Table of Contents
Symbols xxi
CHAPTER 1 Introduction 1
1.1 What and How? 2
1.2 Physical Origins and Rate Equations 3
1.2.1 Conduction 3
1.2.2 Convection 6
1.2.3 Radiation 8
1.2.4 The Thermal Resistance Concept 12
1.3 Relationship to Thermodynamics 12
1.3.1 Relationship to the First Law of Thermodynamics (Conservation of Energy) 13
1.3.2 Relationship to the Second Law of Thermodynamics and the Efficiency of Heat Engines 31
1.4 Units and Dimensions 36
1.5 Analysis of Heat Transfer Problems: Methodology 38
1.6 Relevance of Heat Transfer 41
1.7 Summary 45
References 48
Problems 49
CHAPTER 2 Introduction to Conduction 67
2.1 The Conduction Rate Equation 68
2.2 The Thermal Properties of Matter 70
2.2.1 Thermal Conductivity 70
2.2.2 Other Relevant Properties 78
2.3 The Heat Diffusion Equation 82
2.4 Boundary and Initial Conditions 90
2.5 Summary 94
References 95
Problems 95
CHAPTER 3 One–Dimensional, Steady–State Conduction 111
3.1 The Plane Wall 112
3.1.1 Temperature Distribution 112
3.1.2 Thermal Resistance 114
3.1.3 The Composite Wall 115
3.1.4 Contact Resistance 117
3.1.5 Porous Media 119
3.2 An Alternative Conduction Analysis 132
3.3 Radial Systems 136
3.3.1 The Cylinder 136
3.3.2 The Sphere 141
3.4 Summary of One–Dimensional Conduction Results 142
3.5 Conduction with Thermal Energy Generation 142
3.5.1 The Plane Wall 143
3.5.2 Radial Systems 149
3.5.3 Tabulated Solutions 150
3.5.4 Application of Resistance Concepts 150
3.6 Heat Transfer from Extended Surfaces 154
3.6.1 A General Conduction Analysis 156
3.6.2 Fins of Uniform Cross–Sectional Area 158
3.6.3 Fin Performance 164
3.6.4 Fins of Nonuniform Cross–Sectional Area 167
3.6.5 Overall Surface Efficiency 170
3.7 The Bioheat Equation 178
3.8 Thermoelectric Power Generation 182
3.9 Micro– and Nanoscale Conduction 189
3.9.1 Conduction Through Thin Gas Layers 189
3.9.2 Conduction Through Thin Solid Films 190
3.10 Summary 190
References 193
Problems 193
CHAPTER 4 Two–Dimensional, Steady–State Conduction 229
4.1 Alternative Approaches 230
4.2 The Method of Separation of Variables 231
4.3 The Conduction Shape Factor and the Dimensionless Conduction Heat Rate 235
4.4 Finite–Difference Equations 241
4.4.1 The Nodal Network 241
4.4.2 Finite–Difference Form of the Heat Equation 242
4.4.3 The Energy Balance Method 243
4.5 Solving the Finite–Difference Equations 250
4.5.1 Formulation as a Matrix Equation 250
4.5.2 Verifying the Accuracy of the Solution 251
4.6 Summary 256
References 257
Problems 257
4S.1 The Graphical Method W–1
4S.1.1 Methodology of Constructing a Flux Plot W–1
4S.1.2 Determination of the Heat Transfer Rate W–2
4S.1.3 The Conduction Shape Factor W–3
4S.2 The Gauss Seidel Method: Example of Usage W–5
References W–9
Problems W–10
CHAPTER 5 Transient Conduction 279
5.1 The Lumped Capacitance Method 280
5.2 Validity of the Lumped Capacitance Method 283
5.3 General Lumped Capacitance Analysis 287
5.3.1 Radiation Only 288
5.3.2 Negligible Radiation 288
5.3.3 Convection Only with Variable Convection Coefficient 289
5.3.4 Additional Considerations 289
5.4 Spatial Effects 298
5.5 The Plane Wall with Convection 299
5.5.1 Exact Solution 300
5.5.2 Approximate Solution 300
5.5.3 Total Energy Transfer 302
5.5.4 Additional Considerations 302
5.6 Radial Systems with Convection 303
5.6.1 Exact Solutions 303
5.6.2 Approximate Solutions 304
5.6.3 Total Energy Transfer 304
5.6.4 Additional Considerations 305
5.7 The Semi–Infinite Solid 310
5.8 Objects with Constant Surface Temperatures or Surface Heat Fluxes 317
5.8.1 Constant Temperature Boundary Conditions 317
5.8.2 Constant Heat Flux Boundary Conditions 319
5.8.3 Approximate Solutions 320
5.9 Periodic Heating 327
5.10 Finite–Difference Methods 330
5.10.1 Discretization of the Heat Equation: The Explicit Method 330
5.10.2 Discretization of the Heat Equation: The Implicit Method 337
5.11 Summary 345
References 346
Problems 346
5S.1 Graphical Representation of One–Dimensional, Transient Conduction in the
Plane Wall, Long Cylinder, and Sphere W–12
5S.2 Analytical Solutions of Multidimensional Effects W–16
References W–22
Problems W–22
CHAPTER 6 Introduction to Convection 377
6.1 The Convection Boundary Layers 378
6.1.1 The Velocity Boundary Layer 378
6.1.2 The Thermal Boundary Layer 379
6.1.3 The Concentration Boundary Layer 380
6.1.4 Significance of the Boundary Layers 382
6.2 Local and Average Convection Coefficients 382
6.2.1 Heat Transfer 382
6.2.2 Mass Transfer 383
6.2.3 The Problem of Convection 385
6.3 Laminar and Turbulent Flow 389
6.3.1 Laminar and Turbulent Velocity Boundary Layers 389
6.3.2 Laminar and Turbulent Thermal and Species Concentration Boundary Layers 391
6.4 The Boundary Layer Equations 394
6.4.1 Boundary Layer Equations for Laminar Flow 394
6.4.2 Compressible Flow 397
6.5 Boundary Layer Similarity: The Normalized Boundary Layer Equations 398
6.5.1 Boundary Layer Similarity Parameters 398
6.5.2 Functional Form of the Solutions 400
6.6 Physical Interpretation of the Dimensionless Parameters 407
6.7 Boundary Layer Analogies 409
6.7.1 The Heat and Mass Transfer Analogy 410
6.7.2 Evaporative Cooling 413
6.7.3 The Reynolds Analogy 416
6.8 Summary 417
References 418
Problems 419
6S.1 Derivation of the Convection Transfer Equations W–25
6S.1.1 Conservation of Mass W–25
6S.1.2 Newton s Second Law of Motion W–26
6S.1.3 Conservation of Energy W–29
6S.1.4 Conservation of Species W–32
References W–36
Problems W–36
CHAPTER 7 External Flow 433
7.1 The Empirical Method 435
7.2 The Flat Plate in Parallel Flow 436
7.2.1 Laminar Flow over an Isothermal Plate: A Similarity Solution 437
7.2.2 Turbulent Flow over an Isothermal Plate 443
7.2.3 Mixed Boundary Layer Conditions 444
7.2.4 Unheated Starting Length 445
7.2.5 Flat Plates with Constant Heat Flux Conditions 446
7.2.6 Limitations on Use of Convection Coefficients 446
7.3 Methodology for a Convection Calculation 447
7.4 The Cylinder in Cross Flow 455
7.4.1 Flow Considerations 455
7.4.2 Convection Heat and Mass Transfer 457
7.5 The Sphere 465
7.6 Flow Across Banks of Tubes 468
7.7 Impinging Jets 477
7.7.1 Hydrodynamic and Geometric Considerations 477
7.7.2 Convection Heat and Mass Transfer 478
7.8 Packed Beds 482
7.9 Summary 483
References 486
Problems 486
CHAPTER 8 Internal Flow 517
8.1 Hydrodynamic Considerations 518
8.1.1 Flow Conditions 518
8.1.2 The Mean Velocity 519
8.1.3 Velocity Profile in the Fully Developed Region 520
8.1.4 Pressure Gradient and Friction Factor in Fully Developed Flow 522
8.2 Thermal Considerations 523
8.2.1 The Mean Temperature 524
8.2.2 Newton s Law of Cooling 525
8.2.3 Fully Developed Conditions 525
8.3 The Energy Balance 529
8.3.1 General Considerations 529
8.3.2 Constant Surface Heat Flux 530
8.3.3 Constant Surface Temperature 533
8.4 Laminar Flow in Circular Tubes: Thermal Analysis and Convection Correlations 537
8.4.1 The Fully Developed Region 537
8.4.2 The Entry Region 542
8.4.3 Temperature–Dependent Properties 544
8.5 Convection Correlations: Turbulent Flow in Circular Tubes 544
8.6 Convection Correlations: Noncircular Tubes and the Concentric Tube Annulus 552
8.7 Heat Transfer Enhancement 555
8.8 Flow in Small Channels 558
8.8.1 Microscale Convection in Gases 558
8.8.2 Microscale Convection in Liquids 559
8.8.3 Nanoscale Convection 560
8.9 Convection Mass Transfer 563
8.10 Summary 565
References 568
Problems 569
CHAPTER 9 Free Convection 593
9.1 Physical Considerations 594
9.2 The Governing Equations for Laminar Boundary Layers 597
9.3 Similarity Considerations 598
9.4 Laminar Free Convection on a Vertical Surface 599
9.5 The Effects of Turbulence 602
9.6 Empirical Correlations: External Free Convection Flows 604
9.6.1 The Vertical Plate 605
9.6.2 Inclined and Horizontal Plates 608
9.6.3 The Long Horizontal Cylinder 613
9.6.4 Spheres 617
9.7 Free Convection Within Parallel Plate Channels 618
9.7.1 Vertical Channels 619
9.7.2 Inclined Channels 621
9.8 Empirical Correlations: Enclosures 621
9.8.1 Rectangular Cavities 621
9.8.2 Concentric Cylinders 624
9.8.3 Concentric Spheres 625
9.9 Combined Free and Forced Convection 627
9.10 Convection Mass Transfer 628
9.11 Summary 629
References 630
Problems 631
CHAPTER 10 Boiling and Condensation 653
10.1 Dimensionless Parameters in Boiling and Condensation 654
10.2 Boiling Modes 655
10.3 Pool Boiling 656
10.3.1 The Boiling Curve 656
10.3.2 Modes of Pool Boiling 657
10.4 Pool Boiling Correlations 660
10.4.1 Nucleate Pool Boiling 660
10.4.2 Critical Heat Flux for Nucleate Pool Boiling 662
10.4.3 Minimum Heat Flux 663
10.4.4 Film Pool Boiling 663
10.4.5 Parametric Effects on Pool Boiling 664
10.5 Forced Convection Boiling 669
10.5.1 External Forced Convection Boiling 670
10.5.2 Two–Phase Flow 670
10.5.3 Two–Phase Flow in Microchannels 673
10.6 Condensation: Physical Mechanisms 673
10.7 Laminar Film Condensation on a Vertical Plate 675
10.8 Turbulent Film Condensation 679
10.9 Film Condensation on Radial Systems 684
10.10 Condensation in Horizontal Tubes 689
10.11 Dropwise Condensation 690
10.12 Summary 691
References 691
Problems 693
CHAPTER 11 Heat Exchangers 705
11.1 Heat Exchanger Types 706
11.2 The Overall Heat Transfer Coefficient 708
11.3 Heat Exchanger Analysis: Use of the Log Mean Temperature Difference 711
11.3.1 The Parallel–Flow Heat Exchanger 712
11.3.2 The Counterflow Heat Exchanger 714
11.3.3 Special Operating Conditions 715
11.4 Heat Exchanger Analysis: The Effectiveness NTU Method 722
11.4.1 Definitions 722
11.4.2 Effectiveness NTU Relations 723
11.5 Heat Exchanger Design and Performance Calculations 730
11.6 Additional Considerations 739
11.7 Summary 747
References 748
Problems 748
11S.1 Log Mean Temperature Difference Method for Multipass and Cross–Flow Heat Exchangers W–40
11S.2 Compact Heat Exchangers W–44
References W–49
Problems W–50
CHAPTER 12 Radiation: Processes and Properties 767
12.1 Fundamental Concepts 768
12.2 Radiation Heat Fluxes 771
12.3 Radiation Intensity 773
12.3.1 Mathematical Definitions 773
12.3.2 Radiation Intensity and Its Relation to Emission 774
12.3.3 Relation to Irradiation 779
12.3.4 Relation to Radiosity for an Opaque Surface 781
12.3.5 Relation to the Net Radiative Flux for an Opaque Surface 782
12.4 Blackbody Radiation 782
12.4.1 The Planck Distribution 783
12.4.2 Wien s Displacement Law 784
12.4.3 The Stefan Boltzmann Law 784
12.4.4 Band Emission 785
12.5 Emission from Real Surfaces 792
12.6 Absorption, Reflection, and Transmission by Real Surfaces 801
12.6.1 Absorptivity 802
12.6.2 Reflectivity 803
12.6.3 Transmissivity 805
12.6.4 Special Considerations 805
12.7 Kirchhoff s Law 810
12.8 The Gray Surface 812
12.9 Environmental Radiation 818
12.9.1 Solar Radiation 819
12.9.2 The Atmospheric Radiation Balance 821
12.9.3 Terrestrial Solar Irradiation 823
12.10 Summary 826
References 830
Problems 830
CHAPTER 13 Radiation Exchange Between Surfaces 861
13.1 The View Factor 862
13.1.1 The View Factor Integral 862
13.1.2 View Factor Relations 863
13.2 Blackbody Radiation Exchange 872
13.3 Radiation Exchange Between Opaque, Diffuse, Gray Surfaces in an Enclosure 876
13.3.1 Net Radiation Exchange at a Surface 877
13.3.2 Radiation Exchange Between Surfaces 878
13.3.3 The Two–Surface Enclosure 884
13.3.4 Radiation Shields 886
13.3.5 The Reradiating Surface 888
13.4 Multimode Heat Transfer 893
13.5 Implications of the Simplifying Assumptions 896
13.6 Radiation Exchange with Participating Media 896
13.6.1 Volumetric Absorption 896
13.6.2 Gaseous Emission and Absorption 897
13.7 Summary 901
References 902
Problems 903
CHAPTER 14 Diffusion Mass Transfer 933
14.1 Physical Origins and Rate Equations 934
14.1.1 Physical Origins 934
14.1.2 Mixture Composition 935
14.1.3 Fick s Law of Diffusion 936
14.1.4 Mass Diffusivity 937
14.2 Mass Transfer in Nonstationary Media 939
14.2.1 Absolute and Diffusive Species Fluxes 939
14.2.2 Evaporation in a Column 942
14.3 The Stationary Medium Approximation 947
14.4 Conservation of Species for a Stationary Medium 947
14.4.1 Conservation of Species for a Control Volume 948
14.4.2 The Mass Diffusion Equation 948
14.4.3 Stationary Media with Specified Surface Concentrations 950
14.5 Boundary Conditions and Discontinuous Concentrations at Interfaces 954
14.5.1 Evaporation and Sublimation 955
14.5.2 Solubility of Gases in Liquids and Solids 955
14.5.3 Catalytic Surface Reactions 960
14.6 Mass Diffusion with Homogeneous Chemical Reactions 962
14.7 Transient Diffusion 965
14.8 Summary 971
References 972
Problems 972
APPENDIX A Thermophysical Properties of Matter 981
APPENDIX B Mathematical Relations and Functions 1013
APPENDIX C Thermal Conditions Associated with Uniform Energy Generation in One–Dimensional, Steady–State Systems 1019
APPENDIX D The Gauss Seidel Method 1025
APPENDIX E The Convection Transfer Equations 1027
E.1 Conservation of Mass 1028
E.2 Newton s Second Law of Motion 1028
E.3 Conservation of Energy 1029
E.4 Conservation of Species 1030
APPENDIX F Boundary Layer Equations for Turbulent Flow 1031
APPENDIX G An Integral Laminar Boundary Layer Solution for Parallel Flow over a Flat Plate 1035
Index 1039
