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

4S.1 The Graphical Method W-1

4S.1.1 Methodology of Constructing a Flux Plot W-1

4S.1.2 Determination of the Heat Transfer Rate W-2

4S.1.3 The Conduction Shape Factor W-3

4S.2 The Gauss-Seidel Method: Example of Usage W-5

References W-10

Problems W-10

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

5S.1 Graphical Representation of One-Dimensional, Transient Conduction in the Plane Wall, Long Cylinder, and Sphere W-12

5S.2 Analytical Solutions of Multidimensional Effects W-16

References W-22

Problems W-22

Chapter 6 Introduction to Convection 343

6.1 The Convection Boundary Layers 344

6.1.1 The Velocity Boundary Layer 344

6.1.2 The Thermal Boundary Layer 345

6.1.3 The Concentration Boundary Layer 347

6.1.4 Significance of the Boundary Layers 348

6.2 Local and Average Convection Coefficients 348

6.2.1 Heat Transfer 348

6.2.2 Mass Transfer 349

6.3 Laminar and Turbulent Flow 355

6.3.1 Laminar and Turbulent Velocity Boundary Layers 355

6.3.2 Laminar and Turbulent Thermal and Species Concentration Boundary Layers 357

6.4 The Boundary Layer Equations 360

6.4.1 Boundary Layer Equations for Laminar Flow 361

6.4.2 Compressible Flow 364

6.5 Boundary Layer Similarity: The Normalized Boundary Layer Equations 364

6.5.1 Boundary Layer Similarity Parameters 365

6.5.2 Dependent Dimensionless Parameters 365

6.6 Physical Interpretation of the Dimensionless Parameters 374

6.7 Boundary Layer Analogies 376

6.7.1 The Heat and Mass Transfer Analogy 377

6.7.2 Evaporative Cooling 380

6.7.3 The Reynolds Analogy 383

6.8 Summary 384

References 385

Problems 386

6S.1 Derivation of the Convection Transfer Equations W-25

6S.1.1 Conservation of Mass W-25

6S.1.2 Newton's Second Law of Motion W-26

6S.1.3 Conservation of Energy W-29

6S.1.4 Conservation of Species W-32

References W-36

Problems W-36

Chapter 7 External Flow 399

7.1 The Empirical Method 401

7.2 The Flat Plate in Parallel Flow 402

7.2.1 Laminar Flow over an Isothermal Plate: A Similarity Solution 403

7.2.2 Turbulent Flow over an Isothermal Plate 409

7.2.3 Mixed Boundary Layer Conditions 410

7.2.4 Unheated Starting Length 411

7.2.5 Flat Plates with Constant Heat Flux Conditions 412

7.2.6 Limitations on Use of Convection Coefficients 413

7.3 Methodology for a Convection Calculation 413

7.4 The Cylinder in Cross Flow 421

7.4.1 Flow Considerations 421

7.4.2 Convection Heat and Mass Transfer 423

7.5 The Sphere 431

7.6 Flow Across Banks of Tubes 434

7.7 Impinging Jets 443

7.7.1 Hydrodynamic and Geometric Considerations 443

7.7.2 Convection Heat and Mass Transfer 444

7.8 Packed Beds 448

7.9 Summary 449

References 452

Problems 452

Chapter 8 Internal Flow 475

8.1 Hydrodynamic Considerations 476

8.1.1 Flow Conditions 476

8.1.2 The Mean Velocity 477

8.1.3 Velocity Profile in the Fully Developed Region 478

8.1.4 Pressure Gradient and Friction Factor in Fully Developed Flow 480

8.2 Thermal Considerations 481

8.2.1 The Mean Temperature 482

8.2.2 Newton's Law of Cooling 483

8.2.3 Fully Developed Conditions 483

8.3 The Energy Balance 487

8.3.1 General Considerations 487

8.3.2 Constant Surface Heat Flux 488

8.3.3 Constant Surface Temperature 491

8.4 Laminar Flow in Circular Tubes: Thermal Analysis and Convection Correlations 495

8.4.1 The Fully Developed Region 495

8.4.2 The Entry Region 500

8.4.3 Temperature-Dependent Properties 502

8.5 Convection Correlations: Turbulent Flow in Circular Tubes 502

8.6 Convection Correlations: Noncircular Tubes and the Concentric Tube Annulus 510

8.7 Heat Transfer Enhancement 513

8.8 Forced Convection in Small Channels 516

8.8.1 Microscale Convection in Gases (0.1 ¿m ¿ Dh ¿ 100 ¿m) 516

8.8.2 Microscale Convection in Liquids 517

8.8.3 Nanoscale Convection (Dh ¿ 100 nm) 518

8.9 Convection Mass Transfer 521

8.10 Summary 523

References 526

Problems 527

Chapter 9 Free Convection 547

9.1 Physical Considerations 548

9.2 The Governing Equations for Laminar Boundary Layers 550

9.3 Similarity Considerations 552

9.4 Laminar Free Convection on a Vertical Surface 553

9.5 The Effects of Turbulence 556

9.6 Empirical Correlations: External Free Convection Flows 558

9.6.1 The Vertical Plate 559

9.6.2 Inclined and Horizontal Plates 562

9.6.3 The Long Horizontal Cylinder 567

9.6.4 Spheres 571

9.7 Free Convection Within Parallel Plate Channels 572

9.7.1 Vertical Channels 573

9.7.2 Inclined Channels 575

9.8 Empirical Correlations: Enclosures 575

9.8.1 Rectangular Cavities 575

9.8.2 Concentric Cylinders 578

9.8.3 Concentric Spheres 579

9.9 Combined Free and Forced Convection 581

9.10 Convection Mass Transfer 582

9.11 Summary 583

References 584

Problems 585

Chapter 10 Boiling and Condensation 603

10.1 Dimensionless Parameters in Boiling...