# Fundamentals of Heat and Mass Transfer

, by Bergman, Theodore L.; Lavine, Adrienne S.; Incropera, Frank P.; DeWitt, David P.**Note:**Supplemental materials are not guaranteed with Rental or Used book purchases.

- ISBN: 9781119722489 | 1119722489
- Cover: Loose-leaf
- Copyright: 7/8/2020

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**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.**

Fundamentals of Heat and Mass Transfer 8Fundamentals of Heat and Mass Transfer 8

^{th}Edition**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