Introduction to Heat Transfer 5th Edition Solution Manual

Introduction to Heat Transfer 5th Edition Solution Manual
اسم المؤلف
THEODORE L. BERGMAN , ADRIENNE S. LAVINE , FRANK P. INCROPERA
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6 مايو 2018
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Introduction to Heat Transfer 5th Edition Solution Manual
THEODORE L. BERGMAN
Department of Mechanical Engineering
University of Connecticut
ADRIENNE S. LAVINE
Mechanical and Aerospace Engineering
Department
University of California, Los Angeles
FRANK P. INCROPERA
College of Engineering
University of Notre Dame
DAVID P. DEWITT
School of Mechanical Engineering
Purdue University
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 381.6 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
xii ContentsCHAPTER 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
Contents xiii5.9 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 Solution 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 Significance of the Boundary Layers 380
6.2 Local and Average Convection Coefficients 381
6.2.1 Heat Transfer 381
6.2.2 The Problem of Convection 382
6.3 Laminar and Turbulent Flow 383
6.3.1 Laminar and Turbulent Velocity Boundary Layers 383
6.3.2 Laminar and Turbulent Thermal Boundary Layers 385
6.4 The Boundary Layer Equations 388
6.4.1 Boundary Layer Equations for Laminar Flow 389
6.4.2 Compressible Flow 391
6.5 Boundary Layer Similarity: The Normalized Boundary Layer Equations 392
6.5.1 Boundary Layer Similarity Parameters 392
6.5.2 Functional Form of the Solutions 393
6.6 Physical Interpretation of the Dimensionless Parameters 400
6.7 Momentum and Heat Transfer (Reynolds) Analogy 402
6.8 Summary 404
References 405
Problems 405
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
References W-35
Problems W-35
CHAPTER 7 External Flow 415
7.1 The Empirical Method 416
7.2 The Flat Plate in Parallel Flow 418
7.2.1 Laminar Flow over an Isothermal Plate: A Similarity Solution 418
7.2.2 Turbulent Flow over an Isothermal Plate 424
xiv Contents7.2.3 Mixed Boundary Layer Conditions 425
7.2.4 Unheated Starting Length 426
7.2.5 Flat Plates with Constant Heat Flux Conditions 427
7.2.6 Limitations on Use of Convection Coefficients 427
7.3 Methodology for a Convection Calculation 428
7.4 The Cylinder in Cross Flow 433
7.4.1 Flow Considerations 433
7.4.2 Convection Heat Transfer 436
7.5 The Sphere 443
7.6 Flow Across Banks of Tubes 447
7.7 Impinging Jets 455
7.7.1 Hydrodynamic and Geometric Considerations 456
7.7.2 Convection Heat Transfer 458
7.8 Packed Beds 461
7.9 Summary 462
References 464
Problems 465
CHAPTER 8 Internal Flow 489
8.1 Hydrodynamic Considerations 490
8.1.1 Flow Conditions 490
8.1.2 The Mean Velocity 491
8.1.3 Velocity Profile in the Fully Developed Region 492
8.1.4 Pressure Gradient and Friction Factor in Fully
Developed Flow 494
8.2 Thermal Considerations 495
8.2.1 The Mean Temperature 496
8.2.2 Newton’s Law of Cooling 497
8.2.3 Fully Developed Conditions 497
8.3 The Energy Balance 501
8.3.1 General Considerations 501
8.3.2 Constant Surface Heat Flux 502
8.3.3 Constant Surface Temperature 505
8.4 Laminar Flow in Circular Tubes: Thermal Analysis and
Convection Correlations 509
8.4.1 The Fully Developed Region 509
8.4.2 The Entry Region 514
8.4.3 Temperature-Dependent Properties 516
8.5 Convection Correlations: Turbulent Flow in Circular Tubes 516
8.6 Convection Correlations: Noncircular Tubes and the Concentric Tube Annulus 524
8.7 Heat Transfer Enhancement 527
8.8 Flow in Small Channels 530
8.8.1 Microscale Convection in Gases (0.1 m  Dh  100 m) 530
8.8.2 Microscale Convection in Liquids 531
8.8.3 Nanoscale Convection (Dh  100 nm) 532
8.9 Summary 535
References 537
Problems 538
Contents xvCHAPTER 9 Free Convection 561
9.1 Physical Considerations 562
9.2 The Governing Equations for Laminar Boundary Layers 565
9.3 Similarity Considerations 566
9.4 Laminar Free Convection on a Vertical Surface 567
9.5 The Effects of Turbulence 570
9.6 Empirical Correlations: External Free Convection Flows 572
9.6.1 The Vertical Plate 573
9.6.2 Inclined and Horizontal Plates 576
9.6.3 The Long Horizontal Cylinder 581
9.6.4 Spheres 585
9.7 Free Convection Within Parallel Plate Channels 586
9.7.1 Vertical Channels 587
9.7.2 Inclined Channels 589
9.8 Empirical Correlations: Enclosures 589
9.8.1 Rectangular Cavities 589
9.8.2 Concentric Cylinders 592
9.8.3 Concentric Spheres 593
9.9 Combined Free and Forced Convection 595
9.10 Summary 596
References 597
Problems 598
CHAPTER 10 Boiling and Condensation 619
10.1 Dimensionless Parameters in Boiling and Condensation 620
10.2 Boiling Modes 621
10.3 Pool Boiling 622
10.3.1 The Boiling Curve 622
10.3.2 Modes of Pool Boiling 623
10.4 Pool Boiling Correlations 626
10.4.1 Nucleate Pool Boiling 626
10.4.2 Critical Heat Flux for Nucleate Pool Boiling 628
10.4.3 Minimum Heat Flux 629
10.4.4 Film Pool Boiling 629
10.4.5 Parametric Effects on Pool Boiling 630
10.5 Forced Convection Boiling 635
10.5.1 External Forced Convection Boiling 636
10.5.2 Two-Phase Flow 636
10.5.3 Two-Phase Flow in Microchannels 639
10.6 Condensation: Physical Mechanisms 639
10.7 Laminar Film Condensation on a Vertical Plate 641
10.8 Turbulent Film Condensation 645
10.9 Film Condensation on Radial Systems 650
10.10 Condensation in Horizontal Tubes 655
10.11 Dropwise Condensation 656
xvi Contents10.12 Summary 657
References 657
Problems 659
CHAPTER 11 Heat Exchangers 671
11.1 Heat Exchanger Types 672
11.2 The Overall Heat Transfer Coefficient 674
11.3 Heat Exchanger Analysis: Use of the Log Mean
Temperature Difference 677
11.3.1 The Parallel-Flow Heat Exchanger 678
11.3.2 The Counterflow Heat Exchanger 680
11.3.3 Special Operating Conditions 681
11.4 Heat Exchanger Analysis: The Effectiveness–NTU Method 688
11.4.1 Definitions 688
11.4.2 Effectiveness–NTU Relations 689
11.5 Heat Exchanger Design and Performance Calculations 696
11.6 Additional Considerations 705
11.7 Summary 713
References 714
Problems 714
11S.1 Log Mean Temperature Difference Method for Multipass and
Cross-Flow Heat Exchangers W-38
11S.2 Compact Heat Exchangers W-42
References W-47
Problems W-48
CHAPTER 12 Radiation: Processes and Properties 733
12.1 Fundamental Concepts 734
12.2 Radiation Heat Fluxes 737
12.3 Radiation Intensity 739
12.3.1 Mathematical Definitions 739
12.3.2 Radiation Intensity and Its Relation to Emission 740
12.3.3 Relation to Irradiation 745
12.3.4 Relation to Radiosity for an Opaque Surface 747
12.3.5 Relation to the Net Radiative Flux for an
Opaque Surface 748
12.4 Blackbody Radiation 748
12.4.1 The Planck Distribution 749
12.4.2 Wien’s Displacement Law 750
12.4.3 The Stefan–Boltzmann Law 750
12.4.4 Band Emission 751
12.5 Emission from Real Surfaces 758
12.6 Absorption, Reflection, and Transmission by Real Surfaces 767
12.6.1 Absorptivity 768
12.6.2 Reflectivity 769
Contents xvii12.6.3 Transmissivity 771
12.6.4 Special Considerations 771
12.7 Kirchhoff’s Law 776
12.8 The Gray Surface 778
12.9 Environmental Radiation 784
12.9.1 Solar Radiation 785
12.9.2 The Atmospheric Radiation Balance 787
12.9.3 Terrestrial Solar Irradiation 789
12.10 Summary 792
References 796
Problems 796
CHAPTER 13 Radiation Exchange Between Surfaces 827
13.1 The View Factor 828
13.1.1 The View Factor Integral 828
13.1.2 View Factor Relations 829
13.2 Blackbody Radiation Exchange 838
13.3 Radiation Exchange Between Opaque, Diffuse, Gray Surfaces in
an Enclosure 842
13.3.1 Net Radiation Exchange at a Surface 843
13.3.2 Radiation Exchange Between Surfaces 844
13.3.3 The Two-Surface Enclosure 850
13.3.4 Radiation Shields 852
13.3.5 The Reradiating Surface 854
13.4 Multimode Heat Transfer 859
13.5 Implications of the Simplifying Assumptions 862
13.6 Radiation Exchange with Participating Media 862
13.6.1 Volumetric Absorption 862
13.6.2 Gaseous Emission and Absorption 863
13.7 Summary 867
References 868
Problems 869
APPENDIX A Thermophysical Properties of Matter 897
APPENDIX B Mathematical Relations and Functions 927
APPENDIX C Thermal Conditions Associated with Uniform Energy
Generation in One-Dimensional, Steady-State Systems 933
APPENDIX D The Gauss–Seidel Method 939
xviii ContentsAPPENDIX E The Convection Transfer Equations 941
E.1 Conservation of Mass 942
E.2 Newton’s Second Law of Motion 942
E.3 Conservation of Energy 943
APPENDIX F Boundary Layer Equations for Turbulent Flow 945
APPENDIX G An Integral Laminar Boundary Layer Solution for
Parallel Flow over a Flat Plate 949
Index 95
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