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

Problems 45

Chapter 2 Introduction to Conduction 59

2.1 The Conduction Rate Equation 60

2.2 The Thermal Properties of Matter 62

2.2.1 Thermal Conductivity 63

2.2.2 Other Relevant Properties 70

2.3 The Heat Diffusion Equation 74

2.4 Boundary and Initial Conditions 82

2.5 Summary 86

References 87

Problems 87

Chapter 3 One-Dimensional, Steady-State Conduction 99

3.1 The Plane Wall 100

3.1.1 Temperature Distribution 100

3.1.2 Thermal Resistance 102

3.1.3 The Composite Wall 103

3.1.4 Contact Resistance 105

3.1.5 Porous Media 107

3.2 An Alternative Conduction Analysis 121

3.3 Radial Systems 125

3.3.1 The Cylinder 125

3.3.2 The Sphere 130

3.4 Summary of One-Dimensional Conduction Results 131

3.5 Conduction with Thermal Energy Generation 131

3.5.1 The Plane Wall 132

3.5.2 Radial Systems 138

3.5.3 Tabulated Solutions 139

3.5.4 Application of Resistance Concepts 139

3.6 Heat Transfer from Extended Surfaces 143

3.6.1 A General Conduction Analysis 145

3.6.2 Fins of Uniform Cross-Sectional Area 147

3.6.3 Fin Performance Parameters 153

3.6.4 Fins of Nonuniform Cross-Sectional Area 156

3.6.5 Overall Surface Efficiency 159

3.7 Other Applications of One-Dimensional, Steady-State Conduction 163

3.7.1 The Bioheat Equation 163

3.7.2 Thermoelectric Power Generation 167

3.7.3 Nanoscale Conduction 175

3.8 Summary 179

References 181

Problems 182

Chapter 4 Two-Dimensional, Steady-State Conduction 209

4.1 General Considerations and Solution Techniques 210

4.2 The Method of Separation of Variables 211

4.3 The Conduction Shape Factor and the Dimensionless Conduction Heat Rate 215

4.4 Finite-Difference Equations 221

4.4.1 The Nodal Network 221

4.4.2 Finite-Difference Form of the Heat Equation: No Generation and Constant Properties 222

4.4.3 Finite-Difference Form of the Heat Equation: The Energy Balance Method 223

4.5 Solving the Finite-Difference Equations 230

4.5.1 Formulation as a Matrix Equation 230

4.5.2 Verifying the Accuracy of the Solution 231

4.6 Summary 236

References 237

Problems 237

Chapter 5 Transient Conduction 253

5.1 The Lumped Capacitance Method 254

5.2 Validity of the Lumped Capacitance Method 257

5.3 General Lumped Capacitance Analysis 261

5.3.1 Radiation Only 262

5.3.2 Negligible Radiation 262

5.3.3 Convection Only with Variable Convection Coefficient 263

5.3.4 Additional Considerations 263

5.4 Spatial Effects 272

5.5 The Plane Wall with Convection 273

5.5.1 Exact Solution 274

5.5.2 Approximate Solution 274

5.5.3 Total Energy Transfer: Approximate Solution 276

5.5.4 Additional Considerations 276

5.6 Radial Systems with Convection 277

5.6.1 Exact Solutions 277

5.6.2 Approximate Solutions 278

5.6.3 Total Energy Transfer: Approximate Solutions 278

5.6.4 Additional Considerations 279

5.7 The Semi-Infinite Solid 284

5.8 Objects with Constant Surface Temperatures or Surface Heat Fluxes 291

5.8.1 Constant Temperature Boundary Conditions 291

5.8.2 Constant Heat Flux Boundary Conditions 293

5.8.3 Approximate Solutions 294

5.9 Periodic Heating 301

5.10 Finite-Difference Methods 304

5.10.1 Discretization of the Heat Equation: The Explicit Method 304

5.10.2 Discretization of the Heat Equation: The Implicit Method 311

5.11 Summary 318

References 319

Problems 319

Chapter 6 Introduction to Convection 341

6.1 The Convection Boundary Layers 342

6.1.1 The Velocity Boundary Layer 342

6.1.2 The Thermal Boundary Layer 343

6.1.3 The Concentration Boundary Layer 345

6.1.4 Significance of the Boundary Layers 346

6.2 Local and Average Convection Coefficients 346

6.2.1 Heat Transfer 346

6.2.2 Mass Transfer 347

6.3 Laminar and Turbulent Flow 353

6.3.1 Laminar and Turbulent Velocity Boundary Layers 353

6.3.2 Laminar and Turbulent Thermal and Species Concentration Boundary Layers 355

6.4 The Boundary Layer Equations 358

6.4.1 Boundary Layer Equations for Laminar Flow 359

6.4.2 Compressible Flow 362

6.5 Boundary Layer Similarity: The Normalized Boundary Layer Equations 362

6.5.1 Boundary Layer Similarity Parameters 363

6.5.2 Dependent Dimensionless Parameters 363

6.6 Physical Interpretation of the Dimensionless Parameters 372

6.7 Boundary Layer Analogies 374

6.7.1 The Heat and Mass Transfer Analogy 375

6.7.2 Evaporative Cooling 378

6.7.3 The Reynolds Analogy 381

6.8 Summary 382

References 383

Problems 384

Chapter 7 External Flow 395

7.1 The Empirical Method 397

7.2 The Flat Plate in Parallel Flow 398

7.2.1 Laminar Flow over an Isothermal Plate: A Similarity Solution 399

7.2.2 Turbulent Flow over an Isothermal Plate 405

7.2.3 Mixed Boundary Layer Conditions 406

7.2.4 Unheated Starting Length 407

7.2.5 Flat Plates with Constant Heat Flux Conditions 408

7.2.6 Limitations on Use of Convection Coefficients 409

7.3 Methodology for a Convection Calculation 409

7.4 The Cylinder in Cross Flow 417

7.4.1 Flow Considerations 417

7.4.2 Convection Heat and Mass Transfer 419

7.5 The Sphere 427

7.6 Flow Across Banks of Tubes 430

7.7 Impinging Jets 439

7.7.1 Hydrodynamic and Geometric Considerations 439

7.7.2 Convection Heat and Mass Transfer 440

7.8 Packed Beds 444

7.9 Summary 445

References 448

Problems 448

Chapter 8 Internal Flow 469

8.1 Hydrodynamic Considerations 470

8.1.1 Flow Conditions 470

8.1.2 The Mean Velocity 471

8.1.3 Velocity Profile in the Fully Developed Region 472

8.1.4 Pressure Gradient and Friction Factor in Fully Developed Flow 474

8.2 Thermal Considerations 475

8.2.1 The Mean Temperature 476

8.2.2 Newton''s Law of Cooling 477

8.2.3 Fully Developed Conditions 477

8.3 The Energy Balance 481

8.3.1 General Considerations 481

8.3.2 Constant Surface Heat Flux 482

8.3.3 Constant Surface Temperature 485

8.4 Laminar Flow in Circular Tubes: Thermal Analysis and Convection Correlations 489

8.4.1 The Fully Developed Region 489

8.4.2 The Entry Region 494

8.4.3 Temperature-Dependent Properties 496

8.5 Convection Correlations: Turbulent Flow in Circular Tubes 496

8.6 Convection Correlations: Noncircular Tubes and the Concentric Tube Annulus 504

8.7 Heat Transfer Enhancement 507

8.8 Forced Convection in Small Channels 510

8.8.1 Microscale Convection in Gases (0.1 μm ≤ Dh ≤ 100 μm) 510

8.8.2 Microscale Convection in Liquids 511

8.8.3 Nanoscale Convection (Dh ≤ 100 nm) 512

8.9 Convection Mass Transfer 515

8.10 Summary 517

References 520

Problems 521

Chapter 9 Free Convection 539

9.1 Physical Considerations 540

9.2 The Governing Equations for Laminar Boundary Layers 542

9.3 Similarity Considerations 544

9.4 Laminar Free Convection on a Vertical Surface 545

9.5 The Effects of Turbulence 548

9.6 Empirical Correlations: External Free Convection Flows 550

9.6.1 The Vertical Plate 551

9.6.2 Inclined and Horizontal Plates 554

9.6.3 The Long Horizontal Cylinder 559

9.6.4 Spheres 563

9.7 Free Convection Within Parallel Plate Channels 564

9.7.1 Vertical Channels 565

9.7.2 Inclined Channels 567

9.8 Empirical Correlations: Enclosures 567

9.8.1 Rectangular Cavities 567

9.8.2 Concentric Cylinders 570

9.8.3 Concentric Spheres 571

9.9 Combined Free and Forced Convection 573

9.10 Convection Mass Transfer 574

9.11 Summary 575

References 576

Problems 577

Chapter 10 Boiling and Condensation 595

10.1 Dimensionless Parameters in Boiling and Condensation 596

10.2 Boiling Modes 597

10.3 Pool Boiling 598

10.3.1 The Boiling Curve 598

10.3.2 Modes of Pool Boiling 599

10.4 Pool Boiling Correlations 602

10.4.1 Nucleate Pool Boiling 602

10.4.2 Critical Heat Flux for Nucleate Pool Boiling 604

10.4.3 Minimum Heat Flux 605

10.4.4 Film Pool Boiling 605

10.4.5 Parametric Effects on Pool Boiling 606

10.5 Forced Convection Boiling 611

10.5.1 External Forced Convection Boiling 612

10.5.2 Two-Phase Flow 612

10.5.3 Two-Phase Flow in Microchannels 615

10.6 Condensation: Physical Mechanisms 615

10.7 Laminar Film Condensation on a Vertical Plate 617

10