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More About This Textbook
Overview
The longawaited revision of the bestseller on heat conduction
Heat Conduction, Third Edition is an update of the classic text on heat conduction, replacing some of the coverage of numerical methods with content on micro and nanoscale heat transfer. With an emphasis on the mathematics and underlying physics, this new edition has considerable depth and analytical rigor, providing a systematic framework for each solution scheme with attention to boundary conditions and energy conservation. Chapter coverage includes:
In addition, new capstone examples are included in this edition and extensive problems, cases, and examples have been thoroughly updated. A solutions manual is also available.
Heat Conduction is appropriate reading for students in mainstream courses of conduction heat transfer, students in mechanical engineering, and engineers in research and design functions throughout industry.
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Meet the Author
David W. Hahn is the Knox T. Millsaps Professor of Mechanical and Aerospace Engineering at the University of Florida, Gainesville. His areas of specialization include both thermal sciences and biomedical engineering, including the development and application of laserbased diagnostic techniques and general lasermaterial interactions.
The late M. Necati Özisik retired as Professor Emeritus of North Carolina State University's Mechanical and Aerospace Engineering Department, where he spent most of his academic career. Professor Özisik dedicated his life to education and research in heat transfer. His outstanding contributions earned him several awards, including the Outstanding Engineering Educator Award from the American Society for Engineering Education in 1992.
Table of Contents
Preface xiii
Preface to Second Edition xvii
1 Heat Conduction Fundamentals 1
11 The Heat Flux, 2
12 Thermal Conductivity, 4
13 Differential Equation of Heat Conduction, 6
14 Fourier’s Law and the Heat Equation in Cylindrical and Spherical Coordinate Systems, 14
15 General Boundary Conditions and Initial Condition for the Heat Equation, 16
16 Nondimensional Analysis of the Heat Conduction Equation, 25
17 Heat Conduction Equation for Anisotropic Medium, 27
18 Lumped and Partially Lumped Formulation, 29
References, 36
Problems, 37
2 Orthogonal Functions, Boundary Value Problems, and the Fourier Series 40
21 Orthogonal Functions, 40
22 Boundary Value Problems, 41
23 The Fourier Series, 60
24 Computation of Eigenvalues, 63
25 Fourier Integrals, 67
References, 73
Problems, 73
3 Separation of Variables in the Rectangular Coordinate System 75
31 Basic Concepts in the Separation of Variables Method, 75
32 Generalization to Multidimensional Problems, 85
33 Solution of Multidimensional Homogenous Problems, 86
34 Multidimensional Nonhomogeneous Problems: Method of Superposition, 98
35 Product Solution, 112
36 Capstone Problem, 116
References, 123
Problems, 124
4 Separation of Variables in the Cylindrical Coordinate System 128
41 Separation of Heat Conduction Equation in the Cylindrical Coordinate System, 128
42 Solution of SteadyState Problems, 131
43 Solution of Transient Problems, 151
44 Capstone Problem, 167
References, 179
Problems, 179
5 Separation of Variables in the Spherical Coordinate System 183
51 Separation of Heat Conduction Equation in the Spherical Coordinate System, 183
52 Solution of SteadyState Problems, 188
53 Solution of Transient Problems, 194
54 Capstone Problem, 221
References, 233
Problems, 233
Notes, 235
6 Solution of the Heat Equation for SemiInfinite and Infinite Domains 236
61 OneDimensional Homogeneous Problems in a SemiInfinite Medium for the Cartesian Coordinate System, 236
62 Multidimensional Homogeneous Problems in a SemiInfinite Medium for the Cartesian Coordinate System, 247
63 OneDimensional Homogeneous Problems in An Infinite Medium for the Cartesian Coordinate System, 255
64 OneDimensional homogeneous Problems in a SemiInfinite Medium for the Cylindrical Coordinate System, 260
65 TwoDimensional Homogeneous Problems in a SemiInfinite Medium for the Cylindrical Coordinate System, 265
66 OneDimensional Homogeneous Problems in a SemiInfinite Medium for the Spherical Coordinate System, 268
References, 271
Problems, 271
7 Use of Duhamel’s Theorem 273
71 Development of Duhamel’s Theorem for Continuous TimeDependent Boundary Conditions, 273
72 Treatment of Discontinuities, 276
73 General Statement of Duhamel’s Theorem, 278
74 Applications of Duhamel’s Theorem, 281
75 Applications of Duhamel’s Theorem for Internal Energy Generation, 294
References, 296
Problems, 297
8 Use of Green’s Function for Solution of Heat Conduction Problems 300
81 Green’s Function Approach for Solving Nonhomogeneous Transient Heat Conduction, 300
82 Determination of Green’s Functions, 306
83 Representation of Point, Line, and Surface Heat Sources with Delta Functions, 312
84 Applications of Green’s Function in the Rectangular Coordinate System, 317
85 Applications of Green’s Function in the Cylindrical Coordinate System, 329
86 Applications of Green’s Function in the Spherical Coordinate System, 335
87 Products of Green’s Functions, 344
References, 349
Problems, 349
9 Use of the Laplace Transform 355
91 Definition of Laplace Transformation, 356
92 Properties of Laplace Transform, 357
93 Inversion of Laplace Transform Using the Inversion Tables, 365
94 Application of the Laplace Transform in the Solution of TimeDependent Heat Conduction Problems, 372
95 Approximations for Small Times, 382
References, 390
Problems, 390
10 OneDimensional Composite Medium 393
101 Mathematical Formulation of OneDimensional Transient Heat Conduction in a Composite Medium, 393
102 Transformation of Nonhomogeneous Boundary Conditions into Homogeneous Ones, 395
103 Orthogonal Expansion Technique for Solving MLayer Homogeneous Problems, 401
104 Determination of Eigenfunctions and Eigenvalues, 407
105 Applications of Orthogonal Expansion Technique, 410
106 Green’s Function Approach for Solving Nonhomogeneous Problems, 418
107 Use of Laplace Transform for Solving SemiInfinite and Infinite Medium Problems, 424
References, 429
Problems, 430
11 Moving Heat Source Problems 433
111 Mathematical Modeling of Moving Heat Source Problems, 434
112 OneDimensional QuasiStationary Plane Heat Source Problem, 439
113 TwoDimensional QuasiStationary Line Heat Source Problem, 443
114 TwoDimensional QuasiStationary Ring Heat Source Problem, 445
References, 449
Problems, 450
12 PhaseChange Problems 452
121 Mathematical Formulation of PhaseChange Problems, 454
122 Exact Solution of PhaseChange Problems, 461
123 Integral Method of Solution of PhaseChange Problems, 474
124 Variable Time Step Method for Solving PhaseChange Problems: A Numerical Solution, 478
125 Enthalpy Method for Solution of PhaseChange Problems: A Numerical Solution, 484
References, 490
Problems, 493
Note, 495
13 Approximate Analytic Methods 496
131 Integral Method: Basic Concepts, 496
132 Integral Method: Application to Linear Transient Heat Conduction in a SemiInfinite Medium, 498
133 Integral Method: Application to Nonlinear Transient Heat Conduction, 508
134 Integral Method: Application to a Finite Region, 512
135 Approximate Analytic Methods of Residuals, 516
136 The Galerkin Method, 521
137 Partial Integration, 533
138 Application to Transient Problems, 538
References, 542
Problems, 544
14 Integral Transform Technique 547
141 Use of Integral Transform in the Solution of Heat Conduction Problems, 548
142 Applications in the Rectangular Coordinate System, 556
143 Applications in the Cylindrical Coordinate System, 572
144 Applications in the Spherical Coordinate System, 589
145 Applications in the Solution of Steadystate problems, 599
References, 602
Problems, 603
Notes, 607
15 Heat Conduction in Anisotropic Solids 614
151 Heat Flux for Anisotropic Solids, 615
152 Heat Conduction Equation for Anisotropic Solids, 617
153 Boundary Conditions, 618
154 Thermal Resistivity Coefficients, 620
155 Determination of Principal Conductivities and Principal Axes, 621
156 Conductivity Matrix for Crystal Systems, 623
157 Transformation of Heat Conduction Equation for Orthotropic Medium, 624
158 Some Special Cases, 625
159 Heat Conduction in an Orthotropic Medium, 628
1510 Multidimensional Heat Conduction in an Anisotropic Medium, 637
References, 645
Problems, 647
Notes, 649
16 Introduction to Microscale Heat Conduction 651
161 Microstructure and Relevant Length Scales, 652
162 Physics of Energy Carriers, 656
163 Energy Storage and Transport, 661
164 Limitations of Fourier’s Law and the First Regime of Microscale Heat Transfer, 667
165 Solutions and Approximations for the First Regime of Microscale Heat Transfer, 672
166 Second and Third Regimes of Microscale Heat Transfer, 676
167 Summary Remarks, 676
References, 676
APPENDIXES 679
Appendix I Physical Properties 681
Table I1 Physical Properties of Metals, 681
Table I2 Physical Properties of Nonmetals, 683
Table I3 Physical Properties of Insulating Materials, 684
Appendix II Roots of Transcendental Equations 685
Appendix III Error Functions 688
Appendix IV Bessel Functions 691
Table IV1 Numerical Values of Bessel Functions, 696
Table IV2 First 10 Roots of Jn(z) = 0, n = 0, 1, 2, 3, 4, 5, 704
Table IV3 First Six Roots of βJ1(β) − cJ0(β) = 0, 705
Table IV4 First Five Roots of J0(β)Y0(cβ) − Y0(β)J0(cβ) = 0, 706
Appendix V Numerical Values of Legendre Polynomials of the
First Kind 707
Appendix VI Properties of Delta Functions 710
Index 713