This book supplies the long awaited revision of the bestseller on heat conduction, replacing some of the coverage of numerical methods with content on micro- and nano-scale heat transfer. Extensive problems, cases, and examples have been thoroughly updated, and a solutions manual is available.
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