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### Heat Transfer Practical Approach

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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
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
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
Interface Boundary Conditions 83
Generalized Boundary Conditions 84
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
Problems 113

Chapter 3

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
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
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
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
Boundary Conditions 274
Two-Dimensional
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
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
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
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
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
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
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
Problems 553

Chapter 11

Introduction 562
Solid Angle 572
Spectral Quantities 575
Emissivity 578
Absorptivity, Reflectivity, and Transmissivity 582
Kirchhoff’s Law 584
The Greenhouse Effect 585
Topic of Special Interest:
Solar Heat Gain through Windows 590
Summary 597
Problems 599

Chapter 12

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
Diffuse, Gray Surfaces 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 Effect on Temperature Measurements 637
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
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
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
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
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

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