids 849

B.8 The Equation of Energy in Terms of q 849

B.9 The Equation of Energy for Pure Newtonian Fluids with Constantρand k 850

B.10 The Equation of Continuity for Speciesαin Terms of jα 850

B.11 The Equation of Continuity for Species A in Terms of ωA for ConstantρDAB 851

Appendix C Mathematical Topics 852

C.1 Some Ordinary Differential Equations and Their Solutions 852

C.2 Expansions of Functions in Taylor Series 853

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

C.4 The Gamma Function 855

C.5 The Hyperbolic Functions 856

C.6 The Error Function 857

Appendix D The Kinetic Theory of Gases 858

D.1 The Boltzmann Equation 858

D.2 The Equations of Change 859

D.3 The Molecular Expressions for the Fluxes 859

D.4 The Solution to the Boltzmann Equation 860

D.5 The Fluxes in Terms of the Transport Properties 860

D.6 The Transport Properties in Terms of the Intermolecular Forces 861

D.7 Concluding Comments 861

Appendix E Tables for Prediction of Transport Properties 863

E.1 Intermolecular Force Parameters and Critical Properties 864

E.2 Functions for Prediction of Transport Properties of Gases at Low Densities 866

Appendix F Constants and Conversion Factors 867

F.1 Mathematical Constants 867

F.2 Physical Constants 867

F.3 Conversion Factors 868

Notation 872

Author Index 877

Subject Index 885