## Heat and mass Transfer: Fundamentals & Applications, Fifth Edition

By Yunus a. Çengel and Afshin j. Ghajar

**Contents:**

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INTRODUCTION AND BASIC CONCEPTS 1

1–1 Thermodynamics and Heat Transfer 2

Application Areas of Heat Transfer 3

Historical Background 3

1–2 Engineering Heat Transfer 4

Modeling in Engineering 5

1–3 Heat and Other Forms of Energy 6

Specific Heats of Gases, Liquids, and Solids 7

Energy Transfer 9

1–4 The First Law of Thermodynamics 11

Energy Balance for Closed Systems (Fixed Mass) 12

Energy Balance for Steady-Flow Systems 12

Surface Energy Balance 13

1–5 Heat Transfer Mechanisms 17

1–6 Conduction 17

Thermal Conductivity 19

Thermal Diffusivity 22

1–7 Convection 25

1–8 Radiation 27

1–9 Simultaneous Heat Transfer Mechanisms 30

1–10 Prevention Through Design 35

1–11 Problem-Solving Technique 38

Engineering Software Packages 40

Engineering Equation Solver (EES) 41

A Remark on Significant Digits 42

Topic of Special Interest:

Thermal Comfort 43

Summary 50

References and Suggested Reading 51

Problems 51

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HEAT CONDUCTION EQUATION 67

2–1 Introduction 68

Steady versus Transient Heat Transfer 69

Multidimensional Heat Transfer 70

Heat Generation 72

2–2 One-Dimensional Heat Conduction

Equation 73

Heat Conduction Equation in a Large Plane Wall 73

Heat Conduction Equation in a Long Cylinder 75

Heat Conduction Equation in a Sphere 76

Combined One-Dimensional Heat Conduction Equation 77

2–3 General Heat Conduction Equation 79

Rectangular Coordinates 79

Cylindrical Coordinates 81

Spherical Coordinates 81

2–4 Boundary and Initial Conditions 82

1 Specified Temperature Boundary Condition 84

2 Specified Heat Flux Boundary Condition 84

Special Case: Insulated Boundary 85

Another Special Case: Thermal Symmetry 85

3 Convection Boundary Condition 86

4 Radiation Boundary Condition 88

5 Interface Boundary Conditions 89

6 Generalized Boundary Conditions 89

2–5 Solution of Steady One-Dimensional

Heat Conduction Problems 91

2–6 Heat Generation in a Solid 104

2–7 Variable Thermal Conductivity, k( T) 112

Topic of Special Interest:

A Brief Review of Differential Equations 115

Classification of Differential Equations 117

Solutions of Differential Equations 118

General Solution to Selected Differential Equations 119

Summary 121

References and Suggested Reading 122

Problems 122

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STEADY HEAT CONDUCTION 142

3–1 Steady Heat Conduction in Plane Walls 143

Thermal Resistance Concept 144

Thermal Resistance Network 146

Multilayer Plane Walls 148

3–2 Thermal Contact Resistance 153

3–3 Generalized Thermal Resistance

Networks 158

3–4 Heat Conduction in Cylinders and Spheres 161

Multilayered Cylinders and Spheres 163

3–5 Critical Radius of Insulation 167

3–6 Heat Transfer from Finned Surfaces 170

Fin Equation 171

Fin Efficiency 176

Fin Effectiveness 178

Proper Length of a Fin 181

3–7 Bioheat Transfer Equation 187

3–8 Heat Transfer in Common Configurations 192

Topic of Special Interest:

Heat Transfer through Walls and Roofs 197

Summary 207

References and Suggested Reading 209

Problems 209

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TRANSIENT HEAT CONDUCTION 237

4–1 Lumped System Analysis 238

Criteria for Lumped System Analysis 239

Some Remarks on Heat Transfer in Lumped Systems 241

4–2 Transient Heat Conduction in Large Plane

Walls, Long Cylinders, and Spheres with

Spatial Effects 244

Nondimensionalized One-Dimensional

Transient Conduction Problem 245

Exact Solution of One-Dimensional Transient Conduction

Problem 247

Approximate Analytical and Graphical Solutions 250

4–3 Transient Heat Conduction in Semi-Infinite

Solids 261

Contact of Two Semi-Infinite Solids 265

4–4 Transient Heat Conduction in

Multidimensional Systems 268

Topic of Special Interest:

Refrigeration and Freezing of Foods 276

Control of Microorganisms in Foods 276

Refrigeration and Freezing of Foods 278

Beef Products 279

Poultry Products 283

Summary 287

References and Suggested Reading 289

Problems 289

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NUMERICAL METHODS

IN HEAT CONDUCTION 307

5–1 Why Numerical Methods? 308

1 Limitations 309

2 Better Modeling 309

3 Flexibility 310

4 Complications 310

5 Human Nature 310

5–2 Finite Difference Formulation

of Differential Equations 311

5–3 One-Dimensional Steady Heat Conduction 314

Boundary Conditions 316

Treating Insulated Boundary Nodes as Interior Nodes:

The Mirror Image Concept 318

5–4 Two-Dimensional Steady Heat Conduction 325

Boundary Nodes 326

Irregular Boundaries 330

5–5 Transient Heat Conduction 334

Transient Heat Conduction in a Plane Wall 336

Stability Criterion for Explicit Method: Limitation on Dt 338

Two-Dimensional Transient Heat Conduction 347

Topic of Special Interest:

Controlling the Numerical Error 352

Discretization Error 352

Round-Off Error 353

Controlling the Error in Numerical Methods 354

Summary 355

References and Suggested Reading 356

Problems 357

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FUNDAMENTALS OF CONVECTION 379

6–1 Physical Mechanism of Convection 380

Nusselt Number 382

6–2 Classification of Fluid Flows 384

Viscous versus Inviscid Regions of Flow 384

Internal versus External Flow 384

Compressible versus Incompressible Flow 384

Laminar versus Turbulent Flow 385

Natural (or Unforced) versus Forced Flow 385

Steady versus Unsteady Flow 385

One-, Two-, and Three-Dimensional Flows 386

6–3 Velocity Boundary Layer 387

Wall Shear Stress 388

6–4 Thermal Boundary Layer 389

Prandtl Number 390

6–5 Laminar and Turbulent Flows 390

Reynolds Number 391

6–6 Heat and Momentum Transfer in Turbulent

Flow 392

6–7 Derivation of Differential Convection

Equations 394

The Continuity Equation 395

The Momentum Equations 395

Conservation of Energy Equation 397

6–8 Solutions of Convection Equations for a

Flat Plate 401

The Energy Equation 403

6–9 Nondimensionalized Convection Equations

and Similarity 405

6–10 Functional Forms of Friction and Convection

Coefficients 406

6–11 Analogies Between Momentum and Heat

Transfer 407

Topic of Special Interest:

Microscale Heat Transfer 410

Summary 413

References and Suggested Reading 414

Problems 415

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EXTERNAL FORCED CONVECTION 424

7–1 Drag and Heat Transfer in External Flow 425

Friction and Pressure Drag 425

Heat Transfer 427

7–2 Parallel Flow over Flat Plates 428

Friction Coefficient 429

Heat Transfer Coefficient 430

Flat Plate with Unheated Starting Length 432

Uniform Heat Flux 433

7–3 Flow across Cylinders and Spheres 438

Effect of Surface Roughness 440

Heat Transfer Coefficient 442

7–4 Flow across Tube Banks 446

Pressure Drop 449

Summary 453

References and Suggested Reading 454

Problems 455

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INTERNAL FORCED CONVECTION 473

8–1 Introduction 474

8–2 Average Velocity and Temperature 475

Laminar and Turbulent Flow in Tubes 476

8–3 The Entrance Region 477

Entry Lengths 479

8–4 General Thermal Analysis 480

Constant Surface Heat Flux (q s 5 constant) 481

Constant Surface Temperature (Ts 5 constant) 482

8–5 Laminar Flow in Tubes 485

Pressure Drop 487

Temperature Profile and the Nusselt Number 489

Constant Surface Heat Flux 489

Constant Surface Temperature 490

Laminar Flow in Noncircular Tubes 491

Developing Laminar Flow in the Entrance Region 492

8–6 Turbulent Flow in Tubes 496

Fully Developed Transitional Flow Heat Transfer 497

Rough Surfaces 498

Developing Turbulent Flow in the Entrance Region 500

Turbulent Flow in Noncircular Tubes 500

Flow through Tube Annulus 500

Heat Transfer Enhancement 501

Topic of Special Interest:

Transitional Flow in Tubes 507

Pressure Drop in the Transition Region 508

Heat Transfer in the Transition Region 512

Pressure Drop in the Transition Region

in Mini and Micro Tubes 517

References 517

Summary 518

References and Suggested Reading 519

Problems 520

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NATURAL CONVECTION 533

9–1 Physical Mechanism of Natural Convection 534

9–2 Equation of Motion and the Grashof Number 537

The Grashof Number 539

9–3 Natural Convection over Surfaces 540

Vertical Plates (Ts 5 constant) 541

Vertical Plates (q s 5 constant) 541

Vertical Cylinders 543

Inclined Plates 543

Horizontal Plates 544

Horizontal Cylinders and Spheres 544

9–4 Natural Convection from Finned Surfaces

and PCBs 548

Natural Convection Cooling of Finned Surfaces

(Ts 5 constant) 548

Natural Convection Cooling of Vertical PCBs

(q s 5 constant) 549

Mass Flow Rate through the Space between Plates 550

9–5 Natural Convection Inside Enclosures 552

Effective Thermal Conductivity 553

Horizontal Rectangular Enclosures 553

Inclined Rectangular Enclosures 554

Vertical Rectangular Enclosures 555

Concentric Cylinders 555

Concentric Spheres 556

Combined Natural Convection and Radiation 556

9–6 Combined Natural and Forced Convection 562

Topic of Special Interest:

Heat Transfer through Windows 566

Edge-of-Glass U-Factor of a Window 570

Frame U-Factor 571

Interior and Exterior Surface Heat Transfer Coefficients 571

Overall U-Factor of Windows 572

Summary 577

References and Suggested Reading 578

Problems 579

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BOILING AND CONDENSATION 598

10–1 Boiling Heat Transfer 599

10–2 Pool Boiling 601

Boiling Regimes and the Boiling Curve 601

Natural Convection Boiling (to Point A on the Boiling Curve) 601

Nucleate Boiling (between Points A and C) 602

Transition Boiling (between Points C and D) 603

Film Boiling (beyond Point D) 603

Heat Transfer Correlations in Pool Boiling 604

Nucleate Boiling 604

Peak Heat Flux 605

Minimum Heat Flux 607

Film Boiling 607

Enhancement of Heat Transfer in Pool Boiling 608

10–3 Flow Boiling 612

10–4 Condensation Heat Transfer 613

10–5 Film Condensation 614

Flow Regimes 616

Heat Transfer Correlations for Film Condensation 616

Effect of Vapor Velocity 622

The Presence of Noncondensable Gases in Condensers 622

10–6 Film Condensation Inside Horizontal

Tubes 626

10–7 Dropwise Condensation 628

Topic of Special Interest:

Non-Boiling Two-Phase Flow Heat Transfer 629

Application of Reynolds Analogy to Non-Boiling

Two-Phase Flow 634

References 635

Summary 636

References and Suggested Reading 637

Problems 638

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HEAT EXCHANGERS 649

11–1 Types of Heat Exchangers 650

11–2 The Overall Heat Transfer Coefficient 653

Fouling Factor 656

11–3 Analysis of Heat Exchangers 660

11–4 The Log Mean Temperature Difference

Method 662

Counter-Flow Heat Exchangers 664

Multipass and Cross-Flow Heat Exchangers:

Use of a Correction Factor 665

11–5 The Effectiveness–NTU Method 672

11–6 Selection of Heat Exchangers 685

Heat Transfer Rate 686

Cost 686

Pumping Power 686

Size and Weight 686

Type 687

Materials 687

Other Considerations 687

Topic of Special Interest:

The Human Cardiovascular System as a

Counter-Current Heat Exchanger 689

Summary 695

References and Suggested Reading 696

Problems 696

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FUNDAMENTALS OF THERMAL RADIATION 715

12–1 Introduction 716

12–2 **Thermal Radiation** 717

12–3 Blackbody Radiation 719

12–4 Radiation Intensity 726

Solid Angle 726

Intensity of Emitted Radiation 727

Incident Radiation 729

Radiosity 729

Spectral Quantities 729

12–5 Radiative Properties 732

Emissivity 732

Absorptivity, Reflectivity, and Transmissivity 736

Kirchhoff’s Law 739

The Greenhouse Effect 742

12–6 Atmospheric and Solar Radiation 742

Topic of Special Interest:

Solar Heat Gain through Windows 747

Summary 754

References and Suggested Reading 755

Problems 756

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RADIATION HEAT TRANSFER 767

13–1 The View Factor 768

13–2 View Factor Relations 771

1 The Reciprocity Relation 772

2 The Summation Rule 775

3 The Superposition Rule 777

4 The Symmetry Rule 778

View Factors between Infinitely Long Surfaces:

The Crossed-Strings Method 780

13–3 Radiation Heat Transfer: Black

Surfaces 782

13–4 Radiation Heat Transfer: Diffuse, Gray

Surfaces 784

Radiosity 784

Net Radiation Heat Transfer to or from a Surface 785

Net Radiation Heat Transfer between Any Two Surfaces 786

Methods of Solving Radiation Problems 787

Radiation Heat Transfer in Two-Surface Enclosures 788

Radiation Heat Transfer in Three-Surface Enclosures 790

13–5 Radiation Shields and the Radiation

Effects 796

Radiation Effect on Temperature Measurements 798

13–6 Radiation Exchange with Emitting and

Absorbing Gases 801

Radiation Properties of a Participating Medium 802

Emissivity and Absorptivity of Gases and Gas Mixtures 803

Topic of Special Interest:

Heat Transfer from the Human Body 810

Summary 814

References and Suggested Reading 815

Problems 816

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MASS TRANSFER 835

14–1 Introduction 836

14–2 Analogy Between Heat and Mass

Transfer 837

Temperature 838

Conduction 838

Heat Generation 838

Convection 839

14–3 Mass Diffusion 839

1 Mass Basis 839

2 Mole Basis 840

Special Case: Ideal Gas Mixtures 841

Fick’s Law of Diffusion: Stationary Medium Consisting

of Two Species 841

14–4 Boundary Conditions 845

14–5 Steady Mass Diffusion Through

a Wall 850

14–6 Water Vapor Migration in

Buildings 854

14–7 Transient Mass Diffusion 859

14–8 Diffusion in a Moving Medium 861

Special Case: Gas Mixtures at Constant Pressure and

Temperature 865

Diffusion of Vapor through a Stationary Gas:

Stefan Flow 866

Equimolar Counterdiffusion 868

14–9 Mass Convection 873

Analogy Between Friction, Heat Transfer, and Mass

Transfer Coefficients 877

Special Case: Pr < Sc < 1

(Reynolds Analogy) 877

General Case: Pr Þ Sc Þ 1

(Chilton–Colburn Analogy) 878

Limitation on the Heat–Mass Convection

Analogy 879

Mass Convection Relations 879

14–10 Simultaneous Heat and Mass Transfer 882

Summary 888

References and Suggested Reading 890

Problems 890

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COOLING OF ELECTRONIC EQUIPMENT

15–1 Introduction and History

15–2 Manufacturing of Electronic Equipment

15–3 Cooling Load of Electronic Equipment

15–4 Thermal Environment

15–5 Electronics Cooling in Different Applications

15–6 Conduction Cooling

15–7 Air Cooling: Natural Convection and Radiation

15–8 Air Cooling: Forced Convection

15–19 Liquid Cooling

15–10 Immersion Cooling

Summary

References and Suggested Reading

Problems

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HEATING AND COOLING OF BUILDINGS

16–1 A Brief History

16–2 Human Body and Thermal Comfort

16–3 Heat Transfer from the Human Body

16–4 Design Conditions for Heating and Cooling

16–5 Heat Gain from People, Lights, and Appliances

16–6 Heat Transfer through Walls and Roofs

16–7 Heat Loss from Basement Walls and Floors

16–8 Heat Transfer through Windows

16–9 Solar Heat Gain through Windows

16–10 Infiltration Heat Load and Weatherizing

16–11 Annual Energy Consumption

Summary

References and Suggested Reading

Problems

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REFRIGERATION AND FREEZING OF FOODS

17–1 Control of **Microorganisms in Foods**

17–2 Refrigeration and Freezing of Foods

17–3 Thermal Properties of Food

17–4 Refrigeration of Fruits and Vegetables

17–5 Refrigeration of Meats, Poultry, and Fish

17–6 Refrigeration of Eggs, Milk, and Bakery Products

17–7 Refrigeration Load of Cold Storage Rooms

17–8 Transportation of Refrigerated Foods

Summary

References and Suggested Reading

Problems

A p p e n d i x 1

PROPERTY TABLES AND CHARTS (SI UNITS) 907

Table A–1 Molar mass, gas constant, and ideal-gas

specific heats of some substances 908

Table A–2 Boiling and freezing point

properties 909

Table A–3 Properties of solid metals 910–912

Table A–4 Properties of solid nonmetals 913

Table A–5 Properties of building materials 914–915

Table A–6 Properties of insulating materials 916

Table A–7 Properties of common foods 917–918

Table A–8 Properties of miscellaneous materials 919

Table A–9 Properties of saturated water 920

Table A–10 Properties of saturated refrigerant-134a 921

Table A–11 Properties of saturated ammonia 922

Table A–12 Properties of saturated propane 923

Table A–13 Properties of liquids 924

Table A–14 Properties of liquid metals 925

Table A–15 Properties of air at 1 atm pressure 926

Table A–16 Properties of gases at 1 atm pressure 927–928

Table A–17 Properties of the atmosphere at high altitude 929

Table A–18 Emissivities of surfaces 930–931

Table A–19 Solar radiative properties of materials 932

FIGURE A–20 The Moody chart for the friction factor for fully developed flow in circular pipes 933

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PROPERTY TABLES AND CHARTS (ENGLISH UNITS) 935

Table A–1E Molar mass, gas constant, and

ideal-gas specific heats of some substances 936

Table A–2E Boiling and freezing point properties 937

Table A–3E Properties of solid metals 938–939

Table A–4E Properties of solid nonmentals 940

Table A–5E Properties of building materials 941–942

Table A–6E Properties of insulating materials 943

Table A–7E Properties of common foods 944–945

Table A–8E Properties of miscellaneous materials 946

Table A–9E Properties of saturated water 947

Table A–10E Properties of saturated refrigerant-134a 948

Table A–11E Properties of saturated ammonia 949

Table A–12E Properties of saturated propane 950

Table A–3E Properties of liquids 951

Table A–14E Properties of liquid metals 952

Table A–15E Properties of air at 1 atm pressure 953

Table A–16E Properties of gases at 1 atm pressure 954–955

Table A–17E Properties of the atmosphere at high

altitude 956

INDEX 957