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The long-awaited 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.
Preface xiii
Preface to Second Edition xvii
1 Heat Conduction Fundamentals 1
1-1 The Heat Flux, 2
1-2 Thermal Conductivity, 4
1-3 Differential Equation of Heat Conduction, 6
1-4 Fourier’s Law and the Heat Equation in Cylindrical and Spherical Coordinate Systems, 14
1-5 General Boundary Conditions and Initial Condition for the Heat Equation, 16
1-6 Nondimensional Analysis of the Heat Conduction Equation, 25
1-7 Heat Conduction Equation for Anisotropic Medium, 27
1-8 Lumped and Partially Lumped Formulation, 29
References, 36
Problems, 37
2 Orthogonal Functions, Boundary Value Problems, and the Fourier Series 40
2-1 Orthogonal Functions, 40
2-2 Boundary Value Problems, 41
2-3 The Fourier Series, 60
2-4 Computation of Eigenvalues, 63
2-5 Fourier Integrals, 67
References, 73
Problems, 73
3 Separation of Variables in the Rectangular Coordinate System 75
3-1 Basic Concepts in the Separation of Variables Method, 75
3-2 Generalization to Multidimensional Problems, 85
3-3 Solution of Multidimensional Homogenous Problems, 86
3-4 Multidimensional Nonhomogeneous Problems: Method of Superposition, 98
3-5 Product Solution, 112
3-6 Capstone Problem, 116
References, 123
Problems, 124
4 Separation of Variables in the Cylindrical Coordinate System 128
4-1 Separation of Heat Conduction Equation in the Cylindrical Coordinate System, 128
4-2 Solution of Steady-State Problems, 131
4-3 Solution of Transient Problems, 151
4-4 Capstone Problem, 167
References, 179
Problems, 179
5 Separation of Variables in the Spherical Coordinate System 183
5-1 Separation of Heat Conduction Equation in the Spherical Coordinate System, 183
5-2 Solution of Steady-State Problems, 188
5-3 Solution of Transient Problems, 194
5-4 Capstone Problem, 221
References, 233
Problems, 233
Notes, 235
6 Solution of the Heat Equation for Semi-Infinite and Infinite Domains 236
6-1 One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System, 236
6-2 Multidimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System, 247
6-3 One-Dimensional Homogeneous Problems in An Infinite Medium for the Cartesian Coordinate System, 255
6-4 One-Dimensional homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System, 260
6-5 Two-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System, 265
6-6 One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Spherical Coordinate System, 268
References, 271
Problems, 271
7 Use of Duhamel’s Theorem 273
7-1 Development of Duhamel’s Theorem for Continuous Time-Dependent Boundary Conditions, 273
7-2 Treatment of Discontinuities, 276
7-3 General Statement of Duhamel’s Theorem, 278
7-4 Applications of Duhamel’s Theorem, 281
7-5 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
8-1 Green’s Function Approach for Solving Nonhomogeneous Transient Heat Conduction, 300
8-2 Determination of Green’s Functions, 306
8-3 Representation of Point, Line, and Surface Heat Sources with Delta Functions, 312
8-4 Applications of Green’s Function in the Rectangular Coordinate System, 317
8-5 Applications of Green’s Function in the Cylindrical Coordinate System, 329
8-6 Applications of Green’s Function in the Spherical Coordinate System, 335
8-7 Products of Green’s Functions, 344
References, 349
Problems, 349
9 Use of the Laplace Transform 355
9-1 Definition of Laplace Transformation, 356
9-2 Properties of Laplace Transform, 357
9-3 Inversion of Laplace Transform Using the Inversion Tables, 365
9-4 Application of the Laplace Transform in the Solution of Time-Dependent Heat Conduction Problems, 372
9-5 Approximations for Small Times, 382
References, 390
Problems, 390
10 One-Dimensional Composite Medium 393
10-1 Mathematical Formulation of One-Dimensional Transient Heat Conduction in a Composite Medium, 393
10-2 Transformation of Nonhomogeneous Boundary Conditions into Homogeneous Ones, 395
10-3 Orthogonal Expansion Technique for Solving M-Layer Homogeneous Problems, 401
10-4 Determination of Eigenfunctions and Eigenvalues, 407
10-5 Applications of Orthogonal Expansion Technique, 410
10-6 Green’s Function Approach for Solving Nonhomogeneous Problems, 418
10-7 Use of Laplace Transform for Solving Semi-Infinite and Infinite Medium Problems, 424
References, 429
Problems, 430
11 Moving Heat Source Problems 433
11-1 Mathematical Modeling of Moving Heat Source Problems, 434
11-2 One-Dimensional Quasi-Stationary Plane Heat Source Problem, 439
11-3 Two-Dimensional Quasi-Stationary Line Heat Source Problem, 443
11-4 Two-Dimensional Quasi-Stationary Ring Heat Source Problem, 445
References, 449
Problems, 450
12 Phase-Change Problems 452
12-1 Mathematical Formulation of Phase-Change Problems, 454
12-2 Exact Solution of Phase-Change Problems, 461
12-3 Integral Method of Solution of Phase-Change Problems, 474
12-4 Variable Time Step Method for Solving Phase-Change Problems: A Numerical Solution, 478
12-5 Enthalpy Method for Solution of Phase-Change Problems: A Numerical Solution, 484
References, 490
Problems, 493
Note, 495
13 Approximate Analytic Methods 496
13-1 Integral Method: Basic Concepts, 496
13-2 Integral Method: Application to Linear Transient Heat Conduction in a Semi-Infinite Medium, 498
13-3 Integral Method: Application to Nonlinear Transient Heat Conduction, 508
13-4 Integral Method: Application to a Finite Region, 512
13-5 Approximate Analytic Methods of Residuals, 516
13-6 The Galerkin Method, 521
13-7 Partial Integration, 533
13-8 Application to Transient Problems, 538
References, 542
Problems, 544
14 Integral Transform Technique 547
14-1 Use of Integral Transform in the Solution of Heat Conduction Problems, 548
14-2 Applications in the Rectangular Coordinate System, 556
14-3 Applications in the Cylindrical Coordinate System, 572
14-4 Applications in the Spherical Coordinate System, 589
14-5 Applications in the Solution of Steady-state problems, 599
References, 602
Problems, 603
Notes, 607
15 Heat Conduction in Anisotropic Solids 614
15-1 Heat Flux for Anisotropic Solids, 615
15-2 Heat Conduction Equation for Anisotropic Solids, 617
15-3 Boundary Conditions, 618
15-4 Thermal Resistivity Coefficients, 620
15-5 Determination of Principal Conductivities and Principal Axes, 621
15-6 Conductivity Matrix for Crystal Systems, 623
15-7 Transformation of Heat Conduction Equation for Orthotropic Medium, 624
15-8 Some Special Cases, 625
15-9 Heat Conduction in an Orthotropic Medium, 628
15-10 Multidimensional Heat Conduction in an Anisotropic Medium, 637
References, 645
Problems, 647
Notes, 649
16 Introduction to Microscale Heat Conduction 651
16-1 Microstructure and Relevant Length Scales, 652
16-2 Physics of Energy Carriers, 656
16-3 Energy Storage and Transport, 661
16-4 Limitations of Fourier’s Law and the First Regime of Microscale Heat Transfer, 667
16-5 Solutions and Approximations for the First Regime of Microscale Heat Transfer, 672
16-6 Second and Third Regimes of Microscale Heat Transfer, 676
16-7 Summary Remarks, 676
References, 676
APPENDIXES 679
Appendix I Physical Properties 681
Table I-1 Physical Properties of Metals, 681
Table I-2 Physical Properties of Nonmetals, 683
Table I-3 Physical Properties of Insulating Materials, 684
Appendix II Roots of Transcendental Equations 685
Appendix III Error Functions 688
Appendix IV Bessel Functions 691
Table IV-1 Numerical Values of Bessel Functions, 696
Table IV-2 First 10 Roots of Jn(z) = 0, n = 0, 1, 2, 3, 4, 5, 704
Table IV-3 First Six Roots of βJ1(β) − cJ0(β) = 0, 705
Table IV-4 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
Overview
The long-awaited 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...