Fundamentals of Heat and Mass Transfer

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Fundamentals of Heat and Mass Transfer 8^th Edition has been the gold standard of heat transfer pedagogy for many decades, with a commitment to continuous improvement by four authors’ with more than 150 years of combined experience in heat transfer education, research and practice. Applying the rigorous and systematic problem-solving methodology that this text pioneered an abundance of examples and problems reveal the richness and beauty of the discipline. This edition makes heat and mass transfer more approachable by giving additional emphasis to fundamental concepts, while highlighting the relevance of two of today’s most critical issues: energy and the environment.

Ted Bergman received his Ph.D. from Purdue University, and has been a faculty member at the University of Kansas (2012 - present), the University of Connecticut (1996 - 2012), and The University of Texas at Austin (1985 - 1996). He directed the Thermal Transport Processes Program at the U.S. National Science Foundation from 2008 to 2010. Early in his career, Dr. Bergman designed the cooling systems of large electric power generation stations.

Adrienne Lavine is Professor and past Department Chair (2006 - 2011) in the Mechanical and Aerospace Engineering Department at the University of California, Los Angeles. She began her academic career there in 1984 as an Assistant Professor after obtaining her Ph.D. in Mechanical Engineering from the University of California, Berkeley.

Symbols xix

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 the Efficiency of Heat Engines 28

1.4 Units and Dimensions 33

1.5 Analysis of Heat Transfer Problems: Methodology 35

1.6 Relevance of Heat Transfer 38

1.7 Summary 42

References 45

Chapter 2 Introduction to Conduction 47

2.1 The Conduction Rate Equation 48

2.2 The Thermal Properties of Matter 50

2.2.1 Thermal Conductivity 51

2.2.2 Other Relevant Properties 58

2.3 The Heat Diffusion Equation 62

2.4 Boundary and Initial Conditions 70

2.5 Summary 74

References 75

Chapter 3 One-Dimensional, Steady-State Conduction 77

3.1 The Plane Wall 78

3.1.1 Temperature Distribution 78

3.1.2 Thermal Resistance 80

3.1.3 The Composite Wall 81

3.1.4 Contact Resistance 83

3.1.5 Porous Media 85

3.2 An Alternative Conduction Analysis 99

3.3 Radial Systems 103

3.3.1 The Cylinder 103

3.3.2 The Sphere 108

3.4 Summary of One-Dimensional Conduction Results 109

3.5 Conduction with Thermal Energy Generation 109

3.5.1 The Plane Wall 110

3.5.2 Radial Systems 116

3.5.3 Tabulated Solutions 117

3.5.4 Application of Resistance Concepts 117

3.6 Heat Transfer from Extended Surfaces 121

3.6.1 A General Conduction Analysis 123

3.6.2 Fins of Uniform Cross-Sectional Area 125

3.6.3 Fin Performance Parameters 131

3.6.4 Fins of Nonuniform Cross-Sectional Area 134

3.6.5 Overall Surface Efficiency 137

3.7 Other Applications of One-Dimensional, Steady-State Conduction 141

3.7.1 The Bioheat Equation 141

3.7.2 Thermoelectric Power Generation 145

3.7.3 Nanoscale Conduction 153

3.8 Summary 157

References 159

Chapter 4 Two-Dimensional, Steady-State Conduction 161

4.1 General Considerations and Solution Techniques 162

4.2 The Method of Separation of Variables 163

4.3 The Conduction Shape Factor and the Dimensionless Conduction Heat Rate 167

4.4 Finite-Difference Equations 173

4.4.1 The Nodal Network 173

4.4.2 Finite-Difference Form of the Heat Equation: No Generation and Constant Properties 174

4.4.3 Finite-Difference Form of the Heat Equation: The Energy Balance Method 175

4.5 Solving the Finite-Difference Equations 182

4.5.1 Formulation as a Matrix Equation 182

4.5.2 Verifying the Accuracy of the Solution 183

4.6 Summary 188

References 189

Chapter 5 Transient Conduction 191

5.1 The Lumped Capacitance Method 192

5.2 Validity of the Lumped Capacitance Method 195

5.3 General Lumped Capacitance Analysis 199

5.3.1 Radiation Only 200

5.3.2 Negligible Radiation 200

5.3.3 Convection Only with Variable Convection Coefficient 201

5.3.4 Additional Considerations 201

5.4 Spatial Effects 210

5.5 The Plane Wall with Convection 211

5.5.1 Exact Solution 212

5.5.2 Approximate Solution 212

5.5.3 Total Energy Transfer: Approximate Solution 214

5.5.4 Additional Considerations 214

5.6 Radial Systems with Convection 215

5.6.1 Exact Solutions 215

5.6.2 Approximate Solutions 216

5.6.3 Total Energy Transfer: Approximate Solutions 216

5.6.4 Additional Considerations 217

5.7 The Semi-Infinite Solid 222

5.8 Objects with Constant Surface Temperatures or Surface Heat Fluxes 229

5.8.1 Constant Temperature Boundary Conditions 229

5.8.2 Constant Heat Flux Boundary Conditions 231

5.8.3 Approximate Solutions 232

5.9 Periodic Heating 239

5.10 Finite-Difference Methods 242

5.10.1 Discretization of the Heat Equation: The Explicit Method 242

5.10.2 Discretization of the Heat Equation: The Implicit Method 249

5.11 Summary 256

References 257

Chapter 6 Introduction to Convection 259

6.1 The Convection Boundary Layers 260

6.1.1 The Velocity Boundary Layer 260

6.1.2 The Thermal Boundary Layer 261

6.1.3 The Concentration Boundary Layer 263

6.1.4 Significance of the Boundary Layers 264

6.2 Local and Average Convection Coefficients 264

6.2.1 Heat Transfer 264

6.2.2 Mass Transfer 265

6.3 Laminar and Turbulent Flow 271

6.3.1 Laminar and Turbulent Velocity Boundary Layers 271

6.3.2 Laminar and Turbulent Thermal and Species Concentration Boundary Layers 273

6.4 The Boundary Layer Equations 276

6.4.1 Boundary Layer Equations for Laminar Flow 277

6.4.2 Compressible Flow 280

6.5 Boundary Layer Similarity: The Normalized Boundary Layer Equations 280

6.5.1 Boundary Layer Similarity Parameters 281

6.5.2 Dependent Dimensionless Parameters 281

6.6 Physical Interpretation of the Dimensionless Parameters 290

6.7 Boundary Layer Analogies 292

6.7.1 The Heat and Mass Transfer Analogy 293

6.7.2 Evaporative Cooling 296

6.7.3 The Reynolds Analogy 299

6.8 Summary 300

References 301

Chapter 7 External Flow 303

7.1 The Empirical Method 305

7.2 The Flat Plate in Parallel Flow 306

7.2.1 Laminar Flow over an Isothermal Plate: A Similarity Solution 307

7.2.2 Turbulent Flow over an Isothermal Plate 313

7.2.3 Mixed Boundary Layer Conditions 314

7.2.4 Unheated Starting Length 315

7.2.5 Flat Plates with Constant Heat Flux Conditions 316

7.2.6 Limitations on Use of Convection Coefficients 317

7.3 Methodology for a Convection Calculation 317

7.4 The Cylinder in Cross Flow 325

7.4.1 Flow Considerations 325

7.4.2 Convection Heat and Mass Transfer 327

7.5 The Sphere 335

7.6 Flow Across Banks of Tubes 338

7.7 Impinging Jets 347

7.7.1 Hydrodynamic and Geometric Considerations 347

7.7.2 Convection Heat and Mass Transfer 348

7.8 Packed Beds 352

7.9 Summary 353

References 356

Chapter 8 Internal Flow 357

8.1 Hydrodynamic Considerations 358

8.1.1 Flow Conditions 358

8.1.2 The Mean Velocity 359

8.1.3 Velocity Profile in the Fully Developed Region 360

8.1.4 Pressure Gradient and Friction Factor in Fully Developed Flow 362

8.2 Thermal Considerations 363

8.2.1 The Mean Temperature 364

8.2.2 Newton’s Law of Cooling 365

8.2.3 Fully Developed Conditions 365

8.3 The Energy Balance 369

8.3.1 General Considerations 369

8.3.2 Constant Surface Heat Flux 370

8.3.3 Constant Surface Temperature 373

8.4 Laminar Flow in Circular Tubes: Thermal Analysis and Convection Correlations 377

8.4.1 The Fully Developed Region 377

8.4.2 The Entry Region 382

8.4.3 Temperature-Dependent Properties 384

8.5 Convection Correlations: Turbulent Flow in Circular Tubes 384

8.6 Convection Correlations: Noncircular Tubes and the Concentric Tube Annulus 392

8.7 Heat Transfer Enhancement 395

8.8 Forced Convection in Small Channels 398

8.8.1 Microscale Convection in Gases (0.1 μm ≤ D_h ≤ 100 μm) 398

8.8.2 Microscale Convection in Liquids 399

8.8.3 Nanoscale Convection (D_h ≤ 100 nm) 400

8.9 Convection Mass Transfer 403

8.10 Summary 405

References 408

Chapter 9 Free Convection 409

9.1 Physical Considerations 410

9.2 The Governing Equations for Laminar Boundary Layers 412

9.3 Similarity Considerations 414

9.4 Laminar Free Convection on a Vertical Surface 415

9.5 The Effects of Turbulence 418

9.6 Empirical Correlations: External Free Convection Flows 420

9.6.1 The Vertical Plate 421

9.6.2 Inclined and Horizontal Plates 424

9.6.3 The Long Horizontal Cylinder 429

9.6.4 Spheres 433

9.7 Free Convection Within Parallel Plate Channels 434

9.7.1 Vertical Channels 435

9.7.2 Inclined Channels 437

9.8 Empirical Correlations: Enclosures 437

9.8.1 Rectangular Cavities 437

9.8.2 Concentric Cylinders 440

9.8.3 Concentric Spheres 441

9.9 Combined Free and Forced Convection 443

9.10 Convection Mass Transfer 444

9.11 Summary 445

References 446

Chapter 10 Boiling and Condensation 449

10.1 Dimensionless Parameters in Boiling and Condensation 450

10.2 Boiling Modes 451

10.3 Pool Boiling 452

10.3.1 The Boiling Curve 452

10.3.2 Modes of Pool Boiling 453

10.4 Pool Boiling Correlations 456

10.4.1 Nucleate Pool Boiling 456

10.4.2 Critical Heat Flux for Nucleate Pool Boiling 458

10.4.3 Minimum Heat Flux 459

10.4.4 Film Pool Boiling 459

10.4.5 Parametric Effects on Pool Boiling 460

10.5 Forced Convection Boiling 465

10.5.1 External Forced Convection Boiling 466

10.5.2 Two-Phase Flow 466

10.5.3 Two-Phase Flow in Microchannels 469

10.6 Condensation: Physical Mechanisms 469

10.7 Laminar Film Condensation on a Vertical Plate 471

10.8 Turbulent Film Condensation 475

10.9 Film Condensation on Radial Systems 480

10.10 Condensation in Horizontal Tubes 485

10.11 Dropwise Condensation 486

10.12 Summary 487

References 487

Chapter 11 Heat Exchangers 491

11.1 Heat Exchanger Types 492

11.2 The Overall Heat Transfer Coefficient 494

11.3 Heat Exchanger Analysis: Use of the Log Mean Temperature Difference 497

11.3.1 The Parallel-Flow Heat Exchanger 498

11.3.2 The Counterflow Heat Exchanger 500

11.3.3 Special Operating Conditions 501

11.4 Heat Exchanger Analysis: The Effectiveness–NTU Method 508

11.4.1 Definitions 508

11.4.2 Effectiveness–NTU Relations 509

11.5 Heat Exchanger Design and Performance Calculations 516

11.6 Additional Considerations 525

11.7 Summary 533

References 534

Chapter 12 Radiation: Processes and Properties 535

12.1 Fundamental Concepts 536

12.2 Radiation Heat Fluxes 539

12.3 Radiation Intensity 541

12.3.1 Mathematical Definitions 541

12.3.2 Radiation Intensity and Its Relation to Emission 542

12.3.3 Relation to Irradiation 547

12.3.4 Relation to Radiosity for an Opaque Surface 549

12.3.5 Relation to the Net Radiative Flux for an Opaque Surface 550

12.4 Blackbody Radiation 550

12.4.1 The Planck Distribution 551

12.4.2 Wien’s Displacement Law 552

12.4.3 The Stefan–Boltzmann Law 552

12.4.4 Band Emission 553

12.5 Emission from Real Surfaces 560

12.6 Absorption, Reflection, and Transmission by Real Surfaces 569

12.6.1 Absorptivity 570

12.6.2 Reflectivity 571

12.6.3 Transmissivity 573

12.6.4 Special Considerations 573

12.7 Kirchhoff’s Law 578

12.8 The Gray Surface 580

12.9 Environmental Radiation 586

12.9.1 Solar Radiation 587

12.9.2 The Atmospheric Radiation Balance 589

12.9.3 Terrestrial Solar Irradiation 591

12.10 Summary 594

References 598

Chapter 13 Radiation Exchange Between Surfaces 599

13.1 The View Factor 600

13.1.1 The View Factor Integral 600

13.1.2 View Factor Relations 601

13.2 Blackbody Radiation Exchange 610

13.3 Radiation Exchange Between Opaque, Diffuse, Gray Surfaces in an Enclosure 614

13.3.1 Net Radiation Exchange at a Surface 615

13.3.2 Radiation Exchange Between Surfaces 616

13.3.3 The Two-Surface Enclosure 622

13.3.4 Two-Surface Enclosures in Series and Radiation Shields 624

13.3.5 The Reradiating Surface 626

13.4 Multimode Heat Transfer 631

13.5 Implications of the Simplifying Assumptions 634

13.6 Radiation Exchange with Participating Media 634

13.6.1 Volumetric Absorption 634

13.6.2 Gaseous Emission and Absorption 635

13.7 Summary 639

References 640

Chapter 14 Diffusion Mass Transfer 641

14.1 Physical Origins and Rate Equations 642

14.1.1 Physical Origins 642

14.1.2 Mixture Composition 643

14.1.3 Fick’s Law of Diffusion 644

14.1.4 Mass Diffusivity 645

14.2 Mass Transfer in Nonstationary Media 647

14.2.1 Absolute and Diffusive Species Fluxes 647

14.2.2 Evaporation in a Column 650

14.3 The Stationary Medium Approximation 655

14.4 Conservation of Species for a Stationary Medium 655

14.4.1 Conservation of Species for a Control Volume 656

14.4.2 The Mass Diffusion Equation 656

14.4.3 Stationary Media with Specified Surface Concentrations 658

14.5 Boundary Conditions and Discontinuous Concentrations at Interfaces 662

14.5.1 Evaporation and Sublimation 663

14.5.2 Solubility of Gases in Liquids and Solids 663

14.5.3 Catalytic Surface Reactions 668

14.6 Mass Diffusion with Homogeneous Chemical Reactions 670

14.7 Transient Diffusion 673

14.8 Summary 679

References 680

Appendix A Thermophysical Properties of Matter 681

Appendix B Mathematical Relations and Functions 713

Appendix C Thermal Conditions Associated with Uniform Energy Generation in One-Dimensional, Steady-State Systems 719

APPENDIX D The Gauss–Seidel Method 725

APPENDIX E The Convection Transfer Equations 727

E.1 Conservation of Mass 728

E.2 Newton’s Second Law of Motion 728

E.3 Conservation of Energy 729

E.4 Conservation of Species 730

APPENDIX F Boundary Layer Equations for Turbulent Flow 731

APPENDIX G An Integral Laminar Boundary Layer Solution for Parallel Flow over a Flat Plate 735

Conversion Factors 739

Physical Constants 740

Index 741

Problems P-1

Chapter 1 Problems P-1

Chapter 2 Problems P-13

Chapter 3 Problems P-24

Chapter 4 Problems P-49

Chapter 5 Problems P-63

Chapter 6 Problems P-85

Chapter 7 Problems P-95

Chapter 8 Problems P-115

Chapter 9 Problems P-133

Chapter 10 Problems P-149

Chapter 11 Problems P-157

Chapter 12 Problems P-168

Chapter 13 Problems P-189

Chapter 14 Problems P-210