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