# Fundamentals of Heat and Mass Transfer

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1 2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. SIXTH EDITION Fundamentals of Heat and Mass Transfer FRANK P. INCROPERA College of Engineering University of Notre Dame DAVID P. DEWITT School of Mechanical Engineering Purdue University THEODORE L. BERGMAN Department of Mechanical Engineering University of Connecticut ADRIENNE S. LAVINE Mechanical and Aerospace Engineering Department University of California, Los Angeles JOHN WIUA

2 Contents Symbols xxui CHAPTER 1 Introduction What and How? Physical Origins and Rate Equations Conduction Convection Radiation Relationship to Thermodynamics 12 The Conservation of Energy Requirement Conservation of Energy for a Control Volume The Surface Energy Balance Application of the Conservation Laws: Methodology 28 Analysis of Heat Transfer : Methodology

3 XIV Contents 1.5 Relevance of Heat Transfer 1.6 Units and Dimensions 1.7 Summary CHAPTER 2 Introduction to Conduction 2.1 The Conduction Rate Equation 2.2 The Thermal Properties of Matter Thermal Conductivity Other Relevant Properties The Heat Diffusion Equation 2.4 Boundary and Initial Conditions 2.5 Summary CHAPTER 3 One-Dimensional, Steady-State Conduction 3.1 The Plane Wall Temperature Distribution Thermal Resistance The Composite Wall Contact Resistance An Alternative Conduction Analysis 3.3 Radial Systems The Cylinder The Sphere Summary of One-Dimensional Conduction Results 3.5 Conduction with Thermal Energy Generation The Plane Wall Radial Systems Application of Resistance Concepts Heat Transfer from Extended Surfaces A General Conduction Analysis Fins of Uniform Cross-Sectional Area Fin Performance Fins of Nonuniform Cross-Sectional Area Overall Surface Efficiency The Bioheat Equation 3.8 Summary

4 Contents XV fer ^-Dimensional, Steady-State Conduction Alternative Approaches The Method of Separation of Variables The Conduction Shape Factor and the Dimensionless Conduction Heat Rate Finite-Difference Equations The Nodal Network Finite-Difference Form of the Heat Equation The Energy Balance Method 215 Solving the Finite-Difference Equations The Matrix Inversion Method Gauss-Seidel Iteration Some Precautions 229 Summary 4S.1 The Graphical Method Methodology of Constructing a Flux Plot W-l Determination of the Heat Transfer Rate W The Conduction Shape Factor W W-l W-6 W-6 PER ^Transient Conduction The Lumped Capacitance Method 5.2 Validity of the Lumped Capacitance Method 5.3 General Lumped Capacitance Analysis 5.4 Spatial Effects 5.5 The Plane Wall with Convection Exact Solution Approximate Solution Total Energy Transfer Additional Considerations Radial Systems with Convection Exact Solutions Approximate Solutions Total Energy Transfer Additional Considerations The Semi-Infinite Solid 5.8 Objects with Constant Surface Temperatures or Surface Heat Fluxes Constant Temperature Boundary Conditions Constant Heat Flux Boundary Conditions Approximate Solutions Periodic Heating

5 XVI Contents CHAPTER 6 Introduction to Convection 5.10 Finite-Difference Methods Discretization of the Heat Equation: The Explicit Method Discretization of the Heat Equation: The Implicit Method 5.11 Summary 55.1 Graphical Representation of One-Dimensional, Transient Conduction in the Plane Wall, Long Cylinder, and Sphere 55.2 Analytical Solution of Multidimensional Effects W-8 W-13 W-18 W The Convection Boundary Layers The Velocity Boundary Layer The Thermal Boundary Layer The Concentration Boundary Layer Significance of the Boundary Layers Local and Average Convection Coefficients Heat Transfer Mass Transfer The Problem of Convection Laminar and Turbulent Flow Laminar and Turbulent Velocity Boundary Layers Laminar and Turbulent Thermal and Species Concentration Boundary Layers The Boundary Layer Equations Boundary Layer Equations for Laminar Flow Boundary Layer Similarity: The Normalized Boundary Layer Equations Boundary Layer Similarity Parameters Functional Form of the Solutions Physical Significance of the Dimensionless Parameters 6.7 Boundary Layer Analogies The Heat and Mass Transfer Analogy Evaporative Cooling The Reynolds Analogy The Convection Coefficients 6.9 Summary. 6S.1 Derivation of the Convection Transfer Equations 6S.1.1 Conservation of Mass W-21 6S. 1.2 Newton's Second Law of Motion W-22 6S. 1.3 Conservation of Energy W-26 6S. 1.4 Conservation of Species W W-21 W-33 W-33

6 Contents XVll TER T Ixternal Flow The Empirical Method 7.2 The Flat Plate in Parallel Flow Laminar Flow over an Isothermal Plate: A Similarity Solution Turbulent Flow over an Isothermal Plate Mixed Boundary Layer Conditions A Unheated Starting Length Flat Plates with Constant Heat Flux Conditions Limitations on Use of Convection Coefficients Methodology for a Convection Calculation 7.4 The Cylinder in Cross Flow Flow Considerations Convection Heat and Mass Transfer The Sphere 7.6 Flow Across Banks of Tubes 7.7 Impinging Jets Hydrodynamic and Geometric Considerations Convection Heat and Mass Transfer Packed Beds 7.9 Summary tpter 8 Internal Flow Hydrodynamic Considerations Flow Conditions The Mean Velocity Velocity Profile in the Fully Developed Region Pressure Gradient and Friction Factor in Fully Developed Flow Thermal Considerations The Mean Temperature Newton's Law of Cooling Fully Developed Conditions The Energy Balance General Considerations Constant Surface Heat Flux Constant Surface Temperature Laminar Flow in Circular Tubes: Thermal Analysis and Convection Correlations The Fully Developed Region The Entry Region Convection Correlations: Turbulent Flow in Circular Tubes Convection Correlations: Noncircular Tubes and the Concentric Tube Annulus Heat Transfer Enhancement 521

7 xvin Contents 8.8 Microscale Internal Flow Flow Conditions in Microscale Internal Flow Thermal Considerations in Microscale Internal Flow 8.9 Convection Mass Transfer 8.10 Summary CHAPTER 9 Free Convection Physical Considerations 9.2 The Governing Equations 9.3 Similarity Considerations 9.4 Laminar Free Convection on a Vertical Surface 9.5 The Effects of Turbulence 9.6 Empirical Correlations: External Free Convection Flows The Vertical Plate Inclined and Horizontal Plates The Long Horizontal Cylinder Spheres Free Convection within Parallel Plate Channels Vertical Channels Inclined Channels Empirical Correlations: Enclosures Rectangular Cavities Concentric Cylinders Concentric Spheres Combined Free and Forced Convection 9.10 Convection Mass Transfer 9.11 Summary CHAPTER 10 Boiling and Condensation Dimensionless Parameters in Boiling and Condensation 10.2 Boiling Modes 10.3 Pool Boiling The Boiling Curve Modes of Pool Boiling Pool Boiling Correlations Nucleate Pool Boiling Critical Heat Flux for Nucleate Pool Boiling Minimum Heat Flux Film Pool Boiling Parametric Effects on Pool Boiling

8 Contents XIX Forced Convection Boiling External Forced Convection Boiling Two-Phase Flow Two-Phase Flow in Microchannels 640 Condensation: Physical Mechanisms Laminar Film Condensation on a Vertical Plate Turbulent Film Condensation Film Condensation on Radial Systems Film Condensation in Horizontal Tubes Dropwise Condensation Summary PER 1 1 \eat Exchangers CHAPTER 12 Radiation: Processes and Properties Heat Exchanger Types The Overall Heat Transfer Coefficient Heat Exchanger Analysis: Use of the Log Mean Temperature Difference The Parallel-Flow Heat Exchanger The Counterflow Heat Exchanger Special Operating Conditions 679 Heat Exchanger Analysis: The Effectiveness-NTU Method Definitions Effectiveness-NTU Relations 688 Heat Exchanger Design and Performance Calculations: Using the Effectiveness-NTU Method Compact Heat Exchangers Summary 11S.1 Log Mean Temperature Difference Method for Multipass and Cross-Flow Heat Exchangers W-37 W-41 W Fundamental Concepts Radiation Intensity Mathematical Definitions Radiation Intensity and Its Relation to Emission Relation to Irradiation Relation to Radiosity 735 Blackbody Radiation The Planck Distribution Wien's Displacement Law

9 XX Contents The Stefan-Boltzmann Law Band Emission Emission from Real Surfaces 12.5 Absorption, Reflection, and Transmission by Real Surfaces Absorptivity Reflectivity Transmissivity Special Considerations KirchhoffsLaw 12.7 The Gray Surface 12.8 Environmental Radiation 12.9 Summary CHAPTER 13 Radiation Exchange Between Surfaces The View Factor The View Factor Integral View Factor Relations Radiation Exchange Between Opaque, Diffuse, Gray Surfaces in an Enclosure Net Radiation Exchange at a Surface Radiation Exchange Between Surfaces Blackbody Radiation Exchange The Two-Surface Enclosure Radiation Shields The Reradiating Surface Multimode Heat Transfer Radiation Exchange with Participating Media Volumetric Absorption Gaseous Emission and Absorption Summary CHAPTER 14 Diffusion Mass Transfer Physical Origins and Rate Equations Physical Origins Mixture Composition Fick's Law of Diffusion Mass Diffusivity Mass Transfer in Nonstationary Media Absolute and Diffusive Species Fluxes Evaporation in a Column The Stationary Medium Approximation

10 Contents XXI APPENDIX A Thermophysical Properties of Matter 14.4 Conservation of Species for a Stationary Medium Conservation of Species for a Control Volume The Mass Diffusion Equation Stationary Media with Specified Surface Concentrations Boundary Conditions and Discontinuous Concentrations at Interfaces Evaporation and Sublimation Solubility of Gases in Liquids and Solids Catalytic Surface Reactions Mass Diffusion with Homogeneous Chemical Reactions 14.7 Transient Diffusion 14.8 Summary APPENDIX B Mathematical Relations and Functions 959 APPENDIX C Thermal Conditions Associated with Uniform Energy Generation in One-Dimensional, Steady-State Systems 965 APPENDIX D The Convection Transfer Equations 973 D.I Conservation of Mass D.2 Newton's Second Law of Motion D.3 Conservation of Energy D.4 Conservation of Species APPENDIX E Boundary Layer Equations for Turbulent Flow APPENDIX F An Integral Laminar Boundary Layer Solution for Parallel Flow over a Flat Plate 981 Index 985

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