FIFTH EDITION

Introduction to Heat Transfer

FRANK P. INCROPERA

College of Engineering University ofNotre Dame

DAVID P. DEWITT

School of Mechanical Engineering Purdue University

THEODORE L. BERGMAN

Department of Mechanical Engineering University of Connecticut

ADRIENNE S. LAVINE

Mechanical and Aerospace Engineering Department

University of California, Los Angeles

JOHN WILEY & SONS

CHAPTER 1

Introduction

Contents

Symbols

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 9 1.2.4 Relationship to Thermodynamics 12

1.3 The Conservation of Energy Requirement 13 1.3.1 Conservation of Energy for a Control Volume 13 1.3.2 The Surface Energy Balance 25 1.3.3 Application of the Conservation Laws:

Methodology 28 1.4 Analysis of Heat Transfer Problems: Methodology 29

xiv Contents

1.5 Relevance of Heat Transfer 32 1.6 Units and Dimensions 35 1.7 Summary 38

References 41 Problems 41

CHARTER 2

Introduction to Conduction 57

2.1 The Conduction Rate Equation 58 2.2 The Thermal Properties of Matter 60

2.2.1 Thermal Conductivity 60 2.2.2 Other Relevant Properties 67

2.3 The Heat Diffusion Equation 70 2.4 Boundary and Initial Conditions 77 2.5 Summary 81

References 82 Problems 82

CHAPTER 3

One-Dimensional, Steady-State Conduction 2Ü

3.1 The Plane Wall 96 3.1.1 Temperature Distribution 96 3.1.2 Thermal Resistance 98 3.1.3 The Composite Wall 99 3.1.4 Contact Resistance 101

3.2 An Alternative Conduction Analysis 112 3.3 Radial Systems 116

3.3.1 TheCylinder 116 3.3.2 TheSphere 122

3.4 Summary of One-Dimensional Conduction Results 125 3.5 Conduction with Thermal Energy Generation 126

3.5.1 The Plane Wall 127 3.5.2 Radial Systems 132 3.5.3 Application of Resistance Concepts 137

3.6 Heat Transfer from Extended Surfaces 137 3.6.1 A General Conduction Analysis 139 3.6.2 Fins of Uniform Cross-Sectional Area 141 3.6.3 Fin Performance 747 3.6.4 Fins of Nonuniform Cross-Sectional Area 150 3.6.5 Overall Surface Efficiency 153

3.7 The Bioheat Equation 162 3.8 Summary 166

References 168 Problems 169

Contents X V

CHAPTER4

Two-Dimensional, Steady-State Conduction 201

4.1 Alternative Approaches 202 4.2 The Method of Separation of Variables 203 4.3 The Conduction Shape Factor and the Dimensionless Conduction Heat Rate 207 4.4 Finite-Difference Equations 212

4.4.1 The Nodal Network 213 4.4.2 Finite-Difference Form of the Heat Equation 214 4.4.3 The Energy Balance Method 215

4.5 Solving the Finite-Difference Equations 222 4.5.1 The Matrix Inversion Method 222 4.5.2 Gauss-Seidel Iteration 223 4.5.3 Some Precautions 229

4.6 Summary 234 References ~35 Problems 235

4S.1 The Graphical Method W-l 4S. 1.1 Methodology of Constructing a Flux Plot W-l 45.1.2 Determination of the Heat Transfer Rate W-2 45.1.3 The Conduction Shape Factor W-3 References " -6 Problems " " "

CHAPTER *»

Transient Conduction 2o5

5.1 The Lumped Capacitance Method 256 5.2 Validity of the Lumped Capacitance Method 259 5.3 General Lumped Capacitance Analysis 263 5.4 Spatial Effects 270 5.5 The Plane Wall with Convection 272

5.5.1 Exact Solution 272 5.5.2 Approximate Solution 273 5.5.3 Total Energy Transfer 274 5.5.4 Additional Considerations 275

5.6 Radial Systems with Convection 276 5.6.1 Exact Solutions 276 5.6.2 Approximate Solutions 277 5.6.3 Total Energy Transfer 277 5.6.4 Additional Considerations 278

5.7 The Semi-Infmite Solid 283 5.8 Objects with Constant Surface Temperatures or Surface Heat Fluxes

5.8.1 Constant Temperature Boundary Conditions 290 5.8.2 Constant Heat Flux Boundary Conditions 292 5.8.3 Approximate Solutions 293

5.9 Periodic Heating

290

299

X V I Contents

5.10 Finite-Difference Methods 302 5.10.1 Discretization ofthe Heat Equation: The Explicit Method 302 5.10.2 Discretization of the Heat Equation: The Implicit Method 310

5.11 Summary 317 References 319 Problems 319

55.1 Graphical Representation of One-Dimensional, Transient Conduction in the Plane Wall, Long Cylinder, and Sphere W-8

55.2 Analytical Solution of Multidimensional Effects W-13 References W-18 Problems W-18

CHAPTER 6

Introduction to Convection 347

6.1 The Convection Boundary Layers 348 6.1.1 The Velocity Boundary Layer 348 6.1.2 The Thermal Boundary Layer 349 6.1.3 Significance of the Boundary Layers 350

6.2 Local and Average Convection Coefficients 351 6.2.1 Heat Transfer 351 6.2.2 The Problem of Convection 352

6.3 Laminar and Turbulent Flow 353 6.3.1 Laminar and Turbulent Velocity Boundary Layers 354 6.3.2 Laminar and Turbulent Thermal Boundary Layers 356

6.4 The Boundary Layer Equations 359 6.4.1 Boundary Layer Equations for Laminar Flow 360

6.5 Boundary Layer Similarity: The Normalized Boundary Layer Equations 362 6.5.1 Boundary Layer Similarity Parameters 362 6.5.2 Functional Form of the Solutions 364

6.6 Physical Significance of the Dimensionless Parameters 368 6.7 Momentum and Heat Transfer (Reynolds) Analogy 369 6.8 The Convection Coefficient 372 6.9 Summary 372

References 373 Problems 373

* 6S.1 Derivation ofthe Convection Transfer Equations W-21 65.1.1 Conservation of Mass W-21 65.1.2 Newton's Second Law of Motion W-22 65.1.3 Conservation of Energy W-26 References W-32 Problems W-32

CHAPTER T

Externa! Flow 381

7.1 The Empirical Method 383 7.2 The Fiat Plate in Parallel Flow 384

7.2.1 Laminar Flow over an Isothermal Plate: A Similarity Solution 385

Contents XV11

7.2.2 Turbulent Flow over an Isothermal Plate 389 7.2.3 Mixed Boundary Layer Conditions 390 7.2.4 Unheated Starting Length 391 7.2.5 Fiat Plates with Constant Heat Flux Conditions 392 7.2.6 Liinitations on Use of Convection Coefficients 393

7.3 Methodology f'or a Convection Calculation 393 7.4 The Cylinder in Cross Flow 399

7.4.1 Flow Considerations 399 7.4.2 Convection Heat Transfer 401

7.5 The Sphere 409 7.6 Flow across Banks of Tubes 412 7.7 Impinging Jets 423

7.7.1 Hydrodynamic and Geometrie Considerations 423 7.7.2 Convection Heat Transfer 425

7.8 Packed Beds 428 7.9 Summary 430

References 432 Problems 433

455

8.1 Hydrodynamic Considerations 456 8.1.1 Flow Conditions 456 8.1.2 The Mean Velocity 457 8.1.3 Velocity Profile in the Fully Developed Region 458 8.1.4 Pressure Gradient and Friction Factor in Fully Developed Flow 460

8.2 Thermal Considerations 461 8.2.1 The Mean Temperature 462 8.2.2 Newton's Law ofCooling 463 8.2.3 Fully Developed Conditions 463

8.3 The Energy Balance 467 8.3.1 General Considerations 467 8.3.2 Constant Surface Heat Flux 468 8.3.3 Constant Surface Temperature 471

8.4 Laminar Flow in Circular Tubes: Thermal Analysis and Convection Correlations 475 8.4.1 The Fully Developed Region 475 8.4.2 The Entry Region 482

8.5 Convection Correlations: Turbulent Flow in Circular Tubes 484 8.6 Convection Correlations: Noncircular Tubes and the Concentric Tube Annulus 488 8.7 Heat Transfer Enhancement 491 8.8 Microscale Internal Flow 494

8.8.1 Flow Conditions in Microscale Internal Flow 494 8.8.2 Thermal Considerations in Microscale Internal Flow 495

8.9 Summary 498 References 500 Problems 501

X X Contents

12.7 The Gray Surface 7 26 12.8 Environmental Radiation 732 12.9 Summary 7 3 8

References '42 Problems '42

CHAPTER 13

Radiation Exchange Between Surfaces 7 7 1

13.1 The View Factor 7 7 2

13.1.1 The View Factor Integral 772 13.1.2 View Factor Relations 773

13.2 Radiation Exchange Between Opaque, Diffuse, Gray Surfaces in an Enclosure 782 13.2.1 Net Radiation Exchange at a Surface 783 13.2.2 Radiation Exchange Between Surfaces 784 13.2.3 Blackbody Radiation Exchange 790 13.2.4 The Two-Surface Enclosure 791 13.2.5 Radiation Shields 792 13.2.6 The Reradiating Surface 795

13.3 Multimode Heat Transfer 7 " 13.4 Radiation Exchange with Participating Media 802

13.4.1 Volumetrie Absorption 803 13.4.2 Gaseous Emission and Absorption 803

13.5 Summary 8 0 7

References °""

Problems 809

APPENDIX A

Thermophysical Properties of Matter 8 3 9

APPENDIX B

Mathematical Relations and Functions 8 6 7

APPENDIX C

Thermal Conditions Associated with Uniform Energy Generation in One-Dimensional, Steady-State Systems 873

APPENDIX D

The Convection Transfer Equations 8 8 1

D.l Conservation of Mass 882 D.2 Newton's Second Law of Motion 8 8 2

D.3 Conservation of Energy 883

Contents xx i

APPENDIX E

Boundary Layer Equations for Turbulent Flow 885

APPENDIX F

An Integral Laminar Boundary Layer Solution for Parallel Flow over a Fiat Plate 889

Index 8 9 3