Principles of Heat and Mass Transfer (Paperback, 7th Edition International Student Version)

Symbols xxi

CHAPTER 1 Introduction 1

1.1 What and How? 2

1.2 Physical Origins and Rate Equations 3

1.2.1 Conduction 3

1.2.2 Convection 6

1.2.3 Radiation 8

1.2.4 The Thermal Resistance Concept 12

1.3 Relationship to Thermodynamics 12

1.3.1 Relationship to the First Law of Thermodynamics(Conservation of Energy) 13

1.3.2 Relationship to the Second Law of Thermodynamics and theEfficiency of Heat Engines 31

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

2.2.1 Thermal Conductivity 70

2.2.2 Other Relevant Properties 78

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 Conduction111

3.1 The Plane Wall 112

3.1.1 Temperature Distribution 112

3.1.2 Thermal Resistance 114

3.1.3 The Composite Wall 115

3.1.4 Contact Resistance 117

3.1.5 Porous Media 119

3.2 An Alternative Conduction Analysis 132

3.3 Radial Systems 136

3.3.1 The Cylinder 136

3.3.2 The Sphere 141

3.4 Summary of One-Dimensional Conduction Results 142

3.5 Conduction with Thermal Energy Generation 142

3.5.1 The Plane Wall 143

3.5.2 Radial Systems 149

3.5.3 Tabulated Solutions 150

3.5.4 Application of Resistance Concepts 150

3.6 Heat Transfer from Extended Surfaces 154

3.6.1 A General Conduction Analysis 156

3.6.2 Fins of Uniform Cross-Sectional Area 158

3.6.3 Fin Performance 164

3.6.4 Fins of Nonuniform Cross-Sectional Area 167

3.6.5 Overall Surface Efficiency 170

3.7 The Bioheat Equation 178

3.8 Thermoelectric Power Generation 182

3.9 Micro- and Nanoscale Conduction 189

3.9.1 Conduction Through Thin Gas Layers 189

3.9.2 Conduction Through Thin Solid Films 190

3.10 Summary 190

References 193

Problems 193

CHAPTER 4 Two-Dimensional, Steady-State Conduction229

4.1 Alternative Approaches 230

4.2 The Method of Separation of Variables 231

4.3 The Conduction Shape Factor and the Dimensionless ConductionHeat Rate 235

4.4 Finite-Difference Equations 241

4.4.1 The Nodal Network 241

4.4.2 Finite-Difference Form of the Heat Equation 242

4.4.3 The Energy Balance Method 243

4.5 Solving the Finite-Difference Equations 250

4.5.1 Formulation as a Matrix Equation 250

4.5.2 Verifying the Accuracy of the Solution 251

4.6 Summary 256

References 257

Problems 257

4S.1 The Graphical Method W-1

4S.1.1 Methodology of Constructing a Flux Plot W-1

4S.1.2 Determination of the Heat Transfer Rate W-2

4S.1.3 The Conduction Shape Factor W-3

4S.2 The Gauss–Seidel Method: Example of Usage W-5

References W-9

Problems W-10

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

5.3.1 Radiation Only 288

5.3.2 Negligible Radiation 288

5.3.3 Convection Only with Variable Convection Coefficient289

5.3.4 Additional Considerations 289

5.4 Spatial Effects 298

5.5 The Plane Wall with Convection 299

5.5.1 Exact Solution 300

5.5.2 Approximate Solution 300

5.5.3 Total Energy Transfer 302

5.5.4 Additional Considerations 302

5.6 Radial Systems with Convection 303

5.6.1 Exact Solutions 303

5.6.2 Approximate Solutions 304

5.6.3 Total Energy Transfer 304

5.6.4 Additional Considerations 305

5.7 The Semi-Infinite Solid 310

5.8 Objects with Constant Surface Temperatures or Surface HeatFluxes 317

5.8.1 Constant Temperature Boundary Conditions 317

5.8.2 Constant Heat Flux Boundary Conditions 319

5.8.3 Approximate Solutions 320

5.9 Periodic Heating 327

5.10 Finite-Difference Methods 330

5.10.1 Discretization of the Heat Equation: The Explicit Method330

5.10.2 Discretization of the Heat Equation: The Implicit Method337

5.11 Summary 345

References 346

Problems 346

5S.1 Graphical Representation of One-Dimensional, TransientConduction in the

Plane Wall, Long Cylinder, and Sphere W-12

5S.2 Analytical Solutions of Multidimensional Effects W-16

References W-22

Problems W-22

CHAPTER 6 Introduction to Convection 377

6.1 The Convection Boundary Layers 378

6.1.1 The Velocity Boundary Layer 378

6.1.2 The Thermal Boundary Layer 379

6.1.3 The Concentration Boundary Layer 380

6.1.4 Significance of the Boundary Layers 382

6.2 Local and Average Convection Coefficients 382

6.2.1 Heat Transfer 382

6.2.2 Mass Transfer 383

6.2.3 The Problem of Convection 385

6.3 Laminar and Turbulent Flow 389

6.3.1 Laminar and Turbulent Velocity Boundary Layers 389

6.3.2 Laminar and Turbulent Thermal and Species ConcentrationBoundary Layers 391

6.4 The Boundary Layer Equations 394

6.4.1 Boundary Layer Equations for Laminar Flow 394

6.4.2 Compressible Flow 397

6.5 Boundary Layer Similarity: The Normalized Boundary LayerEquations 398

6.5.1 Boundary Layer Similarity Parameters 398

6.5.2 Functional Form of the Solutions 400

6.6 Physical Interpretation of the Dimensionless Parameters407

6.7 Boundary Layer Analogies 409

6.7.1 The Heat and Mass Transfer Analogy 410

6.7.2 Evaporative Cooling 413

6.7.3 The Reynolds Analogy 416

6.8 Summary 417

References 418

Problems 419

6S.1 Derivation of the Convection Transfer Equations W-25

6S.1.1 Conservation of Mass W-25

6S.1.2 Newton’s Second Law of Motion W-26

6S.1.3 Conservation of Energy W-29

6S.1.4 Conservation of Species W-32

References W-36

Problems W-36

CHAPTER 7 External Flow 433

7.1 The Empirical Method 435

7.2 The Flat Plate in Parallel Flow 436

7.2.1 Laminar Flow over an Isothermal Plate: A SimilaritySolution 437

7.2.2 Turbulent Flow over an Isothermal Plate 443

7.2.3 Mixed Boundary Layer Conditions 444

7.2.4 Unheated Starting Length 445

7.2.5 Flat Plates with Constant Heat Flux Conditions 446

7.2.6 Limitations on Use of Convection Coefficients 446

7.3 Methodology for a Convection Calculation 447

7.4 The Cylinder in Cross Flow 455

7.4.1 Flow Considerations 455

7.4.2 Convection Heat and Mass Transfer 457

7.5 The Sphere 465

7.6 Flow Across Banks of Tubes 468

7.7 Impinging Jets 477

7.7.1 Hydrodynamic and Geometric Considerations 477

7.7.2 Convection Heat and Mass Transfer 478

7.8 Packed Beds 482

7.9 Summary 483

References 486

Problems 486

CHAPTER 8 Internal Flow 517

8.1 Hydrodynamic Considerations 518

8.1.1 Flow Conditions 518

8.1.2 The Mean Velocity 519

8.1.3 Velocity Profile in the Fully Developed Region 520

8.1.4 Pressure Gradient and Friction Factor in Fully DevelopedFlow 522

8.2 Thermal Considerations 523

8.2.1 The Mean Temperature 524

8.2.2 Newton’s Law of Cooling 525

8.2.3 Fully Developed Conditions 525

8.3 The Energy Balance 529

8.3.1 General Considerations 529

8.3.2 Constant Surface Heat Flux 530

8.3.3 Constant Surface Temperature 533

8.4 Laminar Flow in Circular Tubes: Thermal Analysis andConvection Correlations 537

8.4.1 The Fully Developed Region 537

8.4.2 The Entry Region 542

8.4.3 Temperature-Dependent Properties 544

8.5 Convection Correlations: Turbulent Flow in Circular Tubes544

8.6 Convection Correlations: Noncircular Tubes and theConcentric Tube Annulus 552

8.7 Heat Transfer Enhancement 555

8.8 Flow in Small Channels 558

8.8.1 Microscale Convection in Gases 558

8.8.2 Microscale Convection in Liquids 559

8.8.3 Nanoscale Convection 560

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 Flows604

9.6.1 The Vertical Plate 605

9.6.2 Inclined and Horizontal Plates 608

9.6.3 The Long Horizontal Cylinder 613

9.6.4 Spheres 617

9.7 Free Convection Within Parallel Plate Channels 618

9.7.1 Vertical Channels 619

9.7.2 Inclined Channels 621

9.8 Empirical Correlations: Enclosures 621

9.8.1 Rectangular Cavities 621

9.8.2 Concentric Cylinders 624

9.8.3 Concentric Spheres 625

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 Condensation654

10.2 Boiling Modes 655

10.3 Pool Boiling 656

10.3.1 The Boiling Curve 656

10.3.2 Modes of Pool Boiling 657

10.4 Pool Boiling Correlations 660

10.4.1 Nucleate Pool Boiling 660

10.4.2 Critical Heat Flux for Nucleate Pool Boiling 662

10.4.3 Minimum Heat Flux 663

10.4.4 Film Pool Boiling 663

10.4.5 Parametric Effects on Pool Boiling 664

10.5 Forced Convection Boiling 669

10.5.1 External Forced Convection Boiling 670

10.5.2 Two-Phase Flow 670

10.5.3 Two-Phase Flow in Microchannels 673

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 TemperatureDifference 711

11.3.1 The Parallel-Flow Heat Exchanger 712

11.3.2 The Counterflow Heat Exchanger 714

11.3.3 Special Operating Conditions 715

11.4 Heat Exchanger Analysis: The Effectiveness–NTU Method722

11.4.1 Definitions 722

11.4.2 Effectiveness–NTU Relations 723

11.5 Heat Exchanger Design and Performance Calculations 730

11.6 Additional Considerations 739

11.7 Summary 747

References 748

Problems 748

11S.1 Log Mean Temperature Difference Method for Multipass andCross-Flow Heat Exchangers W-40

11S.2 Compact Heat Exchangers W-44

References W-49

Problems W-50

CHAPTER 12 Radiation: Processes and Properties 767

12.1 Fundamental Concepts 768

12.2 Radiation Heat Fluxes 771

12.3 Radiation Intensity 773

12.3.1 Mathematical Definitions 773

12.3.2 Radiation Intensity and Its Relation to Emission 774

12.3.3 Relation to Irradiation 779

12.3.4 Relation to Radiosity for an Opaque Surface 781

12.3.5 Relation to the Net Radiative Flux for an Opaque Surface782

12.4 Blackbody Radiation 782

12.4.1 The Planck Distribution 783

12.4.2 Wien’s Displacement Law 784

12.4.3 The Stefan–Boltzmann Law 784

12.4.4 Band Emission 785

12.5 Emission from Real Surfaces 792

12.6 Absorption, Reflection, and Transmission by Real Surfaces801

12.6.1 Absorptivity 802

12.6.2 Reflectivity 803

12.6.3 Transmissivity 805

12.6.4 Special Considerations 805

12.7 Kirchhoff’s Law 810

12.8 The Gray Surface 812

12.9 Environmental Radiation 818

12.9.1 Solar Radiation 819

12.9.2 The Atmospheric Radiation Balance 821

12.9.3 Terrestrial Solar Irradiation 823

12.10 Summary 826

References 830

Problems 830

CHAPTER 13 Radiation Exchange Between Surfaces 861

13.1 The View Factor 862

13.1.1 The View Factor Integral 862

13.1.2 View Factor Relations 863

13.2 Blackbody Radiation Exchange 872

13.3 Radiation Exchange Between Opaque, Diffuse, Gray Surfacesin an Enclosure 876

13.3.1 Net Radiation Exchange at a Surface 877

13.3.2 Radiation Exchange Between Surfaces 878

13.3.3 The Two-Surface Enclosure 884

13.3.4 Radiation Shields 886

13.3.5 The Reradiating Surface 888

13.4 Multimode Heat Transfer 893

13.5 Implications of the Simplifying Assumptions 896

13.6 Radiation Exchange with Participating Media 896

13.6.1 Volumetric Absorption 896

13.6.2 Gaseous Emission and Absorption 897

13.7 Summary 901

References 902

Problems 903

CHAPTER 14 Diffusion Mass Transfer 933

14.1 Physical Origins and Rate Equations 934

14.1.1 Physical Origins 934

14.1.2 Mixture Composition 935

14.1.3 Fick’s Law of Diffusion 936

14.1.4 Mass Diffusivity 937

14.2 Mass Transfer in Nonstationary Media 939

14.2.1 Absolute and Diffusive Species Fluxes 939

14.2.2 Evaporation in a Column 942

14.3 The Stationary Medium Approximation 947

14.4 Conservation of Species for a Stationary Medium 947

14.4.1 Conservation of Species for a Control Volume 948

14.4.2 The Mass Diffusion Equation 948

14.4.3 Stationary Media with Specified Surface Concentrations950

14.5 Boundary Conditions and Discontinuous Concentrations atInterfaces 954

14.5.1 Evaporation and Sublimation 955

14.5.2 Solubility of Gases in Liquids and Solids 955

14.5.3 Catalytic Surface Reactions 960

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 EnergyGeneration in One-Dimensional, Steady-State Systems 1019

APPENDIX D The Gauss–Seidel Method 1025

APPENDIX E The Convection Transfer Equations 1027

E.1 Conservation of Mass 1028

E.2 Newton’s Second Law of Motion 1028

E.3 Conservation of Energy 1029

E.4 Conservation of Species 1030

APPENDIX F Boundary Layer Equations for Turbulent Flow 1031

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

Index 1039