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 laser-based diagnostic techniques and general laser-material 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 ÖziŞik 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.

• Preface xiiiPreface to Second Edition xvii1 Heat Conduction Fundamentals 11-1 The Heat Flux 21-2 Thermal Conductivity 41-3 Differential Equation of Heat Conduction 61-4 Fourier’s Law and the Heat Equation in Cylindrical and Spherical Coordinate Systems 141-5 General Boundary Conditions and Initial Condition for the Heat Equation 161-6 Nondimensional Analysis of the Heat Conduction Equation 251-7 Heat Conduction Equation for Anisotropic Medium 271-8 Lumped and Partially Lumped Formulation 29References 36Problems 372 Orthogonal Functions, Boundary Value Problems, and the Fourier Series 402-1 Orthogonal Functions 402-2 Boundary Value Problems 412-3 The Fourier Series 602-4 Computation of Eigenvalues 632-5 Fourier Integrals 67References 73Problems 733 Separation of Variables in the Rectangular Coordinate System 753-1 Basic Concepts in the Separation of Variables Method 753-2 Generalization to Multidimensional Problems 853-3 Solution of Multidimensional Homogenous Problems 863-4 Multidimensional Nonhomogeneous Problems: Method of Superposition 983-5 Product Solution 1123-6 Capstone Problem 116References 123Problems 1244 Separation of Variables in the Cylindrical Coordinate System 1284-1 Separation of Heat Conduction Equation in the Cylindrical Coordinate System 1284-2 Solution of Steady-State Problems 1314-3 Solution of Transient Problems 1514-4 Capstone Problem 167References 179Problems 1795 Separation of Variables in the Spherical Coordinate System 1835-1 Separation of Heat Conduction Equation in the Spherical Coordinate System 1835-2 Solution of Steady-State Problems 1885-3 Solution of Transient Problems 1945-4 Capstone Problem 221References 233Problems 233Notes 2356 Solution of the Heat Equation for Semi-Infinite and Infinite Domains 2366-1 One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System 2366-2 Multidimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System 2476-3 One-Dimensional Homogeneous Problems in An Infinite Medium for the Cartesian Coordinate System 2556-4 One-Dimensional homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System 2606-5 Two-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System 2656-6 One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Spherical Coordinate System 268References 271Problems 2717 Use of Duhamel’s Theorem 2737-1 Development of Duhamel’s Theorem for Continuous Time-Dependent Boundary Conditions 2737-2 Treatment of Discontinuities 2767-3 General Statement of Duhamel’s Theorem 2787-4 Applications of Duhamel’s Theorem 2817-5 Applications of Duhamel’s Theorem for Internal Energy Generation 294References 296Problems 2978 Use of Green’s Function for Solution of Heat Conduction Problems 3008-1 Green’s Function Approach for Solving Nonhomogeneous Transient Heat Conduction 3008-2 Determination of Green’s Functions 3068-3 Representation of Point, Line, and Surface Heat Sources with Delta Functions 3128-4 Applications of Green’s Function in the Rectangular Coordinate System 3178-5 Applications of Green’s Function in the Cylindrical Coordinate System 3298-6 Applications of Green’s Function in the Spherical Coordinate System 3358-7 Products of Green’s Functions 344References 349Problems 3499 Use of the Laplace Transform 3559-1 Definition of Laplace Transformation 3569-2 Properties of Laplace Transform 3579-3 Inversion of Laplace Transform Using the Inversion Tables 3659-4 Application of the Laplace Transform in the Solution of Time-Dependent Heat Conduction Problems 3729-5 Approximations for Small Times 382References 390Problems 39010 One-Dimensional Composite Medium 39310-1 Mathematical Formulation of One-Dimensional Transient Heat Conduction in a Composite Medium 39310-2 Transformation of Nonhomogeneous Boundary Conditions into Homogeneous Ones 39510-3 Orthogonal Expansion Technique for Solving M-Layer Homogeneous Problems 40110-4 Determination of Eigenfunctions and Eigenvalues 40710-5 Applications of Orthogonal Expansion Technique 41010-6 Green’s Function Approach for Solving Nonhomogeneous Problems 41810-7 Use of Laplace Transform for Solving Semi-Infinite and Infinite Medium Problems 424References 429Problems 43011 Moving Heat Source Problems 43311-1 Mathematical Modeling of Moving Heat Source Problems 43411-2 One-Dimensional Quasi-Stationary Plane Heat Source Problem 43911-3 Two-Dimensional Quasi-Stationary Line Heat Source Problem 44311-4 Two-Dimensional Quasi-Stationary Ring Heat Source Problem 445References 449Problems 45012 Phase-Change Problems 45212-1 Mathematical Formulation of Phase-Change Problems 45412-2 Exact Solution of Phase-Change Problems 46112-3 Integral Method of Solution of Phase-Change Problems 47412-4 Variable Time Step Method for Solving Phase-Change Problems: A Numerical Solution 47812-5 Enthalpy Method for Solution of Phase-Change Problems: A Numerical Solution 484References 490Problems 493Note 49513 Approximate Analytic Methods 49613-1 Integral Method: Basic Concepts 49613-2 Integral Method: Application to Linear Transient Heat Conduction in a Semi-Infinite Medium 49813-3 Integral Method: Application to Nonlinear Transient Heat Conduction 50813-4 Integral Method: Application to a Finite Region 51213-5 Approximate Analytic Methods of Residuals 51613-6 The Galerkin Method 52113-7 Partial Integration 53313-8 Application to Transient Problems 538References 542Problems 54414 Integral Transform Technique 54714-1 Use of Integral Transform in the Solution of Heat Conduction Problems 54814-2 Applications in the Rectangular Coordinate System 55614-3 Applications in the Cylindrical Coordinate System 57214-4 Applications in the Spherical Coordinate System 58914-5 Applications in the Solution of Steady-state problems 599References 602Problems 603Notes 60715 Heat Conduction in Anisotropic Solids 61415-1 Heat Flux for Anisotropic Solids 61515-2 Heat Conduction Equation for Anisotropic Solids 61715-3 Boundary Conditions 61815-4 Thermal Resistivity Coefficients 62015-5 Determination of Principal Conductivities and Principal Axes 62115-6 Conductivity Matrix for Crystal Systems 62315-7 Transformation of Heat Conduction Equation for Orthotropic Medium 62415-8 Some Special Cases 62515-9 Heat Conduction in an Orthotropic Medium 62815-10 Multidimensional Heat Conduction in an Anisotropic Medium 637References 645Problems 647Notes 64916 Introduction to Microscale Heat Conduction 65116-1 Microstructure and Relevant Length Scales 65216-2 Physics of Energy Carriers 65616-3 Energy Storage and Transport 66116-4 Limitations of Fourier’s Law and the First Regime of Microscale Heat Transfer 66716-5 Solutions and Approximations for the First Regime of Microscale Heat Transfer 67216-6 Second and Third Regimes of Microscale Heat Transfer 67616-7 Summary Remarks 676References 676Appendixes 679Appendix I Physical Properties 681Table I-1 Physical Properties of Metals 681Table I-2 Physical Properties of Nonmetals 683Table I-3 Physical Properties of Insulating Materials 684Appendix II Roots of Transcendental Equations 685Appendix III Error Functions 688Appendix IV Bessel Functions 691Table IV-1 Numerical Values of Bessel Functions 696Table IV-2 First 10 Roots of Jn(z) = 0, n = 0,1,2,3,4,5 704Table IV-3 First Six Roots of βJ1(β) − cJ0(β) = 0 705Table IV-4 First Five Roots of J0(β)Y0(cβ) − Y0(β)J0(cβ) = 0 706Appendix V Numerical Values of Legendre Polynomials of the First Kind 707Appendix VI Properties of Delta Functions 710Index 713

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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 laser-based diagnostic techniques and general laser-material 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 ÖziŞik 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.

• Preface xiiiPreface to Second Edition xvii1 Heat Conduction Fundamentals 11-1 The Heat Flux 21-2 Thermal Conductivity 41-3 Differential Equation of Heat Conduction 61-4 Fourier’s Law and the Heat Equation in Cylindrical and Spherical Coordinate Systems 141-5 General Boundary Conditions and Initial Condition for the Heat Equation 161-6 Nondimensional Analysis of the Heat Conduction Equation 251-7 Heat Conduction Equation for Anisotropic Medium 271-8 Lumped and Partially Lumped Formulation 29References 36Problems 372 Orthogonal Functions, Boundary Value Problems, and the Fourier Series 402-1 Orthogonal Functions 402-2 Boundary Value Problems 412-3 The Fourier Series 602-4 Computation of Eigenvalues 632-5 Fourier Integrals 67References 73Problems 733 Separation of Variables in the Rectangular Coordinate System 753-1 Basic Concepts in the Separation of Variables Method 753-2 Generalization to Multidimensional Problems 853-3 Solution of Multidimensional Homogenous Problems 863-4 Multidimensional Nonhomogeneous Problems: Method of Superposition 983-5 Product Solution 1123-6 Capstone Problem 116References 123Problems 1244 Separation of Variables in the Cylindrical Coordinate System 1284-1 Separation of Heat Conduction Equation in the Cylindrical Coordinate System 1284-2 Solution of Steady-State Problems 1314-3 Solution of Transient Problems 1514-4 Capstone Problem 167References 179Problems 1795 Separation of Variables in the Spherical Coordinate System 1835-1 Separation of Heat Conduction Equation in the Spherical Coordinate System 1835-2 Solution of Steady-State Problems 1885-3 Solution of Transient Problems 1945-4 Capstone Problem 221References 233Problems 233Notes 2356 Solution of the Heat Equation for Semi-Infinite and Infinite Domains 2366-1 One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System 2366-2 Multidimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System 2476-3 One-Dimensional Homogeneous Problems in An Infinite Medium for the Cartesian Coordinate System 2556-4 One-Dimensional homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System 2606-5 Two-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System 2656-6 One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Spherical Coordinate System 268References 271Problems 2717 Use of Duhamel’s Theorem 2737-1 Development of Duhamel’s Theorem for Continuous Time-Dependent Boundary Conditions 2737-2 Treatment of Discontinuities 2767-3 General Statement of Duhamel’s Theorem 2787-4 Applications of Duhamel’s Theorem 2817-5 Applications of Duhamel’s Theorem for Internal Energy Generation 294References 296Problems 2978 Use of Green’s Function for Solution of Heat Conduction Problems 3008-1 Green’s Function Approach for Solving Nonhomogeneous Transient Heat Conduction 3008-2 Determination of Green’s Functions 3068-3 Representation of Point, Line, and Surface Heat Sources with Delta Functions 3128-4 Applications of Green’s Function in the Rectangular Coordinate System 3178-5 Applications of Green’s Function in the Cylindrical Coordinate System 3298-6 Applications of Green’s Function in the Spherical Coordinate System 3358-7 Products of Green’s Functions 344References 349Problems 3499 Use of the Laplace Transform 3559-1 Definition of Laplace Transformation 3569-2 Properties of Laplace Transform 3579-3 Inversion of Laplace Transform Using the Inversion Tables 3659-4 Application of the Laplace Transform in the Solution of Time-Dependent Heat Conduction Problems 3729-5 Approximations for Small Times 382References 390Problems 39010 One-Dimensional Composite Medium 39310-1 Mathematical Formulation of One-Dimensional Transient Heat Conduction in a Composite Medium 39310-2 Transformation of Nonhomogeneous Boundary Conditions into Homogeneous Ones 39510-3 Orthogonal Expansion Technique for Solving M-Layer Homogeneous Problems 40110-4 Determination of Eigenfunctions and Eigenvalues 40710-5 Applications of Orthogonal Expansion Technique 41010-6 Green’s Function Approach for Solving Nonhomogeneous Problems 41810-7 Use of Laplace Transform for Solving Semi-Infinite and Infinite Medium Problems 424References 429Problems 43011 Moving Heat Source Problems 43311-1 Mathematical Modeling of Moving Heat Source Problems 43411-2 One-Dimensional Quasi-Stationary Plane Heat Source Problem 43911-3 Two-Dimensional Quasi-Stationary Line Heat Source Problem 44311-4 Two-Dimensional Quasi-Stationary Ring Heat Source Problem 445References 449Problems 45012 Phase-Change Problems 45212-1 Mathematical Formulation of Phase-Change Problems 45412-2 Exact Solution of Phase-Change Problems 46112-3 Integral Method of Solution of Phase-Change Problems 47412-4 Variable Time Step Method for Solving Phase-Change Problems: A Numerical Solution 47812-5 Enthalpy Method for Solution of Phase-Change Problems: A Numerical Solution 484References 490Problems 493Note 49513 Approximate Analytic Methods 49613-1 Integral Method: Basic Concepts 49613-2 Integral Method: Application to Linear Transient Heat Conduction in a Semi-Infinite Medium 49813-3 Integral Method: Application to Nonlinear Transient Heat Conduction 50813-4 Integral Method: Application to a Finite Region 51213-5 Approximate Analytic Methods of Residuals 51613-6 The Galerkin Method 52113-7 Partial Integration 53313-8 Application to Transient Problems 538References 542Problems 54414 Integral Transform Technique 54714-1 Use of Integral Transform in the Solution of Heat Conduction Problems 54814-2 Applications in the Rectangular Coordinate System 55614-3 Applications in the Cylindrical Coordinate System 57214-4 Applications in the Spherical Coordinate System 58914-5 Applications in the Solution of Steady-state problems 599References 602Problems 603Notes 60715 Heat Conduction in Anisotropic Solids 61415-1 Heat Flux for Anisotropic Solids 61515-2 Heat Conduction Equation for Anisotropic Solids 61715-3 Boundary Conditions 61815-4 Thermal Resistivity Coefficients 62015-5 Determination of Principal Conductivities and Principal Axes 62115-6 Conductivity Matrix for Crystal Systems 62315-7 Transformation of Heat Conduction Equation for Orthotropic Medium 62415-8 Some Special Cases 62515-9 Heat Conduction in an Orthotropic Medium 62815-10 Multidimensional Heat Conduction in an Anisotropic Medium 637References 645Problems 647Notes 64916 Introduction to Microscale Heat Conduction 65116-1 Microstructure and Relevant Length Scales 65216-2 Physics of Energy Carriers 65616-3 Energy Storage and Transport 66116-4 Limitations of Fourier’s Law and the First Regime of Microscale Heat Transfer 66716-5 Solutions and Approximations for the First Regime of Microscale Heat Transfer 67216-6 Second and Third Regimes of Microscale Heat Transfer 67616-7 Summary Remarks 676References 676Appendixes 679Appendix I Physical Properties 681Table I-1 Physical Properties of Metals 681Table I-2 Physical Properties of Nonmetals 683Table I-3 Physical Properties of Insulating Materials 684Appendix II Roots of Transcendental Equations 685Appendix III Error Functions 688Appendix IV Bessel Functions 691Table IV-1 Numerical Values of Bessel Functions 696Table IV-2 First 10 Roots of Jn(z) = 0, n = 0,1,2,3,4,5 704Table IV-3 First Six Roots of βJ1(β) − cJ0(β) = 0 705Table IV-4 First Five Roots of J0(β)Y0(cβ) − Y0(β)J0(cβ) = 0 706Appendix V Numerical Values of Legendre Polynomials of the First Kind 707Appendix VI Properties of Delta Functions 710Index 713

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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 laser-based diagnostic techniques and general laser-material 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 ÖziŞik 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.

• Preface xiiiPreface to Second Edition xvii1 Heat Conduction Fundamentals 11-1 The Heat Flux 21-2 Thermal Conductivity 41-3 Differential Equation of Heat Conduction 61-4 Fourier’s Law and the Heat Equation in Cylindrical and Spherical Coordinate Systems 141-5 General Boundary Conditions and Initial Condition for the Heat Equation 161-6 Nondimensional Analysis of the Heat Conduction Equation 251-7 Heat Conduction Equation for Anisotropic Medium 271-8 Lumped and Partially Lumped Formulation 29References 36Problems 372 Orthogonal Functions, Boundary Value Problems, and the Fourier Series 402-1 Orthogonal Functions 402-2 Boundary Value Problems 412-3 The Fourier Series 602-4 Computation of Eigenvalues 632-5 Fourier Integrals 67References 73Problems 733 Separation of Variables in the Rectangular Coordinate System 753-1 Basic Concepts in the Separation of Variables Method 753-2 Generalization to Multidimensional Problems 853-3 Solution of Multidimensional Homogenous Problems 863-4 Multidimensional Nonhomogeneous Problems: Method of Superposition 983-5 Product Solution 1123-6 Capstone Problem 116References 123Problems 1244 Separation of Variables in the Cylindrical Coordinate System 1284-1 Separation of Heat Conduction Equation in the Cylindrical Coordinate System 1284-2 Solution of Steady-State Problems 1314-3 Solution of Transient Problems 1514-4 Capstone Problem 167References 179Problems 1795 Separation of Variables in the Spherical Coordinate System 1835-1 Separation of Heat Conduction Equation in the Spherical Coordinate System 1835-2 Solution of Steady-State Problems 1885-3 Solution of Transient Problems 1945-4 Capstone Problem 221References 233Problems 233Notes 2356 Solution of the Heat Equation for Semi-Infinite and Infinite Domains 2366-1 One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System 2366-2 Multidimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System 2476-3 One-Dimensional Homogeneous Problems in An Infinite Medium for the Cartesian Coordinate System 2556-4 One-Dimensional homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System 2606-5 Two-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System 2656-6 One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Spherical Coordinate System 268References 271Problems 2717 Use of Duhamel’s Theorem 2737-1 Development of Duhamel’s Theorem for Continuous Time-Dependent Boundary Conditions 2737-2 Treatment of Discontinuities 2767-3 General Statement of Duhamel’s Theorem 2787-4 Applications of Duhamel’s Theorem 2817-5 Applications of Duhamel’s Theorem for Internal Energy Generation 294References 296Problems 2978 Use of Green’s Function for Solution of Heat Conduction Problems 3008-1 Green’s Function Approach for Solving Nonhomogeneous Transient Heat Conduction 3008-2 Determination of Green’s Functions 3068-3 Representation of Point, Line, and Surface Heat Sources with Delta Functions 3128-4 Applications of Green’s Function in the Rectangular Coordinate System 3178-5 Applications of Green’s Function in the Cylindrical Coordinate System 3298-6 Applications of Green’s Function in the Spherical Coordinate System 3358-7 Products of Green’s Functions 344References 349Problems 3499 Use of the Laplace Transform 3559-1 Definition of Laplace Transformation 3569-2 Properties of Laplace Transform 3579-3 Inversion of Laplace Transform Using the Inversion Tables 3659-4 Application of the Laplace Transform in the Solution of Time-Dependent Heat Conduction Problems 3729-5 Approximations for Small Times 382References 390Problems 39010 One-Dimensional Composite Medium 39310-1 Mathematical Formulation of One-Dimensional Transient Heat Conduction in a Composite Medium 39310-2 Transformation of Nonhomogeneous Boundary Conditions into Homogeneous Ones 39510-3 Orthogonal Expansion Technique for Solving M-Layer Homogeneous Problems 40110-4 Determination of Eigenfunctions and Eigenvalues 40710-5 Applications of Orthogonal Expansion Technique 41010-6 Green’s Function Approach for Solving Nonhomogeneous Problems 41810-7 Use of Laplace Transform for Solving Semi-Infinite and Infinite Medium Problems 424References 429Problems 43011 Moving Heat Source Problems 43311-1 Mathematical Modeling of Moving Heat Source Problems 43411-2 One-Dimensional Quasi-Stationary Plane Heat Source Problem 43911-3 Two-Dimensional Quasi-Stationary Line Heat Source Problem 44311-4 Two-Dimensional Quasi-Stationary Ring Heat Source Problem 445References 449Problems 45012 Phase-Change Problems 45212-1 Mathematical Formulation of Phase-Change Problems 45412-2 Exact Solution of Phase-Change Problems 46112-3 Integral Method of Solution of Phase-Change Problems 47412-4 Variable Time Step Method for Solving Phase-Change Problems: A Numerical Solution 47812-5 Enthalpy Method for Solution of Phase-Change Problems: A Numerical Solution 484References 490Problems 493Note 49513 Approximate Analytic Methods 49613-1 Integral Method: Basic Concepts 49613-2 Integral Method: Application to Linear Transient Heat Conduction in a Semi-Infinite Medium 49813-3 Integral Method: Application to Nonlinear Transient Heat Conduction 50813-4 Integral Method: Application to a Finite Region 51213-5 Approximate Analytic Methods of Residuals 51613-6 The Galerkin Method 52113-7 Partial Integration 53313-8 Application to Transient Problems 538References 542Problems 54414 Integral Transform Technique 54714-1 Use of Integral Transform in the Solution of Heat Conduction Problems 54814-2 Applications in the Rectangular Coordinate System 55614-3 Applications in the Cylindrical Coordinate System 57214-4 Applications in the Spherical Coordinate System 58914-5 Applications in the Solution of Steady-state problems 599References 602Problems 603Notes 60715 Heat Conduction in Anisotropic Solids 61415-1 Heat Flux for Anisotropic Solids 61515-2 Heat Conduction Equation for Anisotropic Solids 61715-3 Boundary Conditions 61815-4 Thermal Resistivity Coefficients 62015-5 Determination of Principal Conductivities and Principal Axes 62115-6 Conductivity Matrix for Crystal Systems 62315-7 Transformation of Heat Conduction Equation for Orthotropic Medium 62415-8 Some Special Cases 62515-9 Heat Conduction in an Orthotropic Medium 62815-10 Multidimensional Heat Conduction in an Anisotropic Medium 637References 645Problems 647Notes 64916 Introduction to Microscale Heat Conduction 65116-1 Microstructure and Relevant Length Scales 65216-2 Physics of Energy Carriers 65616-3 Energy Storage and Transport 66116-4 Limitations of Fourier’s Law and the First Regime of Microscale Heat Transfer 66716-5 Solutions and Approximations for the First Regime of Microscale Heat Transfer 67216-6 Second and Third Regimes of Microscale Heat Transfer 67616-7 Summary Remarks 676References 676Appendixes 679Appendix I Physical Properties 681Table I-1 Physical Properties of Metals 681Table I-2 Physical Properties of Nonmetals 683Table I-3 Physical Properties of Insulating Materials 684Appendix II Roots of Transcendental Equations 685Appendix III Error Functions 688Appendix IV Bessel Functions 691Table IV-1 Numerical Values of Bessel Functions 696Table IV-2 First 10 Roots of Jn(z) = 0, n = 0,1,2,3,4,5 704Table IV-3 First Six Roots of βJ1(β) − cJ0(β) = 0 705Table IV-4 First Five Roots of J0(β)Y0(cβ) − Y0(β)J0(cβ) = 0 706Appendix V Numerical Values of Legendre Polynomials of the First Kind 707Appendix VI Properties of Delta Functions 710Index 713

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