Fundamentals of Heat and Mass Transfer

Symbols xxi CHAPTER 1 Introduction 1

1.1 What and How? 2

1.2 Physical Origins and Rate Equations 3

1.3 Relationship to Thermodynamics 12

1.4 Units and Dimensions 36

1.5 Analysis of Heat Transfer Problems: Methodology 38

1.6 Relevance of Heat Transfer 41

1.7 Summary 45

References 48

Problems 49

CHAPTER 2 Introduction to Conduction 67

2.1 The Conduction Rate Equation 68

2.2 The Thermal Properties of Matter 70

2.3 The Heat Diffusion Equation 82

2.4 Boundary and Initial Conditions 90

2.5 Summary 94

References 95

Problems 95

CHAPTER 3 One-Dimensional, Steady-State Conduction 111

3.1 The Plane Wall 112

3.2 An Alternative Conduction Analysis 132

3.3 Radial Systems 136

3.4 Summary of One-Dimensional Conduction Results 142

3.5 Conduction with Thermal Energy Generation 142

3.6 Heat Transfer from Extended Surfaces 154

3.7 The Bioheat Equation 178

3.8 Thermoelectric Power Generation 182

3.9 Micro- and Nanoscale Conduction 189

3.10 Summary 190

References 193

Problems 193

CHAPTER 4 Two-Dimensional, Steady-State Conduction 229

4.1 Alternative Approaches 230

4.2 The Method of Separation of Variables 231

4.3 The Conduction Shape Factor and the Dimensionless Conduction Heat Rate 235

4.4 Finite-Difference Equations 241

4.5 Solving the Finite-Difference Equations 250

4.6 Summary 256

References 257

Problems 257

CHAPTER 5 Transient Conduction 279

5.1 The Lumped Capacitance Method 280

5.2 Validity of the Lumped Capacitance Method 283

5.3 General Lumped Capacitance Analysis 287

5.4 Spatial Effects 298

5.5 The Plane Wall with Convection 299

5.6 Radial Systems with Convection 303

5.7 The Semi-Infinite Solid 310

5.8 Objects with Constant Surface Temperatures or Surface Heat Fluxes 317

5.9 Periodic Heating 327

5.10 Finite-Difference Methods 330

5.11 Summary 345

References 346

Problems 346

CHAPTER 6 Introduction to Convection 377

6.1 The Convection Boundary Layers 378

6.2 Local and Average Convection Coefficients 382

6.3 Laminar and Turbulent Flow 389

6.4 The Boundary Layer Equations 394

6.5 Boundary Layer Similarity: The Normalized Boundary Layer Equations 398

6.6 Physical Interpretation of the Dimensionless Parameters 407

6.7 Boundary Layer Analogies 409

6.8 Summary 417

References 418

Problems 419

CHAPTER 7 External Flow 433

7.1 The Empirical Method 435

7.2 The Flat Plate in Parallel Flow 436

7.3 Methodology for a Convection Calculation 447

7.4 The Cylinder in Cross Flow 455

7.5 The Sphere 465

7.6 Flow Across Banks of Tubes 468

7.7 Impinging Jets 477

7.8 Packed Beds 482

7.9 Summary 483

References 486

Problems 486

CHAPTER 8 Internal Flow 517

8.1 Hydrodynamic Considerations 518

8.2 Thermal Considerations 523

8.3 The Energy Balance 529

8.4 Laminar Flow in Circular Tubes: Thermal Analysis and Convection Correlations 537

8.5 Convection Correlations: Turbulent Flow in Circular Tubes 544

8.6 Convection Correlations: Noncircular Tubes and the Concentric Tube Annulus 552

8.7 Heat Transfer Enhancement 555

8.8 Flow in Small Channels 558

8.9 Convection Mass Transfer 563

8.10 Summary 565

References 568

Problems 569

CHAPTER 9 Free Convection 593

9.1 Physical Considerations 594

9.2 The Governing Equations for Laminar Boundary Layers 597

9.3 Similarity Considerations 598

9.4 Laminar Free Convection on a Vertical Surface 599

9.5 The Effects of Turbulence 602

9.6 Empirical Correlations: External Free Convection Flows 604

9.7 Free Convection Within Parallel Plate Channels 618

9.8 Empirical Correlations: Enclosures 621

9.9 Combined Free and Forced Convection 627

9.10 Convection Mass Transfer 628

9.11 Summary 629

References 630

Problems 631

CHAPTER 10 Boiling and Condensation 653

10.1 Dimensionless Parameters in Boiling and Condensation 654

10.2 Boiling Modes 655

10.3 Pool Boiling 656

10.4 Pool Boiling Correlations 660

10.5 Forced Convection Boiling 669

10.6 Condensation: Physical Mechanisms 673

10.7 Laminar Film Condensation on a Vertical Plate 675

10.8 Turbulent Film Condensation 679

10.9 Film Condensation on Radial Systems 684

10.10 Condensation in Horizontal Tubes 689

10.11 Dropwise Condensation 690

10.12 Summary 691

References 691

Problems 693

CHAPTER 11 Heat Exchangers 705

11.1 Heat Exchanger Types 706

11.2 The Overall Heat Transfer Coefficient 708

11.3 Heat Exchanger Analysis: Use of the Log Mean Temperature Difference 711

11.4 Heat Exchanger Analysis: The Effectiveness–NTU Method 722

11.5 Heat Exchanger Design and Performance Calculations 730

11.6 Additional Considerations 739

11.7 Summary 747

References 748

Problems 748

CHAPTER 12 Radiation: Processes and Properties 767

12.1 Fundamental Concepts 768

12.2 Radiation Heat Fluxes 771

12.3 Radiation Intensity 773

12.4 Blackbody Radiation 782

12.5 Emission from Real Surfaces 792

12.6 Absorption, Reflection, and Transmission by Real Surfaces 801

12.7 Kirchhoff’s Law 810

12.8 The Gray Surface 812

12.9 Environmental Radiation 818

12.10 Summary 826

References 830

Problems 830

CHAPTER 13 Radiation Exchange Between Surfaces 861

13.1 The View Factor 862

13.2 Blackbody Radiation Exchange 872

13.3 Radiation Exchange Between Opaque, Diffuse, Gray Surfaces in an Enclosure 876

13.4 Multimode Heat Transfer 893

13.5 Implications of the Simplifying Assumptions 896

13.6 Radiation Exchange with Participating Media 896

13.7 Summary 901

References 902

Problems 903

CHAPTER 14 Diffusion Mass Transfer 933

14.1 Physical Origins and Rate Equations 934

14.2 Mass Transfer in Nonstationary Media 939

14.3 The Stationary Medium Approximation 947

14.4 Conservation of Species for a Stationary Medium 947

14.5 Boundary Conditions and Discontinuous Concentrations at Interfaces 954

14.6 Mass Diffusion with Homogeneous Chemical Reactions 962

14.7 Transient Diffusion 965

14.8 Summary 971

References 972

Problems 972

APPENDIX A Thermophysical Properties of Matter 981

APPENDIX B Mathematical Relations and Functions 1013

APPENDIX C Thermal Conditions Associated with Uniform Energy

Generation in One-Dimensional, Steady-State Systems 1019

APPENDIX D The Gauss–Seidel Method 1025

APPENDIX E The Convection Transfer Equations 1027

APPENDIX F Boundary Layer Equations for Turbulent Flow 1031

APPENDIX G An Integral Laminar Boundary Layer Solution for Parallel Flow over a Flat Plate 1035

Index 1039