Table of contents:
1. Heat Conduction Fundamentals --
2. Orthogonal Functions, Boundary Value Problems, and the Fourier Series --
3. Separation of Variables in the Rectangular Coordinate System --
4. Separation of Variables in the Cylindrical Coordinate System --
5. Separation of Variables in the Spherical Coordinate System --
6. Solution of the Heat Equation for Semi-Infinite and Infinite Domains --
7. Use of Duhamel's Theorem --
8. Use of Green's Function for Solution of Heat Conduction Problems --
9. Use of the Laplace Transform --
10. One-Dimensional Composite Medium --
11. Moving Heat Source Problems --
12. Phase-Change Problems --
13. Approximate Analytic Methods --
14. Integral Transform Technique --
15. Heat Conduction in Anisotropic Solids --
16. Introduction to Microscale Heat Conduction. 1. Heat Conduction Fundamentals --
1.1. The Heat Flux --
1.2. Thermal Conductivity --
1.3. Differential Equation of Heat Conduction --
1.4. Fourier's Law and the Heat Equation in Cylindrical and Spherical Coordinate Systems --
1.5. General Boundary Conditions and Initial Condition for the Heat Equation --
1.6. Nondimensional Analysis of the Heat Conduction Equation --
1.7. Heat Conduction Equation for Anisotropic Medium --
1.8. Lumped and Partially Lumped Formulation --
2. Orthogonal Functions, Boundary Value Problems, and the Fourier Series --
2.1. Orthogonal Functions --
2.2. Boundary Value Problems --
2.3. The Fourier Series --
2.4. Computation of Eigenvalues --
2.5. Fourier Integrals --
3. Separation of Variables in the Rectangular Coordinate System --
3.1. Basic Concepts in the Separation of Variables Method --
3.2. Generalization to Multidimensional Problems --
3.3. Solution of Multidimensional Homogenous Problems --
3.4. Multidimensional Nonhomogeneous Problems: Method of Superposition --
3.5. Product Solution --
3.6. Capstone Problem --
4. Separation of Variables in the Cylindrical Coordinate System --
4.1. Separation of Heat Conduction Equation in the Cylindrical Coordinate System --
4.2. Solution of Steady-State Problems --
4.3. Solution of Transient Problems --
4.4. Capstone Problem --
5. Separation of Variables in the Spherical Coordinate System --
5.1. Separation of Heat Conduction Equation in the Spherical Coordinate System --
5.2. Solution of Steady-State Problems --
5.3. Solution of Transient Problems --
5.4. Capstone Problem --
6. Solution of the Heat Equation for Semi-Infinite and Infinite Domains --
6.1. One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System --
6.2. Multidimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System --
6.3. One-Dimensional Homogeneous Problems in An Infinite Medium for the Cartesian Coordinate System --
6.4. One-Dimensional homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System --
6.5. Two-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System --
6.6. One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Spherical Coordinate System --
7. Use of Duhamel's Theorem --
7.1. Development of Duhamel's Theorem for Continuous Time-Dependent Boundary Conditions --
7.2. Treatment of Discontinuities --
7.3. General Statement of Duhamel's Theorem --
7.4. Applications of Duhamel's Theorem --
7.5. Applications of Duhamel's Theorem for Internal Energy Generation --
8. Use of Green's Function for Solution of Heat Conduction Problems --
8.1. Green's Function Approach for Solving Nonhomogeneous Transient Heat Conduction --
8.2. Determination of Green's Functions --
8.3. Representation of Point, Line, and Surface Heat Sources with Delta Functions --
8.4. Applications of Green's Function in the Rectangular Coordinate System --
8.5. Applications of Green's Function in the Cylindrical Coordinate System --
8.6. Applications of Green's Function in the Spherical Coordinate System --
8.7. Products of Green's Functions --
9. Use of the Laplace Transform --
9.1. Definition of Laplace Transformation --
9.2. Properties of Laplace Transform --
9.3. Inversion of Laplace Transform Using the Inversion Tables --
9.4. Application of the Laplace Transform in the Solution of Time-Dependent Heat Conduction Problems --
9.5. Approximations for Small Times --
10. One-Dimensional Composite Medium --
10.1. Mathematical Formulation of One-Dimensional Transient Heat Conduction in a Composite Medium --
10.2. Transformation of Nonhomogeneous Boundary Conditions into Homogeneous Ones --
10.3. Orthogonal Expansion Technique for Solving M-Layer Homogeneous Problems --
10.4. Determination of Eigenfunctions and Eigenvalues --
10.5. Applications of Orthogonal Expansion Technique --
10.6. Green's Function Approach for Solving Nonhomogeneous Problems --
10.7. Use of Laplace Transform for Solving Semi-Infinite and Infinite Medium Problems --
11. Moving Heat Source Problems --
11.1. Mathematical Modeling of Moving Heat Source Problems --
11.2. One-Dimensional Quasi-Stationary Plane Heat Source Problem --
11.3. Two-Dimensional Quasi-Stationary Line Heat Source Problem --
11.4. Two-Dimensional Quasi-Stationary Ring Heat Source Problem --
12. Phase-Change Problems --
12.1. Mathematical Formulation of Phase-Change Problems --
12.2. Exact Solution of Phase-Change Problems --
12.3. Integral Method of Solution of Phase-Change Problems --
12.4. Variable Time Step Method for Solving Phase-Change Problems: A Numerical Solution --
12.5. Enthalpy Method for Solution of Phase-Change Problems: A Numerical Solution --
13. Approximate Analytic Methods --
13.1. Integral Method: Basic Concepts --
13.2. Integral Method: Application to Linear Transient Heat Conduction in a Semi-Infinite Medium --
13.3. Integral Method: Application to Nonlinear Transient Heat Conduction --
13.4. Integral Method: Application to a Finite Region --
13.5. Approximate Analytic Methods of Residuals --
13.6. The Galerkin Method --
13.7. Partial Integration --
13.8. Application to Transient Problems --
14. Integral Transform Technique --
14.1. Use of Integral Transform in the Solution of Heat Conduction Problems --
14.2. Applications in the Rectangular Coordinate System --
14.3. Applications in the Cylindrical Coordinate System --
14.4. Applications in the Spherical Coordinate System --
14.5. Applications in the Solution of Steady-state problems --
15. Heat Conduction in Anisotropic Solids --
15.1. Heat Flux for Anisotropic Solids --
15.2. Heat Conduction Equation for Anisotropic Solids --
15.3. Boundary Conditions --
15.4. Thermal Resistivity Coefficients --
15.5. Determination of Principal Conductivities and Principal Axes --
15.6. Conductivity Matrix for Crystal Systems --
15.7. Transformation of Heat Conduction Equation for Orthotropic Medium --
15.8. Some Special Cases --
15.9. Heat Conduction in an Orthotropic Medium --
15.10. Multidimensional Heat Conduction in an Anisotropic Medium --
16. Introduction to Microscale Heat Conduction --
16.1. Microstructure and Relevant Length Scales --
16.2. Physics of Energy Carriers --
16.3. Energy Storage and Transport --
16.4. Limitations of Fourier's Law and the First Regime of Microscale Heat Transfer --
16.5. Solutions and Approximations for the First Regime of Microscale Heat Transfer --
16.6. Second and Third Regimes of Microscale Heat Transfer --
16.7. Summary Remarks --
Appendix I. Physical Properties --
Appendix II. Roots of Transcendental Equations --
Appendix III. Error Functions --
Appendix IV. Bessel Functions --
Appendix V. Numerical Values of Legendre Polynomials of the First Kind --
Appendix VI. Properties of Delta Functions.

Summary:
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.