Introduction to Heat Transfer

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1 FIFTH EDITION Introduction to Heat Transfer FRANK P. INCROPERA College of Engineering University ofnotre Dame DAVID P. DEWITT School of Mechanical Purdue University Engineering THEODORE L. BERGMAN Department of Mechanical Engineering University of Connecticut ADRIENNE S. LAVINE Mechanical and Aerospace Engineering Department University of California, Los Angeles JOHN WILEY & SONS

2 Contents Symbols CHAPTER 1 Introduction 1.1 What and How? Physical Origins and Rate Equations Conduction Convection Radiation Relationship to Thermodynamics The Conservation of Energy Requirement Conservation of Energy for a Control Volume The Surface Energy Balance Application of the Conservation Laws: Methodology Analysis of Heat Transfer Problems: Methodology 29

3 xiv Contents 1.5 Relevance of Heat Transfer Units and Dimensions Summary 38 References 41 Problems 41 CHARTER 2 Introduction to Conduction The Conduction Rate Equation The Thermal Properties of Matter Thermal Conductivity Other Relevant Properties The Heat Diffusion Equation Boundary and Initial Conditions Summary 81 References 82 Problems 82 CHAPTER 3 One-Dimensional, Steady-State Conduction 2Ü 3.1 The Plane Wall Temperature Distribution Thermal Resistance The Composite Wall Contact Resistance An Alternative Conduction Analysis Radial Systems TheCylinder TheSphere Summary of One-Dimensional Conduction Results 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 Summary 166 References 168 Problems 169

4 Contents XV CHAPTER4 Two-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 Solving the Finite-Difference Equations The Matrix Inversion Method Gauss-Seidel Iteration Some Precautions Summary 234 References ~35 Problems 235 4S.1 The Graphical Method W-l 4S. 1.1 Methodology of Constructing a Flux Plot W-l Determination of the Heat Transfer Rate W The Conduction Shape Factor W-3 References "-6 Problems """ CHAPTER *» Transient Conduction 2o5 5.1 The Lumped Capacitance Method Validity of the Lumped Capacitance Method General Lumped Capacitance Analysis Spatial Effects 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-Infmite Solid Objects with Constant Surface Temperatures or Surface Heat Fluxes Constant Temperature Boundary Conditions Constant Heat Flux Boundary Conditions Approximate Solutions Periodic Heating 299

5 XVI Contents 5.10 Finite-Difference Methods Discretization ofthe Heat Equation: The Explicit Method Discretization of the Heat Equation: The Implicit Method Summary 317 References 319 Problems Graphical Representation of One-Dimensional, Transient Conduction in the Plane Wall, Long Cylinder, and Sphere W Analytical Solution of Multidimensional Effects W-13 References W-18 Problems W-18 CHAPTER 6 Introduction to Convection The Convection Boundary Layers The Velocity Boundary Layer The Thermal Boundary Layer Significance of the Boundary Layers Local and Average Convection Coefficients Heat Transfer The Problem of Convection Laminar and Turbulent Flow Laminar and Turbulent Velocity Boundary Layers Laminar and Turbulent Thermal 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 Momentum and Heat Transfer (Reynolds) Analogy The Convection Coefficient Summary 372 References 373 Problems 373 * 6S.1 Derivation ofthe Convection Transfer Equations W Conservation of Mass W Newton's Second Law of Motion W Conservation of Energy W-26 References W-32 Problems W-32 CHAPTER T Externa! Flow The Empirical Method The Fiat Plate in Parallel Flow Laminar Flow over an Isothermal Plate: A Similarity Solution 385

6 Contents XV Turbulent Flow over an Isothermal Plate Mixed Boundary Layer Conditions Unheated Starting Length Fiat Plates with Constant Heat Flux Conditions Liinitations on Use of Convection Coefficients Methodology f'or a Convection Calculation The Cylinder in Cross Flow Flow Considerations Convection Heat Transfer The Sphere Flow across Banks of Tubes Impinging Jets Hydrodynamic and Geometrie Considerations Convection Heat Transfer Packed Beds Summary 430 References 432 Problems 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 ofcooling 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 Microscale Internal Flow Flow Conditions in Microscale Internal Flow Thermal Considerations in Microscale Internal Flow Summary 498 References 500 Problems 501

7 XX Contents 12.7 The Gray Surface 12.8 Environmental Radiation Summary 738 References '42 Problems ' 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 7 " 13.4 Radiation Exchange with Participating Media Volumetrie Absorption Gaseous Emission and Absorption Summary 807 References "" Problems APPENDIX A Thermophysical Properties of Matter 839 APPENDIX B Mathematical Relations and Functions 867 APPENDIX C Thermal Conditions Associated with Uniform Energy Generation in One-Dimensional, Steady-State Systems 873 APPENDIX D The Convection Transfer Equations D.l Conservation of Mass 882 D.2 Newton's Second Law of Motion 882 D.3 Conservation of Energy

8 Contents xxi APPENDIX E Boundary Layer Equations for Turbulent Flow 885 APPENDIX F An Integral Laminar Boundary Layer Solution for Parallel Flow over a Fiat Plate 889 Index 893

C ONTENTS CHAPTER TWO HEAT CONDUCTION EQUATION 61 CHAPTER ONE BASICS OF HEAT TRANSFER 1 CHAPTER THREE STEADY HEAT CONDUCTION 127

C ONTENTS CHAPTER TWO HEAT CONDUCTION EQUATION 61 CHAPTER ONE BASICS OF HEAT TRANSFER 1 CHAPTER THREE STEADY HEAT CONDUCTION 127 C ONTENTS Preface xviii Nomenclature xxvi CHAPTER ONE BASICS OF HEAT TRANSFER 1 1-1 Thermodynamics and Heat Transfer 2 Application Areas of Heat Transfer 3 Historical Background 3 1-2 Engineering Heat

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