Preface xv

Preface to the Third Edition xvii

Preface to the Second Edition xxi

Preface to the First Edition xxiii

List of Symbols xxv

**1 Fundamental Principles 1**

1.1 Mass Conservation / 2

1.2 Force Balances (Momentum Equations) / 4

1.3 First Law of Thermodynamics / 8

1.4 Second Law of Thermodynamics / 15

1.5 Rules of Scale Analysis / 17

1.6 Heatlines for Visualizing Convection / 21

References / 22

Problems / 25

**2 Laminar Boundary Layer Flow 30**

2.1 Fundamental Problem in Convective Heat Transfer / 31

2.2 Concept of Boundary Layer / 34

2.3 Scale Analysis / 37

2.4 Integral Solutions / 42

2.5 Similarity Solutions / 48

2.5.1 Method / 48

2.5.2 Flow Solution / 51

2.5.3 Heat Transfer Solution / 53

2.6 Other Wall Heating Conditions / 56

2.6.1 Unheated Starting Length / 57

2.6.2 Arbitrary Wall Temperature / 58

2.6.3 Uniform Heat Flux / 60

2.6.4 Film Temperature / 61

2.7 Longitudinal Pressure Gradient: Flow Past a Wedge and Stagnation Flow / 61

2.8 Flow Through the Wall: Blowing and Suction / 64

2.9 Conduction Across a Solid Coating Deposited on a Wall / 68

2.10 Entropy Generation Minimization in Laminar Boundary Layer Flow / 71

2.11 Heatlines in Laminar Boundary Layer Flow / 74

2.12 Distribution of Heat Sources on a Wall Cooled by Forced Convection / 77

2.13 The Flow of Stresses / 79

References / 80

Problems / 82

**3 Laminar Duct Flow 96**

3.1 Hydrodynamic Entrance Length / 97

3.2 Fully Developed Flow / 100

3.3 Hydraulic Diameter and Pressure Drop / 103

3.4 Heat Transfer To Fully Developed Duct Flow / 110

3.4.1 Mean Temperature / 110

3.4.2 Fully Developed Temperature Profile / 112

3.4.3 Uniform Wall Heat Flux / 114

3.4.4 Uniform Wall Temperature / 117

3.5 Heat Transfer to Developing Flow / 120

3.5.1 Scale Analysis / 121

3.5.2 Thermally Developing Hagen–Poiseuille Flow / 122

3.5.3 Thermally and Hydraulically Developing Flow / 128

3.6 Stack of Heat-Generating Plates / 129

3.7 Heatlines in Fully Developed Duct Flow / 134

3.8 Duct Shape for Minimum Flow Resistance / 137

3.9 Tree-Shaped Flow / 139

References / 147

Problems / 153

**4 External Natural Convection 168**

4.1 Natural Convection as a Heat Engine in Motion / 169

4.2 Laminar Boundary Layer Equations / 173

4.3 Scale Analysis / 176

4.3.1 High-Pr Fluids / 177

4.3.2 Low-Pr Fluids / 179

4.3.3 Observations / 180

4.4 Integral Solution / 182

4.4.1 High-Pr Fluids / 183

4.4.2 Low-Pr Fluids / 184

4.5 Similarity Solution / 186

4.6 Uniform Wall Heat Flux / 189

4.7 Effect of Thermal Stratification / 192

4.8 Conjugate Boundary Layers / 195

4.9 Vertical Channel Flow / 197

4.10 Combined Natural and Forced Convection (Mixed Convection) / 200

4.11 Heat Transfer Results Including the Effect of Turbulence / 203

4.11.1 Vertical Walls / 203

4.11.2 Inclined Walls / 205

4.11.3 Horizontal Walls / 207

4.11.4 Horizontal Cylinder / 209

4.11.5 Sphere / 209

4.11.6 Vertical Cylinder / 210

4.11.7 Other Immersed Bodies / 211

4.12 Stack of Vertical Heat-Generating Plates / 213

4.13 Distribution of Heat Sources on a Vertical Wall / 216

References / 218

Problems / 221

**5 Internal Natural Convection 233**

5.1 Transient Heating from the Side / 233

5.1.1 Scale Analysis / 233

5.1.2 Criterion for Distinct Vertical Layers / 237

5.1.3 Criterion for Distinct Horizontal Jets / 238

5.2 Boundary Layer Regime / 241

5.3 Shallow Enclosure Limit / 248

5.4 Summary of Results for Heating from the Side / 255

5.4.1 Isothermal Sidewalls / 255

5.4.2 Sidewalls with Uniform Heat Flux / 259

5.4.3 Partially Divided Enclosures / 259

5.4.4 Triangular Enclosures / 262

5.5 Enclosures Heated from Below / 262

5.5.1 Heat Transfer Results / 263

5.5.2 Scale Theory of the Turbulent Regime / 265

5.5.3 Constructal Theory of B´enard Convection / 267

5.6 Inclined Enclosures / 274

5.7 Annular Space Between Horizontal Cylinders / 276

5.8 Annular Space Between Concentric Spheres / 278

5.9 Enclosures for Thermal Insulation and Mechanical

Strength / 278

References / 284

Problems / 289

**6 Transition to Turbulence 295**

6.1 Empirical Transition Data / 295

6.2 Scaling Laws of Transition / 297

6.3 Buckling of Inviscid Streams / 300

6.4 Local Reynolds Number Criterion for Transition / 304

6.5 Instability of Inviscid Flow / 307

6.6 Transition in Natural Convection on a Vertical Wall / 313

References / 315

Problems / 318

**7 Turbulent Boundary Layer Flow 320**

7.1 Large-Scale Structure / 320

7.2 Time-Averaged Equations / 322

7.3 Boundary Layer Equations / 325

7.4 Mixing Length Model / 328

7.5 Velocity Distribution / 329

7.6 Wall Friction in Boundary Layer Flow / 336

7.7 Heat Transfer in Boundary Layer Flow / 338

7.8 Theory of Heat Transfer in Turbulent Boundary Layer Flow / 342

7.9 Other External Flows / 347

7.9.1 Single Cylinder in Cross Flow / 347

7.9.2 Sphere / 349

7.9.3 Other Body Shapes / 350

7.9.4 Arrays of Cylinders in Cross Flow / 351

7.10 Natural Convection Along Vertical Walls / 356

References / 359

Problems / 361

**8 Turbulent Duct Flow 369**

8.1 Velocity Distribution / 369

8.2 Friction Factor and Pressure Drop / 371

8.3 Heat Transfer Coefficient / 376

8.4 Total Heat Transfer Rate / 380

8.4.1 Isothermal Wall / 380

8.4.2 Uniform Wall Heating / 382

8.4.3 Time-Dependent Heat Transfer / 382

8.5 More Refined Turbulence Models / 383

8.6 Heatlines in Turbulent Flow Near a Wall / 387

8.7 Channel Spacings for Turbulent Flow / 389

References / 390

Problems / 392

**9 Free Turbulent Flows 398**

9.1 Free Shear Layers / 398

9.1.1 Free Turbulent Flow Model / 398

9.1.2 Velocity Distribution / 401

9.1.3 Structure of Free Turbulent Flows / 402

9.1.4 Temperature Distribution / 404

9.2 Jets / 405

9.2.1 Two-Dimensional Jets / 406

9.2.2 Round Jets / 409

9.2.3 Jet in Density-Stratified Reservoir / 411

9.3 Plumes / 413

9.3.1 Round Plume and the Entrainment Hypothesis / 413

9.3.2 Pulsating Frequency of Pool Fires / 418

9.3.3 Geometric Similarity of Free Turbulent Flows / 421

9.4 Thermal Wakes Behind Concentrated Sources / 422

References / 425

Problems / 426

**10 Convection with Change of Phase 428**

10.1 Condensation / 428

10.1.1 Laminar Film on a Vertical Surface / 428

10.1.2 Turbulent Film on a Vertical Surface / 435

10.1.3 Film Condensation in Other Configurations / 438

10.1.4 Drop Condensation / 445

10.2 Boiling / 447

10.2.1 Pool Boiling Regimes / 447

10.2.2 Nucleate Boiling and Peak Heat Flux / 451

10.2.3 Film Boiling and Minimum Heat Flux / 454

10.2.4 Flow Boiling / 457

10.3 Contact Melting and Lubrication / 457

10.3.1 Plane Surfaces with Relative Motion / 458

10.3.2 Other Contact Melting Configurations / 462

10.3.3 Scale Analysis and Correlation / 464

10.3.4 Melting Due to Viscous Heating in the Liquid Film / 466

10.4 Melting By Natural Convection / 469

10.4.1 Transition from the Conduction Regime to the Convection Regime / 469

10.4.2 Quasisteady Convection Regime / 472

10.4.3 Horizontal Spreading of the Melt Layer / 474

References / 478

Problems / 482

**11 Mass Transfer 489**

11.1 Properties of Mixtures / 489

11.2 Mass Conservation / 492

11.3 Mass Diffusivities / 497

11.4 Boundary Conditions / 499

11.5 Laminar Forced Convection / 501

11.6 Impermeable Surface Model / 504

11.7 Other External Forced Convection Configurations / 506

11.8 Internal Forced Convection / 509

11.9 Natural Convection / 511

11.9.1 Mass-Transfer-Driven Flow / 512

11.9.2 Heat-Transfer-Driven Flow / 513

11.10 Turbulent Flow / 516

11.10.1 Time-Averaged Concentration Equation / 516

11.10.2 Forced Convection Results / 517

11.10.3 Contaminant Removal from a Ventilated Enclosure / 520

11.11 Massfunction and Masslines / 527

11.12 Effect of Chemical Reaction / 527

References / 531

Problems / 532

**12 Convection in Porous Media 537**

12.1 Mass Conservation / 537

12.2 Darcy Flow Model and the Forchheimer Modification / 540

12.3 First Law of Thermodynamics / 542

12.4 Second Law of Thermodynamics / 546

12.5 Forced Convection / 547

12.5.1 Boundary Layers / 547

12.5.2 Concentrated Heat Sources / 552

12.5.3 Sphere and Cylinder in Cross Flow / 553

12.5.4 Channel Filled with Porous Medium / 554

12.6 Natural Convection Boundary Layers / 555

12.6.1 Boundary Layer Equations: Vertical Wall / 555

12.6.2 Uniform Wall Temperature / 556

12.6.3 Uniform Wall Heat Flux / 558

12.6.4 Spacings for Channels Filled with Porous Structures / 559

12.6.5 Conjugate Boundary Layers / 562

12.6.6 Thermal Stratification / 563

12.6.7 Sphere and Horizontal Cylinder / 566

12.6.8 Horizontal Walls / 567

12.6.9 Concentrated Heat Sources / 567

12.7 Enclosed Porous Media Heated from the Side / 571

12.7.1 Four Heat Transfer Regimes / 571

12.7.2 Convection Results / 575

12.8 Penetrative Convection / 577

12.8.1 Lateral Penetration / 577

12.8.2 Vertical Penetration / 578

12.9 Enclosed Porous Media Heated from Below / 579

12.9.1 Onset of Convection / 579

12.9.2 Darcy Flow / 583

12.9.3 Forchheimer Flow / 585

12.10 Multiple Flow Scales Distributed Nonuniformly / 587

12.10.1 Heat Transfer / 590

12.10.2 Fluid Friction / 591

12.10.3 Heat Transfer Rate Density: The Smallest Scale for Convection / 591

12.11 Natural Porous Media: Alternating Trees / 592

References / 595

Problems / 598

**Appendixes 607**

A Constants and Conversion Factors / 609

B Properties of Solids / 615

C Properties of Liquids / 625

D Properties of Gases / 633

E Mathematical Formulas / 639

Author Index 641

Subject Index 653