Fundamentals of Momentum, Heat, and Mass Transfer

1. Introduction to Momentum Transfer 1

1.1 Fluids and the Continuum 1

1.2 Properties at a Point 2

1.3 Point-to-Point Variation of Properties in a Fluid 5

1.4 Units 8

1.5 Compressibility 10

1.6 Surface Tension 11

2. Fluid Statics 16

2.1 Pressure Variation in a Static Fluid 16

2.2 Uniform Rectilinear Acceleration 19

2.3 Forces on Submerged Surfaces 20

2.4 Buoyancy 23

2.5 Closure 25

3. Description of a Fluid in Motion 29

3.1 Fundamental Physical Laws 29

3.2 Fluid-Flow Fields: Lagrangian and Eulerian Representations 29

3.3 Steady and Unsteady Flows 30

3.4 Streamlines 31

3.5 Systems and Control Volumes 32

4. Conservation of Mass: Control-Volume Approach 34

4.1 Integral Relation 34

4.2 Specific Forms of the Integral Expression 35

4.3 Closure 40

5. Newton’s Second Law of Motion: Control-Volume Approach 44

5.1 Integral Relation for Linear Momentum 44

5.2 Applications of the Integral Expression for Linear Momentum 47

5.3 Integral Relation for Moment of Momentum 53

5.4 Applications to Pumps and Turbines 55

5.5 Closure 59

6. Conservation of Energy: Control-Volume Approach 65

6.1 Integral Relation for the Conservation of Energy 65

6.2 Applications of the Integral Expression 71

6.3 The Bernoulli Equation 74

6.4 Closure 79

7. Shear Stress in Laminar Flow 85

7.1 Newton’s Viscosity Relation 85

7.2 Non-Newtonian Fluids 86

7.3 Viscosity 88

7.4 Shear Stress in Multidimensional Laminar Flows of a Newtonian Fluid 93

7.5 Closure 97

8. Analysis of a Differential Fluid Element in Laminar Flow 99

8.1 Fully Developed Laminar Flow in a Circular Conduit of Constant Cross Section 99

8.2 Laminar Flow of a Newtonian Fluid Down an Inclined-Plane Surface 102

8.3 Closure 104

9. Differential Equations of Fluid Flow 107

9.1 The Differential Continuity Equation 107

9.2 Navier–Stokes Equations 110

9.3 Bernoulli’s Equation 118

9.4 Spherical Coordinate Forms of the Navier–Stokes Equations 119

9.5 Closure 121

10. Inviscid Fluid Flow 124

10.1 Fluid Rotation at a Point 124

10.2 The Stream Function 127

10.3 Inviscid, Irrotational Flow about an Infinite Cylinder 129

10.4 Irrotational Flow, the Velocity Potential 131

10.5 Total Head in Irrotational Flow 134

10.6 Utilization of Potential Flow 135

10.7 Potential Flow Analysis—Simple Plane Flow Cases 136

10.8 Potential Flow Analysis—Superposition 137

10.9 Closure 139

11. Dimensional Analysis and Similitude 141

11.1 Dimensions 141

11.2 Dimensional Analysis of Governing Differential Equations 142

11.3 The Buckingham Method 144

11.4 Geometric, Kinematic, and Dynamic Similarity 147

11.5 Model Theory 148

11.6 Closure 150

12. Viscous Flow 154

12.1 Reynolds’s Experiment 154

12.2 Drag 155

12.3 The Boundary-Layer Concept 160

12.4 The Boundary-Layer Equations 161

12.5 Blasius’s Solution for the Laminar Boundary Layer on a Flat Plate 163

12.6 Flow with a Pressure Gradient 167

12.7 von Kármán Momentum Integral Analysis 169

12.8 Description of Turbulence 172

12.9 Turbulent Shearing Stresses 174

12.10 The Mixing-Length Hypothesis 175

12.11 Velocity Distribution from the Mixing-Length Theory 177

12.12 The Universal Velocity Distribution 178

12.13 Further Empirical Relations for Turbulent Flow 179

12.14 The Turbulent Boundary Layer on a Flat Plate 180

12.15 Factors Affecting the Transition from Laminar to Turbulent Flow 182

12.16 Closure 183

13. Flow in Closed Conduits 186

13.1 Dimensional Analysis of Conduit Flow 186

13.2 Friction Factors for Fully Developed Laminar, Turbulent, and Transition Flow in Circular Conduits 188

13.3 Friction Factor and Head-Loss Determination for Pipe Flow 191

13.4 Pipe-Flow Analysis 195

13.5 Friction Factors for Flow in the Entrance to a Circular Conduit 198

13.6 Closure 201

14. Fluid Machinery 204

14.1 Centrifugal Pumps 205

14.2 Scaling Laws for Pumps and Fans 213

14.3 Axial- and Mixed-Flow Pump Configurations 216

14.4 Turbines 216

14.5 Closure 217

15. Fundamentals of Heat Transfer 220

15.1 Conduction 220

15.2 Thermal Conductivity 221

15.3 Convection 226

15.4 Radiation 228

15.5 Combined Mechanisms of Heat Transfer 228

15.6 Closure 232

16. Differential Equations of Heat Transfer 236

16.1 The General Differential Equation for Energy Transfer 236

16.2 Special Forms of the Differential Energy Equation 239

16.3 Commonly Encountered Boundary Conditions 240

16.4 Closure 244

17. Steady-State Conduction 247

17.1 One-Dimensional Conduction 247

17.2 One-Dimensional Conduction with Internal Generation of Energy 253

17.3 Heat Transfer from Extended Surfaces 256

17.4 Two- and Three-Dimensional Systems 263

17.5 Closure 269

18. Unsteady-State Conduction 277

18.1 Analytical Solutions 277

18.2 Temperature-Time Charts for Simple Geometric Shapes 286

18.3 Numerical Methods for Transient Conduction Analysis 288

18.4 An Integral Method for One-Dimensional Unsteady Conduction 291

18.5 Closure 295

19. Convective Heat Transfer 301

19.1 Fundamental Considerations in Convective Heat Transfer 301

19.2 Significant Parameters in Convective Heat Transfer 302

19.3 Dimensional Analysis of Convective Energy Transfer 303

19.4 Exact Analysis of the Laminar Boundary Layer 306

19.5 Approximate Integral Analysis of the Thermal Boundary Layer 310

19.6 Energy- and Momentum-Transfer Analogies 312

19.7 Turbulent Flow Considerations 314

19.8 Closure 320

20. Convective Heat-Transfer Correlations 324

20.1 Natural Convection 324

20.2 Forced Convection for Internal Flow 332

20.3 Forced Convection for External Flow 338

20.4 Closure 345

21. Boiling and Condensation 352

21.1 Boiling 352

21.2 Condensation 357

21.3 Closure 363

22. Heat-Transfer Equipment 365

22.1 Types of Heat Exchangers 365

22.2 Single-Pass Heat-Exchanger Analysis: The Log-Mean Temperature Difference 368

22.3 Crossflow and Shell-and-Tube Heat-Exchanger Analysis 372

22.4 The Number-of-Transfer-Units (NTU) Method of Heat-Exchanger Analysis and Design 376

22.5 Additional Considerations in Heat-Exchanger Design 383

22.6 Closure 385

23. Radiation Heat Transfer 390

23.1 Nature of Radiation 390

23.2 Thermal Radiation 391

23.3 The Intensity of Radiation 393

23.4 Planck’s Law of Radiation 394

23.5 Stefan–Boltzmann Law 398

23.6 Emissivity and Absorptivity of Solid Surfaces 400

23.7 Radiant Heat Transfer Between Black Bodies 405

23.8 Radiant Exchange in Black Enclosures 412

23.9 Radiant Exchange with Reradiating Surfaces Present 413

23.10 Radiant Heat Transfer Between Gray Surfaces 414

23.11 Radiation from Gases 421

23.12 The Radiation Heat-Transfer Coefficient 423

23.13 Closure 426

24. Fundamentals of Mass Transfer 431

24.1 Molecular Mass Transfer 432

24.2 The Diffusion Coefficient 441

24.3 Convective Mass Transfer 461

24.4 Closure 462

25. Differential Equations of Mass Transfer 467

25.1 The Differential Equation for Mass Transfer 467

25.2 Special Forms of the Differential Mass-Transfer Equation 470

25.3 Commonly Encountered Boundary Conditions 472

25.4 Steps for Modeling Processes Involving Molecular Diffusion 475

25.5 Closure 484

26. Steady-State Molecular Diffusion 489

26.1 One-Dimensional Mass Transfer Independent of Chemical Reaction 489

26.2 One-Dimensional Systems Associated with Chemical Reaction 500

26.3 Two- and Three-Dimensional Systems 510

26.4 Simultaneous Momentum, Heat, and Mass Transfer 513

26.5 Closure 520

27. Unsteady-State Molecular Diffusion 533

27.1 Unsteady-State Diffusion and Fick’s Second Law 533

27.2 Transient Diffusion in a Semi-Infinite Medium 534

27.3 Transient Diffusion in a Finite-Dimensional Medium under Conditions of Negligible Surface Resistance 538

27.4 Concentration-Time Charts for Simple Geometric Shapes 546

27.5 Closure 550

28. Convective Mass Transfer 556

28.1 Fundamental Considerations in Convective Mass Transfer 556

28.2 Significant Parameters in Convective Mass Transfer 559

28.3 Dimensional Analysis of Convective Mass Transfer 562

28.4 Exact Analysis of the Laminar Concentration Boundary Layer 564

28.5 Approximate Analysis of the Concentration Boundary Layer 572

28.6 Mass-, Energy-, and Momentum-Transfer Analogies 577

28.7 Models for Convective Mass-Transfer Coefficients 584

28.8 Closure 586

29. Convective Mass Transfer Between Phases 592

29.1 Equilibrium 592

29.2 Two-Resistance Theory 595

29.3 Closure 610

30. Convective Mass-Transfer Correlations 617

30.1 Mass Transfer to Plates, Spheres, and Cylinders 618

30.2 Mass Transfer Involving Flow Through Pipes 626

30.3 Mass Transfer in Wetted-Wall Columns 627

30.4 Mass Transfer in Packed and Fluidized Beds 630

30.5 Gas–Liquid Mass Transfer in Bubble Columns and Stirred Tanks 631

30.6 Capacity Coefficients for Packed Towers 634

30.7 Steps for Modeling Mass-Transfer Processes Involving Convection 635

30.8 Closure 644

31. Mass-Transfer Equipment 655

31.1 Types of Mass-Transfer Equipment 655

31.2 Gas–Liquid Mass-Transfer Operations in Well-Mixed Tanks 657

31.3 Mass Balances for Continuous-Contact Towers: Operating-Line Equations 662

31.4 Enthalpy Balances for Continuous-Contacts Towers 670

31.5 Mass-Transfer Capacity Coefficients 671

31.6 Continuous-Contact Equipment Analysis 672

31.7 Closure 686

Nomenclature 693

Appendixes

A. Transformations of the Operators ∇ and ∇² to Cylindrical Coordinates 700

B. Summary of Differential Vector Operations in Various Coordinate Systems 703

C. Symmetry of the Stress Tensor 706

D. The Viscous Contribution to the Normal Stress 707

E. The Navier–Stokes Equations for Constant p and μ in Cartesian, Cylindrical, and Spherical Coordinates 709

F. Charts for Solution of Unsteady Transport Problems 711

G. Properties of the Standard Atmosphere 724

H. Physical Properties of Solids 727

I. Physical Properties of Gases and Liquids 730

J. Mass-Transfer Diffusion Coefficients in Binary Systems 743

K. Lennard–Jones Constants 746

L. The Error Function 749

M. Standard Pipe Sizes 750

N. Standard Tubing Gages 752

Index 754

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