Convection Heat Transfer

A new edition of the bestseller on convection heat transfer

A revised edition of the industry classic, Convection Heat Transfer, Fourth Edition, chronicles how the field of heat transfer has grown and prospered over the last two decades. This new edition is more accessible, while not sacrificing its thorough treatment of the most up-to-date information on current research and applications in the field.

One of the foremost leaders in the field, Adrian Bejan has pioneered and taught many of the methods and practices commonly used in the industry today. He continues this book's long-standing role as an inspiring, optimal study tool by providing:

• Coverage of how convection affects performance, and how convective flows can be configured so that performance is enhanced
• How convective configurations have been evolving, from the flat plates, smooth pipes, and single-dimension fins of the earlier editions to new populations of configurations: tapered ducts, plates with multiscale features, dendritic fins, duct and plate assemblies (packages) for heat transfer density and compactness, etc.
• New, updated, and enhanced examples and problems that reflect the author's research and advances in the field since the last edition
• A solutions manual

Complete with hundreds of informative and original illustrations, Convection Heat Transfer, Fourth Edition is the most comprehensive and approachable text for students in schools of mechanical engineering.

ADRIAN BEJAN, PhD, is the J. A. Jones Professor of Mechanical Engineering at Duke University. An internationally recognized authority on heat transfer and thermodynamics, Bejan has pioneered the methods of entropy generation minimization, scale analysis, heatlines and masslines, intersection of asymptotes, dendritic architectures, and the constructal law of design in nature. He is the recipient of numerous awards, including the Max Jakob Memorial Award (ASME & AICHE), the Worcester Reed Warner Medal (ASME), and the Ralph Coats Roe Award (ASEE). He is the author of twenty-five books and 550 journal articles, and is listed among the 100 most-cited engineering researchers (all disciplines, all countries). He has been awarded sixteen honorary doctorates by universities in eleven foreign countries.

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

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