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### Heat Transfer Practical Approach

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Engineering Heat Transfer

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Heat transfer is a basic science that deals with the rate of transfer of thermal energy. This introductory text is intended for use in a first course in heat transfer for undergraduate engineering students, and as a reference book for practicing engineers. The objectives of this text are

• To cover the basic principles of heat transfer.

• To present a wealth of real-world engineering applications to give students a feel for engineering practice.

• To develop an intuitive understanding of the subject matter by emphasizing the physics and physical arguments.

In engineering practice, an understanding of the mechanisms of heat transfer is becoming increasingly important since heat transfer plays a crucial role in the design of vehicles, power plants, refrigerators, electronic devices, buildings and bridges, among other things. Even a chef needs to have an intuitive understanding of the heat transfer mechanism in order to cook the food “right” by adjusting the rate of heat transfer. We may not be aware of it, but we already use the principles of heat transfer when seeking thermal comfort. We insulate our bodies by putting on heavy coats in winter, and we minimize heat gain by radiation by staying in shady places in summer. We speed up the cooling of hot food by blowing on it and keep warm in cold weather by cuddling up and thus minimizing the exposed surface area. That is, we already use heat transfer whether we realize it or not.

Chapter 1

BASICS OF HEAT TRANSFER 1

Thermodynamics and Heat Transfer 2

Application Areas of Heat Transfer 3

Historical Background 3

Engineering Heat Transfer 4

Modeling in Heat Transfer 5

Heat and Other Forms of Energy 6

Specific Heats of Gases, Liquids, and Solids 7

Energy Transfer 9

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

Heat Transfer Mechanisms 17

Conduction 17

Thermal Conductivity 19

Thermal Diffusivity 23

Convection 25

Radiation 27

Simultaneous Heat Transfer Mechanisms 30

Problem-Solving Technique 35

A Remark on Significant Digits 37

Engineering Software Packages 38

Engineering Equation Solver (EES) 39

Heat Transfer Tools (HTT) 39

Topic of Special Interest:

Thermal Comfort 40

Summary 46

References and Suggested Reading 47

Problems 47

Chapter 2

HEAT CONDUCTION EQUATION 61

Introduction 62

Steady versus Transient Heat Transfer 63

Multidimensional Heat Transfer 64

Heat Generation 66

One-Dimensional

Heat Conduction Equation 68

Heat Conduction Equation in a Large Plane Wall 68

Heat Conduction Equation in a Long Cylinder 69

Heat Conduction Equation in a Sphere 71

Combined One-Dimensional

Heat Conduction Equation 72

General Heat Conduction Equation 74

Rectangular Coordinates 74

Cylindrical Coordinates 75

Spherical Coordinates 76

Boundary and Initial Conditions 77

Specified Temperature Boundary Condition 78

Specified Heat Flux Boundary Condition 79

Convection Boundary Condition 81

Radiation Boundary Condition 82

Interface Boundary Conditions 83

Generalized Boundary Conditions 84

Solution of Steady One-Dimensional

Heat Conduction Problems 86

Heat Generation in a Solid 97

Variable Thermal Conductivity, k(T) 104

Topic of Special Interest:

A Brief Review of Differential Equations 107

Summary 111

References and Suggested Reading 112

Problems 113

Chapter 3

STEADY HEAT CONDUCTION 127

Steady Heat Conduction in Plane Walls 128

The Thermal Resistance Concept 129

Thermal Resistance Network 131

Multilayer Plane Walls 133

Thermal Contact Resistance 138

Generalized Thermal Resistance Networks 143

Heat Conduction in Cylinders and Spheres 146

Multilayered Cylinders and Spheres 148

Critical Radius of Insulation 153

Heat Transfer from Finned Surfaces 156

Fin Equation 157

Fin Efficiency 160

Fin Effectiveness 163

Proper Length of a Fin 165

Heat Transfer in Common Configurations 169

Topic of Special Interest:

Heat Transfer Through Walls and Roofs 175

Summary 185

References and Suggested Reading 186

Problems 18

Chapter 4

TRANSIENT HEAT CONDUCTION 209

Lumped System Analysis 210

Criteria for Lumped System Analysis 211

Some Remarks on Heat Transfer in Lumped Systems 213

Transient Heat Conduction in

Large Plane Walls, Long Cylinders,

and Spheres with Spatial Effects 216

Transient Heat Conduction in

Semi-Infinite Solids 228

Transient Heat Conduction in

Multidimensional Systems 231

Topic of Special Interest:

Refrigeration and Freezing of Foods 239

Summary 250

References and Suggested Reading 251

Problems 252

Chapter 5

NUMERICAL METHODS

IN HEAT CONDUCTION 265

Why Numerical Methods? 266

1 Limitations 267

2 Better Modeling 267

3 Flexibility 268

4 Complications 268

5 Human Nature 268

Finite Difference Formulation of Differential Equations 269

One-Dimensional Steady Heat Conduction 272

Boundary Conditions 274

Two-Dimensional

Steady Heat Conduction 282

Boundary Nodes 283

Irregular Boundaries 287

Transient Heat Conduction 291

Transient Heat Conduction in a Plane Wall 293

Two-Dimensional Transient Heat Conduction 304

Topic of Special Interest:

Controlling Numerical Error 309

Summary 312

References and Suggested Reading 314

Problems 314

Chapter 6

FUNDAMENTALS OF CONVECTION 333

Physical Mechanism on Convection 334

Nusselt Number 336

Classification of Fluid Flows 337

Viscous versus Inviscid Flow 337

Internal versus External Flow 337

Compressible versus Incompressible Flow 337

Laminar versus Turbulent Flow 338

Natural (or Unforced) versus Forced Flow 338

Steady versus Unsteady (Transient) Flow 338

One-, Two-, and Three-Dimensional Flows 338

Velocity Boundary Layer 339

Surface Shear Stress 340

Thermal Boundary Layer 341

Prandtl Number 341

Laminar and Turbulent Flows 342

Reynolds Number 343

Heat and Momentum Transfer in Turbulent Flow 343

Derivation of Differential

Convection Equations 345

Conservation of Mass Equation 345

Conservation of Momentum Equations 346

Conservation of Energy Equation 348

Solutions of Convection Equations

for a Flat Plate 352

The Energy Equation 354

Nondimensionalized Convection

Equations and Similarity 356

Functional Forms of Friction and

Convection Coefficients 357

Analogies between Momentum and Heat Transfer 358

Summary 361

References and Suggested Reading 362

Problems 362

Chapter 7

EXTERNAL FORCED CONVECTION 367

Drag Force and Heat Transfer in External Flow 368

Friction and Pressure Drag 368

Heat Transfer 370

Parallel Flow over Flat Plates 371

Friction Coefficient 372

Heat Transfer Coefficient 373

Flat Plate with Unheated Starting Length 375

Uniform Heat Flux 375

Flow across Cylinders and Spheres 380

Effect of Surface Roughness 382

Heat Transfer Coefficient 384

Flow across Tube Banks 389

Pressure Drop 392

Topic of Special Interest:

Reducing Heat Transfer through Surfaces 395

Summary 406

References and Suggested Reading 407

Problems 408

Chapter 8

INTERNAL FORCED CONVECTION 419

Introduction 420

Mean Velocity and Mean Temperature 420

Laminar and Turbulent Flow in Tubes 422

The Entrance Region 423

Entry Lengths 425

General Thermal Analysis 426

Constant Surface Heat Flux 427

Constant Surface Temperature 428

Laminar Flow in Tubes 431

Pressure Drop 433

Temperature Profile and the Nusselt Number 434

Constant Surface Heat Flux 435

Constant Surface Temperature 436

Laminar Flow in Noncircular Tubes 436

Developing Laminar Flow in the Entrance Region 436

Turbulent Flow in Tubes 441

Rough Surfaces 442

Developing Turbulent Flow in the Entrance Region 443

Turbulent Flow in Noncircular Tubes 443

Flow through Tube Annulus 444

Heat Transfer Enhancement 444

Summary 449

References and Suggested Reading 450

Problems 452

Chapter 9

NATURAL CONVECTION 459

Physical Mechanism of

Natural Convection 460

Equation of Motion and the Grashof Number 463

The Grashof Number 465

Natural Convection over Surfaces 466

Vertical Plates 467

Vertical Plates 467

Vertical Cylinders 467

Inclined Plates 467

Horizontal Plates 469

Horizontal Cylinders and Spheres 469

Natural Convection from

Finned Surfaces and PCBs 473

Natural Convection Cooling of Finned Surfaces 473

Natural Convection Cooling of Vertical PCBs 474

Mass Flow Rate through the Space between Plates 475

Natural Convection inside Enclosures 477

Effective Thermal Conductivity 478

Horizontal Rectangular Enclosures 479

Inclined Rectangular Enclosures 479

Vertical Rectangular Enclosures 480

Concentric Cylinders 480

Concentric Spheres 481

Combined Natural Convection and Radiation 481

Combined Natural and Forced Convection 486

Topic of Special Interest:

Heat Transfer through Windows 489

Summary 499

References and Suggested Reading 500

Problems 501

Chapter 10

BOILING AND CONDENSATION 515

Boiling Heat Transfer 516

Pool Boiling 518

Boiling Regimes and the Boiling Curve 518

Heat Transfer Correlations in Pool Boiling 522

Enhancement of Heat Transfer in Pool Boiling 526

Flow Boiling 530

Condensation Heat Transfer 532

Film Condensation 532

Flow Regimes 534

Heat Transfer Correlations for Film Condensation 535

Film Condensation Inside

Horizontal Tubes 545

Dropwise Condensation 545

Topic of Special Interest:

Heat Pipes 546

Summary 551

References and Suggested Reading 553

Problems 553

Chapter 11

FUNDAMENTALS OF THERMAL RADIATION 561

Introduction 562

Thermal Radiation 563

Blackbody Radiation 565

Radiation Intensity 571

Solid Angle 572

Intensity of Emitted Radiation 573

Incident Radiation 574

Radiosity 575

Spectral Quantities 575

Radiative Properties 577

Emissivity 578

Absorptivity, Reflectivity, and Transmissivity 582

Kirchhoff’s Law 584

The Greenhouse Effect 585

Atmospheric and Solar Radiation 586

Topic of Special Interest:

Solar Heat Gain through Windows 590

Summary 597

References and Suggested Reading 599

Problems 599

Chapter 12

RADIATION HEAT TRANSFER 605

The View Factor 606

View Factor Relations 609

1 The Reciprocity Relation 610

2 The Summation Rule 613

3 The Superposition Rule 615

4 The Symmetry Rule 616

View Factors between Infinitely Long Surfaces:

The Crossed-Strings Method 618

Radiation Heat Transfer: Black Surfaces 620

Radiation Heat Transfer:

Diffuse, Gray Surfaces 623

Radiosity 623

Net Radiation Heat Transfer to or from a Surface 623

Net Radiation Heat Transfer between Any

Two Surfaces 625

Methods of Solving Radiation Problems 626

Radiation Heat Transfer in Two-Surface Enclosures 627

Radiation Heat Transfer in Three-Surface Enclosures 629

Radiation Shields and the Radiation Effect 635

Radiation Effect on Temperature Measurements 637

Radiation Exchange with Emitting and

Absorbing Gases 639

Radiation Properties of a Participating Medium 640

Emissivity and Absorptivity of Gases and Gas Mixtures 642

Topic of Special Interest:

Heat Transfer from the Human Body 649

Summary 653

References and Suggested Reading 655

Problems 655

Chapter 13

HEAT EXCHANGERS 667

Types of Heat Exchangers 668

The Overall Heat Transfer Coefficient 671

Fouling Factor 674

Analysis of Heat Exchangers 678

The Log Mean Temperature

Difference Method 680

Counter-Flow Heat Exchangers 682

Multipass and Cross-Flow Heat Exchangers:

Use of a Correction Factor 683

The Effectiveness–NTU Method 690

Selection of Heat Exchangers 700

Heat Transfer Rate 700

Cost 700

Pumping Power 701

Size and Weight 701

Type 701

Materials 701

Other Considerations 702

Summary 703

References and Suggested Reading 704

Problems 705

Chapter 14

MASS TRANSFER 717

Introduction 718

Analogy between Heat and Mass Transfer 719

Temperature 720

Conduction 720

Heat Generation 720

Convection 721

Mass Diffusion 721

1 Mass Basis 722

2 Mole Basis 722

Special Case: Ideal Gas Mixtures 723

Fick’s Law of Diffusion: Stationary Medium Consisting of Two Species 723

Boundary Conditions 727

Steady Mass Diffusion through a Wall 732

Water Vapor Migration in Buildings 736

Transient Mass Diffusion 740

Diffusion in a Moving Medium 743

Special Case: Gas Mixtures at Constant Pressure and Temperature 747

Diffusion of Vapor through a Stationary Gas:

Stefan Flow 748

Equimolar Counterdiffusion 750

Mass Convection 754

Analogy between Friction, Heat Transfer, and Mass

Transfer Coefficients 758

Limitation on the Heat–Mass Convection Analogy 760

Mass Convection Relations 760

Simultaneous Heat and Mass Transfer 763

Summary 769

References and Suggested Reading 771

Problems 772

Chapter 15

COOLING OF ELECTRONIC EQUIPMENT 785

Introduction and History 786

Manufacturing of Electronic Equipment 787

The Chip Carrier 787

Printed Circuit Boards 789

The Enclosure 791

Cooling Load of Electronic Equipment 793

Thermal Environment 794

Electronics Cooling in

Different Applications 795

Conduction Cooling 797

Conduction in Chip Carriers 798

Conduction in Printed Circuit Boards 803

Heat Frames 805

The Thermal Conduction Module (TCM) 810

Air Cooling: Natural Convection and Radiation 812

Air Cooling: Forced Convection 820

Fan Selection 823

Cooling Personal Computers 826

Liquid Cooling 833

Immersion Cooling 836

Summary 841

References and Suggested Reading 842

Problems 842

Appendix 1

PROPERTY TABLES AND CHARTS

(SI UNITS) 855

Table A-1 Molar Mass, Gas Constant, and

Critical-Point Properties 856

Table A-2 Boiling- and Freezing-Point

Properties 857

Table A-3 Properties of Solid Metals 858

Table A-4 Properties of Solid Nonmetals 861

Table A-5 Properties of Building Materials 862

Table A-6 Properties of Insulating Materials 864

Table A-7 Properties of Common Foods 865

Table A-8 Properties of Miscellaneous Materials 867

Table A-9 Properties of Saturated Water 868

Table A-10 Properties of Saturated Refrigerant-134a 869

Table A-11 Properties of Saturated Ammonia 870

Table A-12 Properties of Saturated Propane 871

Table A-13 Properties of Liquids 872

Table A-14 Properties of Liquid Metals 873

Table A-15 Properties of Air at 1 atm Pressure 874

Table A-16 Properties of Gases at 1 atm Pressure 875

Table A-17 Properties of the Atmosphere at High Altitude 877

Table A-18 Emissivities of Surfaces 878

Table A-19 Solar Radiative Properties of Materials 880

Figure A-20 The Moody Chart for the Friction Factor for Fully Developed Flow in Circular Tubes 881

Appendix 2

PROPERTY TABLES AND CHARTS (ENGLISH UNITS) 883

Table A-1E Molar Mass, Gas Constant, and Critical-Point Properties 884

Table A-2E Boiling- and Freezing-Point Properties 885

Table A-3E Properties of Solid Metals 886

Table A-4E Properties of Solid Nonmetals 889

Table A-5E Properties of Building Materials 890

Table A-6E Properties of Insulating Materials 892

Table A-7E Properties of Common Foods 893

Table A-8E Properties of Miscellaneous Materials 895

Table A-9E Properties of Saturated Water 896

Table A-10E Properties of Saturated Refrigerant-134a 897

Table A-11E Properties of Saturated Ammonia 898

Table A-12E Properties of Saturated Propane 899

Table A-13E Properties of Liquids 900

Table A-14E Properties of Liquid Metals 901

Table A-15E Properties of Air at 1 atm Pressure 902

Table A-16E Properties of Gases at 1 atm Pressure 903

Table A-17E Properties of the Atmosphere at High Altitude 905

Appendix 3

INTRODUCTION TO EES 907

INDEX 921