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Symbols xix 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 28 1.4 Units and Dimensions 33 1.5 Analysis of Heat Transfer Problems: Methodology 35 1.6 Relevance of Heat Transfer 38 1.7 Summary 42 References 45 Problems 45 Chapter 2 Introduction to Conduction 59 2.1 The Conduction Rate Equation 60 2.2 The Thermal Properties of Matter 62 2.2.1 Thermal Conductivity 63 2.2.2 Other Relevant Properties 70 2.3 The Heat Diffusion Equation 74 2.4 Boundary and Initial Conditions 82 2.5 Summary 86 References 87 Problems 87 Chapter 3 One-Dimensional, Steady-State Conduction 99 3.1 The Plane Wall 100 3.1.1 Temperature Distribution 100 3.1.2 Thermal Resistance 102 3.1.3 The Composite Wall 103 3.1.4 Contact Resistance 105 3.1.5 Porous Media 107 3.2 An Alternative Conduction Analysis 121 3.3 Radial Systems 125 3.3.1 The Cylinder 125 3.3.2 The Sphere 130 3.4 Summary of One-Dimensional Conduction Results 131 3.5 Conduction with Thermal Energy Generation 131 3.5.1 The Plane Wall 132 3.5.2 Radial Systems 138 3.5.3 Tabulated Solutions 139 3.5.4 Application of Resistance Concepts 139 3.6 Heat Transfer from Extended Surfaces 143 3.6.1 A General Conduction Analysis 145 3.6.2 Fins of Uniform Cross-Sectional Area 147 3.6.3 Fin Performance Parameters 153 3.6.4 Fins of Nonuniform Cross-Sectional Area 156 3.6.5 Overall Surface Efficiency 159 3.7 Other Applications of One-Dimensional, Steady-State Conduction 163 3.7.1 The Bioheat Equation 163 3.7.2 Thermoelectric Power Generation 167 3.7.3 Nanoscale Conduction 175 3.8 Summary 179 References 181 Problems 182 Chapter 4 Two-Dimensional, Steady-State Conduction 209 4.1 General Considerations and Solution Techniques 210 4.2 The Method of Separation of Variables 211 4.3 The Conduction Shape Factor and the Dimensionless Conduction Heat Rate 215 4.4 Finite-Difference Equations 221 4.4.1 The Nodal Network 221 4.4.2 Finite-Difference Form of the Heat Equation: No Generation and Constant Properties 222 4.4.3 Finite-Difference Form of the Heat Equation: The Energy Balance Method 223 4.5 Solving the Finite-Difference Equations 230 4.5.1 Formulation as a Matrix Equation 230 4.5.2 Verifying the Accuracy of the Solution 231 4.6 Summary 236 References 237 Problems 237 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-10 Problems W-10 Chapter 5 Transient Conduction 253 5.1 The Lumped Capacitance Method 254 5.2 Validity of the Lumped Capacitance Method 257 5.3 General Lumped Capacitance Analysis 261 5.3.1 Radiation Only 262 5.3.2 Negligible Radiation 262 5.3.3 Convection Only with Variable Convection Coefficient 263 5.3.4 Additional Considerations 263 5.4 Spatial Effects 272 5.5 The Plane Wall with Convection 273 5.5.1 Exact Solution 274 5.5.2 Approximate Solution 274 5.5.3 Total Energy Transfer: Approximate Solution 276 5.5.4 Additional Considerations 276 5.6 Radial Systems with Convection 277 5.6.1 Exact Solutions 277 5.6.2 Approximate Solutions 278 5.6.3 Total Energy Transfer: Approximate Solutions 278 5.6.4 Additional Considerations 279 5.7 The Semi-Infinite Solid 284 5.8 Objects with Constant Surface Temperatures or Surface Heat Fluxes 291 5.8.1 Constant Temperature Boundary Conditions 291 5.8.2 Constant Heat Flux Boundary Conditions 293 5.8.3 Approximate Solutions 294 5.9 Periodic Heating 301 5.10 Finite-Difference Methods 304 5.10.1 Discretization of the Heat Equation: The Explicit Method 304 5.10.2 Discretization of the Heat Equation: The Implicit Method 311 5.11 Summary 318 References 319 Problems 319 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 343 6.1 The Convection Boundary Layers 344 6.1.1 The Velocity Boundary Layer 344 6.1.2 The Thermal Boundary Layer 345 6.1.3 The Concentration Boundary Layer 347 6.1.4 Significance of the Boundary Layers 348 6.2 Local and Average Convection Coefficients 348 6.2.1 Heat Transfer 348 6.2.2 Mass Transfer 349 6.3 Laminar and Turbulent Flow 355 6.3.1 Laminar and Turbulent Velocity Boundary Layers 355 6.3.2 Laminar and Turbulent Thermal and Species Concentration Boundary Layers 357 6.4 The Boundary Layer Equations 360 6.4.1 Boundary Layer Equations for Laminar Flow 361 6.4.2 Compressible Flow 364 6.5 Boundary Layer Similarity: The Normalized Boundary Layer Equations 364 6.5.1 Boundary Layer Similarity Parameters 365 6.5.2 Dependent Dimensionless Parameters 365 6.6 Physical Interpretation of the Dimensionless Parameters 374 6.7 Boundary Layer Analogies 376 6.7.1 The Heat and Mass Transfer Analogy 377 6.7.2 Evaporative Cooling 380 6.7.3 The Reynolds Analogy 383 6.8 Summary 384 References 385 Problems 386 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 399 7.1 The Empirical Method 401 7.2 The Flat Plate in Parallel Flow 402 7.2.1 Laminar Flow over an Isothermal Plate: A Similarity Solution 403 7.2.2 Turbulent Flow over an Isothermal Plate 409 7.2.3 Mixed Boundary Layer Conditions 410 7.2.4 Unheated Starting Length 411 7.2.5 Flat Plates with Constant Heat Flux Conditions 412 7.2.6 Limitations on Use of Convection Coefficients 413 7.3 Methodology for a Convection Calculation 413 7.4 The Cylinder in Cross Flow 421 7.4.1 Flow Considerations 421 7.4.2 Convection Heat and Mass Transfer 423 7.5 The Sphere 431 7.6 Flow Across Banks of Tubes 434 7.7 Impinging Jets 443 7.7.1 Hydrodynamic and Geometric Considerations 443 7.7.2 Convection Heat and Mass Transfer 444 7.8 Packed Beds 448 7.9 Summary 449 References 452 Problems 452 Chapter 8 Internal Flow 475 8.1 Hydrodynamic Considerations 476 8.1.1 Flow Conditions 476 8.1.2 The Mean Velocity 477 8.1.3 Velocity Profile in the Fully Developed Region 478 8.1.4 Pressure Gradient and Friction Factor in Fully Developed Flow 480 8.2 Thermal Considerations 481 8.2.1 The Mean Temperature 482 8.2.2 Newton's Law of Cooling 483 8.2.3 Fully Developed Conditions 483 8.3 The Energy Balance 487 8.3.1 General Considerations 487 8.3.2 Constant Surface Heat Flux 488 8.3.3 Constant Surface Temperature 491 8.4 Laminar Flow in Circular Tubes: Thermal Analysis and Convection Correlations 495 8.4.1 The Fully Developed Region 495 8.4.2 The Entry Region 500 8.4.3 Temperature-Dependent Properties 502 8.5 Convection Correlations: Turbulent Flow in Circular Tubes 502 8.6 Convection Correlations: Noncircular Tubes and the Concentric Tube Annulus 510 8.7 Heat Transfer Enhancement 513 8.8 Forced Convection in Small Channels 516 8.8.1 Microscale Convection in Gases (0.1 µm ? Dh ? 100 µm) 516 8.8.2 Microscale Convection in Liquids 517 8.8.3 Nanoscale Convection (Dh ? 100 nm) 518 8.9 Convection Mass Transfer 521 8.10 Summary 523 References 526 Problems 527 Chapter 9 Free Convection 547 9.1 Physical Considerations 548 9.2 The Governing Equations for Laminar Boundary Layers 550 9.3 Similarity Considerations 552 9.4 Laminar Free Convection on a Vertical Surface 553 9.5 The Effects of Turbulence 556 9.6 Empirical Correlations: External Free Convection Flows 558 9.6.1 The Vertical Plate 559 9.6.2 Inclined and Horizontal Plates 562 9.6.3 The Long Horizontal Cylinder 567 9.6.4 Spheres 571 9.7 Free Convection Within Parallel Plate Channels 572 9.7.1 Vertical Channels 573 9.7.2 Inclined Channels 575 9.8 Empirical Correlations: Enclosures 575 9.8.1 Rectangular Cavities 575 9.8.2 Concentric Cylinders 578 9.8.3 Concentric Spheres 579 9.9 Combined Free and Forced Convection 581 9.10 Convection Mass Transfer 582 9.11 Summary 583 References 584 Problems 585 Chapter 10 Boiling and Condensation 603 10.1 Dimensionless Parameters in Boiling and Condensation 604 10.2 Boiling Modes 605 10.3 Pool Boiling 606 10.3.1 The Boiling Curve 606 10.3.2 Modes of Pool Boiling 607 10.4 Pool Boiling Correlations 610 10.4.1 Nucleate Pool Boiling 610 10.4.2 Critical Heat Flux for Nucleate Pool Boiling 612 10.4.3 Minimum Heat Flux 613 10.4.4 Film Pool Boiling 613 10.4.5 Parametric Effects on Pool Boiling 614 10.5 Forced Convection Boiling 619 10.5.1 External Forced Convection Boiling 620 10.5.2 Two-Phase Flow 620 10.5.3 Two-Phase Flow in Microchannels 623 10.6 Condensation: Physical Mechanisms 623 10.7 Laminar Film Condensation on a Vertical Plate 625 10.8 Turbulent Film Condensation 629 10.9 Film Condensation on Radial Systems 634 10.10 Condensation in Horizontal Tubes 639 10.11 Dropwise Condensation 640 10.12 Summary 641 References 641 Problems 643 Chapter 11 Heat Exchangers 653 11.1 Heat Exchanger Types 654 11.2 The Overall Heat Transfer Coefficient 656 11.3 Heat Exchanger Analysis: Use of the Log Mean Temperature Difference 659 11.3.1 The Parallel-Flow Heat Exchanger 660 11.3.2 The Counterflow Heat Exchanger 662 11.3.3 Special Operating Conditions 663 11.4 Heat Exchanger Analysis: The Effectiveness-NTU Method 670 11.4.1 Definitions 670 11.4.2 Effectiveness-NTU Relations 671 11.5 Heat Exchanger Design and Performance Calculations 678 11.6 Additional Considerations 687 11.7 Summary 695 References 696 Problems 696 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 711 12.1 Fundamental Concepts 712 12.2 Radiation Heat Fluxes 715 12.3 Radiation Intensity 717 12.3.1 Mathematical Definitions 717 12.3.2 Radiation Intensity and Its Relation to Emission 718 12.3.3 Relation to Irradiation 723 12.3.4 Relation to Radiosity for an Opaque Surface 725 12.3.5 Relation to the Net Radiative Flux for an Opaque Surface 726 12.4 Blackbody Radiation 726 12.4.1 The Planck Distribution 727 12.4.2 Wien's Displacement Law 728 12.4.3 The Stefan-Boltzmann Law 728 12.4.4 Band Emission 729 12.5 Emission from Real Surfaces 736 12.6 Absorption, Reflection, and Transmission by Real Surfaces 745 12.6.1 Absorptivity 746 12.6.2 Reflectivity 747 12.6.3 Transmissivity 749 12.6.4 Special Considerations 749 12.7 Kirchhoff's Law 754 12.8 The Gray Surface 756 12.9 Environmental Radiation 762 12.9.1 Solar Radiation 763 12.9.2 The Atmospheric Radiation Balance 765 12.9.3 Terrestrial Solar Irradiation 767 12.10 Summary 770 References 774 Problems 774 Chapter 13 Radiation Exchange Between Surfaces 797 13.1 The View Factor 798 13.1.1 The View Factor Integral 798 13.1.2 View Factor Relations 799 13.2 Blackbody Radiation Exchange 808 13.3 Radiation Exchange Between Opaque, Diffuse, Gray Surfaces in an Enclosure 812 13.3.1 Net Radiation Exchange at a Surface 813 13.3.2 Radiation Exchange Between Surfaces 814 13.3.3 The Two-Surface Enclosure 820 13.3.4 Two-Surface Enclosures in Series and Radiation Shields 822 13.3.5 The Reradiating Surface 824 13.4 Multimode Heat Transfer 829 13.5 Implications of the Simplifying Assumptions 832 13.6 Radiation Exchange with Participating Media 832 13.6.1 Volumetric Absorption 832 13.6.2 Gaseous Emission and Absorption 833 13.7 Summary 837 References 838 Problems 839 Chapter 14 Diffusion Mass Transfer 863 14.1 Physical Origins and Rate Equations 864 14.1.1 Physical Origins 864 14.1.2 Mixture Composition 865 14.1.3 Fick's Law of Diffusion 866 14.1.4 Mass Diffusivity 867 14.2 Mass Transfer in Nonstationary Media 869 14.2.1 Absolute and Diffusive Species Fluxes 869 14.2.2 Evaporation in a Column 872 14.3 The Stationary Medium Approximation 877 14.4 Conservation of Species for a Stationary Medium 877 14.4.1 Conservation of Species for a Control Volume 878 14.4.2 The Mass Diffusion Equation 878 14.4.3 Stationary Media with Specified Surface Concentrations 880 14.5 Boundary Conditions and Discontinuous Concentrations at Interfaces 884 14.5.1 Evaporation and Sublimation 885 14.5.2 Solubility of Gases in Liquids and Solids 885 14.5.3 Catalytic Surface Reactions 890 14.6 Mass Diffusion with Homogeneous Chemical Reactions 892 14.7 Transient Diffusion 895 14.8 Summary 901 References 902 Problems 902 Appendix A Thermophysical Properties of Matter 911 Appendix B Mathematical Relations and Functions 943 Appendix C Thermal Conditions Associated with Uniform Energy Generation in One-Dimensional, Steady-State Systems 949 Appendix D The Gauss-Seidel Method 955 Appendix E The Convection Transfer Equations 957 E.1 Conservation of Mass 958 E.2 Newton's Second Law of Motion 958 E.3 Conservation of Energy 959 E.4 Conservation of Species 960 Appendix F Boundary Layer Equations for Turbulent Flow 961 Appendix G An Integral Laminar Boundary Layer Solution for Parallel Flow over a Flat Plate 965 Index 969

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