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This book presents an elementary treatment of the principles of heat transfer. As a text it contains more than enough material for a one-semester course that may be presented at the junior level, or higher, depending on individual course objectives. The course is normally required in chemical and mechanical engineering curricula but is recommended for electrical engineering students as well, because of the signiﬁcance of cooling problems in various electronics applications. In the author’s experience, electrical engineering students do quite well in a heat-transfer course, even with no formal coursework background in thermodynamics or ﬂuid mechanics. A background in ordinary differential equations is helpful for proper understanding of the material.

Presentation of the subject follows classical lines of separate discussions for conduc-tion, convection, and radiation, although it is emphasized that the physical mechanism of convection heat transfer is one of conduction through the stationary ﬂuid layer near the heat-transfer surface. Throughout the book emphasis has been placed on physical understanding while, at the same time, relying on meaningful experimental data in those circumstances that do not permit a simple analytical solution.

Conduction is treated from both the analytical and the numerical viewpoint, so that the reader is afforded the insight that is gained from analytical solutions as well as the important tools of numerical analysis that must often be used in practice. A liberal number of numerical examples are given that include heat sources and radiation boundary conditions, non-uniform mesh size, and one example of a three-dimensional nodal system. A similar procedure is followed in the presentation of convection heat transfer. An integral analysis of both free- and forced-convection boundary layers is used to present a physical picture of the convection process. From this physical description, inferences may be drawn that naturally lead to the presentation of empirical and practical relations for calculating convection heat-transfer coefﬁcients. Because it provides an easier instruction vehicle than other methods, the radiation-network method is used extensively in the introduction of analysis of radiation systems, while a more generalized formulation is given later. Systems of nonlinear equations requiring iterative solutions are also discussed in the conduction and radiation chapters but

the details of solution are relegated to cited software references. The assumption is madethat the well-disposed reader should select his or her own preferred vehicle for solution ofsystems of nonlinear equations

C HAPT E R 1

Introduction 1

1-1 Conduction Heat Transfer 1

1-2 Thermal Conductivity 5

1-3 Convection Heat Transfer 10

1-4 Radiation Heat Transfer 12

1-5 Dimensions and Units 13

1-6 Summary 19

Review Questions 20

List of Worked Examples 21

Problems 21

References 25

C HAPT E R 2

Steady-State Conduction—

One Dimension 27

2-1 Introduction 27

2-2 The Plane Wall 27

2-3 Insulation and R Values 28

2-4 Radial Systems 29

2-5 The Overall Heat-Transfer Coefﬁcient 33

2-6 Critical Thickness of Insulation 39

2-7 Heat-Source Systems 41

2-8 Cylinder with Heat Sources 43

2-9 Conduction-Convection Systems 45

2-10 Fins 48

2-11 Thermal Contact Resistance 57

Review Questions 60

List of Worked Examples 60

Problems 61

References 75

C HAPT E R 3

Steady-State Conduction—Multiple

Dimensions 77

3-1 Introduction 77

3-2 Mathematical Analysis of Two-Dimensional

Heat Conduction 77

3-3 Graphical Analysis 81

3-4 The Conduction Shape Factor 83

3-5 Numerical Method of Analysis 88

3-6 Numerical Formulation in Terms of

Resistance Elements 98

3-7 Gauss-Seidel Iteration 99

3-8 Accuracy Considerations 102

3-9 Electrical Analogy for Two-Dimensional

Conduction 118

3-10 Summary 119

Review Questions 119

List of Worked Examples 120

Problems 120

References 136

C HAPT E R 4

Unsteady-State Conduction 139

4-1 Introduction 139

4-2 Lumped-Heat-Capacity System 141

4-3 Transient Heat Flow in a Semi-Inﬁnite

Solid 143

4-4 Convection Boundary Conditions 147

4-5 Multidimensional Systems 162

4-6 Transient Numerical Method 168

4-7 Thermal Resistance and Capacity

Formulation 176

4-8 Summary 192

Review Questions 193

List of Worked Examples 193

Problems 194

References 214

vi Contents

CHAPTER 5

Principles of Convection 215

5-1 Introduction 215

5-2 Viscous Flow 215

5-3 Inviscid Flow 218

5-4 Laminar Boundary Layer on a Flat Plate 222

5-5 Energy Equation of the Boundary Layer 228

5-6 The Thermal Boundary Layer 231

5-7 The Relation Between Fluid Friction

and Heat Transfer 241

5-8 Turbulent-Boundary-Layer Heat Transfer 243

5-9 Turbulent-Boundary-Layer Thickness 250

5-10 Heat Transfer in Laminar Tube Flow 253

5-11 Turbulent Flow in a Tube 257

5-12 Heat Transfer in High-Speed Flow 259

5-13 Summary 264

Review Questions 264

List of Worked Examples 266

Problems 266

References 274

CHAPTER 6

Empirical and Practical Relations

for Forced-Convection Heat Transfer 277

6-1 Introduction 277

6-2 Empirical Relations for Pipe and Tube Flow 279

6-3 Flow Across Cylinders and Spheres 293

6-4 Flow Across Tube Banks 303

6-5 Liquid-Metal Heat Transfer 308

6-6 Summary 311

Review Questions 313

List of Worked Examples 314

Problems 314

References 324

CHAPTER 7

Natural Convection Systems 327

7-1 Introduction 327

7-2 Free-Convection Heat Transfer on a

Vertical Flat Plate 327

7-3 Empirical Relations for Free Convection 332

7-4 Free Convection from Vertical Planes

and Cylinders 334

7-5 Free Convection from Horizontal Cylinders 340

7-6 Free Convection from Horizontal Plates 342

7-7 Free Convection from Inclined Surfaces 344

7-8 Nonnewtonian Fluids 345

7-9 Simpliﬁed Equations for Air 345

7-10 Free Convection from Spheres 346

7-11 Free Convection in Enclosed Spaces 347

-12 Combined Free and Forced Convection 358

7-13 Summary 362

7-14 Summary Procedure for all Convection

Problems 362

Review Questions 363

List of Worked Examples 365

Problems 365

References 375

CHAPTER 8

Radiation Heat Transfer 379

8-1 Introduction 379

8-2 Physical Mechanism 379

8-3 Radiation Properties 381

8-4 Radiation Shape Factor 388

8-5 Relations Between Shape Factors 398

8-6 Heat Exchange Between Nonblackbodies 404

8-7 Inﬁnite Parallel Surfaces 411

8-8 Radiation Shields 416

8-9 Gas Radiation 420

8-10 Radiation Network for an Absorbing

and Transmitting Medium 421

8-11 Radiation Exchange with Specular Surfaces 426

8-12 Radiation Exchange with Transmitting,

Reﬂecting, and Absorbing Media 430

8-13 Formulation for Numerical Solution 437

8-14 Solar Radiation 451

8-15 Radiation Properties of the Environment 458

8-16 Effect of Radiation on Temperature

Measurement 459

8-17 The Radiation Heat-Transfer Coefﬁcient 460

8-18 Summary 461

Review Questions 462

List of Worked Examples 462

Problems 463

References 485

Contents vii

CHAPTER 9

Condensation and Boiling Heat Transfer 487

9-1 Introduction 487

9-2 Condensation Heat-Transfer Phenomena 487

9-3 The Condensation Number 492

9-4 Film Condensation Inside Horizontal

Tubes 493

9-5 Boiling Heat Transfer 496

9-6 Simpliﬁed Relations for Boiling Heat Transfer

with Water 507

9-7 The Heat Pipe 509

9-8 Summary and Design Information 511

Review Questions 512

List of Worked Examples 513

Problems 513

References 517

CHAPTER 10

Heat Exchangers 521

10-1 Introduction 521

10-2 The Overall Heat-Transfer Coefﬁcient 521

10-3 Fouling Factors 527

10-4 Types of Heat Exchangers 528

10-5 The Log Mean Temperature Difference 531

10-6 Effectiveness-NTU Method 540

10-7 Compact Heat Exchangers 555

10-8 Analysis for Variable Properties 559

10-9 Heat-Exchanger Design Considerations 567

Review Questions 567

List of Worked Examples 568

Problems 568

References 584

CHAPTER 11

Mass Transfer 587

11-1 Introduction 587

11-2 Fick’s Law of Diffusion 587

11-3 Diffusion in Gases 589

11-4 Diffusion in Liquids and Solids 593

11-5 The Mass-Transfer Coefﬁcient 594

11-6 Evaporation Processes in the

Atmosphere 597

Review Questions 600

List of Worked Examples 601

Problems 601

References 603

CHAPTER 12

Summary and Design Information 605

12-1 Introduction 605

12-2 Conduction Problems 606

12-3 Convection Heat-Transfer Relations 608

12-4 Radiation Heat Transfer 623

12-5 Heat Exchangers 628

List of Worked Examples 645

Problems 645

APPENDIX A

Tables 649

A-1 The Error Function 649

A-2 Property Values for Metals 650

A-3 Properties of Nonmetals 654

A-4 Properties of Saturated Liquids 656

A-5 Properties of Air at Atmospheric

Pressure 658

A-6 Properties of Gases at Atmospheric

Pressure 659

A-7 Physical Properties of Some Common

Low-Melting-Point Metals 661

A-8 Diffusion Coefﬁcients of Gases and Vapors

in Air at 25◦C and 1 atm 661

A-9 Properties of Water (Saturated Liquid) 662

A-10 Normal Total Emissivity of Various

Surfaces 663

A-11 Steel-Pipe Dimensions 665

A-12 Conversion Factors 666

APPENDIX B

Exact Solutions of Laminar-Boundary-Layer Equations 667

APPENDIX C

Analytical Relations for the

Heisler Charts 673

viii Contents

APPENDIX D

Use of Microsoft Excel for Solution

of Heat-Transfer Problems 679

D-1 Introduction 679

D-2 Excel Template for Solution of

Steady-State Heat-Transfer

Problems 679

D-3 Solution of Equations for Nonuniform

Grid and/or Nonuniform

Properties 683

D-4 Heat Sources and Radiation

Boundary Conditions 683

D-5 Excel Procedure for Transient

Heat Transfer 684

-6 Formulation for Heating of Lumped Capacity with Convection and Radiation 697

List of Worked Examples 712

References 712

Index 713

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