| |

| |

Preface | |

| |

| |

Preface to Second Edition | |

| |

| |

| |

Heat Conduction Fundamentals | |

| |

| |

| |

The Heat Flux | |

| |

| |

| |

Thermal Conductivity | |

| |

| |

| |

Differential Equation of Heat Conduction | |

| |

| |

| |

Fourier's Law and the Heat Equation in Cylindrical and Spherical Coordinate Systems | |

| |

| |

| |

General Boundary Conditions and Initial Condition for the Heat Equation | |

| |

| |

| |

Nondimensional Analysis of the Heat Conduction Equation | |

| |

| |

| |

Heat Conduction Equation for Anisotropic Medium | |

| |

| |

| |

Lumped and Partially Lumped Formulation | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Orthogonal Functions, Boundary Value Problems, and the Fourier Series | |

| |

| |

| |

Orthogonal Functions | |

| |

| |

| |

Boundary Value, Problems | |

| |

| |

| |

The Fourier Series | |

| |

| |

| |

Computation of Eigenvalues | |

| |

| |

| |

Fourier Integrals | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Separation of Variables in the Rectangular Coordinate System | |

| |

| |

| |

Basic Concepts in the Separation of Variables Method | |

| |

| |

| |

Generalization to Multidimensional Problems | |

| |

| |

| |

Solution of Multidimensional Homogenous Problems | |

| |

| |

| |

Multidimensional Nonhomogeneous Problems: Method of Superposition | |

| |

| |

| |

Product Solution | |

| |

| |

| |

Capstone Problem | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Separation of Variables in the Cylindrical Coordinate System | |

| |

| |

| |

Separation of Heat Conduction Equation in the Cylindrical Coordinate System | |

| |

| |

| |

Solution of Steady-State Problems | |

| |

| |

| |

Solution of Transient Problems | |

| |

| |

| |

Capstone Problem | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Separation of Variables in the Spherical Coordinate System | |

| |

| |

| |

Separation of Heat Conduction Equation in the Spherical Coordinate System | |

| |

| |

| |

Solution of Steady-State Problems | |

| |

| |

| |

Solution of Transient Problems | |

| |

| |

| |

Capstone Problem | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

Notes | |

| |

| |

| |

Solution of the Heat Equation for Semi-Infinite and Infinite Domains | |

| |

| |

| |

One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System | |

| |

| |

| |

Multidimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System | |

| |

| |

| |

One-Dimensional Homogeneous Problems in an Infinite Medium for the Cartesian Coordinate System | |

| |

| |

| |

One-Dimensional homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System | |

| |

| |

| |

Two-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System | |

| |

| |

| |

One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Spherical Coordinate System | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Use of Duhamel's Theorem | |

| |

| |

| |

Development of Duhamel's Theorem for Continuous Time-Dependent Boundary Conditions | |

| |

| |

| |

Treatment of Discontinuities | |

| |

| |

| |

General Statement of Duhamel's Theorem | |

| |

| |

| |

Applications of Duhamel's Theorem | |

| |

| |

| |

Applications of Duhamel's Theorem for Internal Energy Generation | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Use of Green's Function for Solution of Heat Conduction Problems | |

| |

| |

| |

Green's Function Approach for Solving Nonhomogeneous Transient Heat Conduction | |

| |

| |

| |

Determination of Green's Functions | |

| |

| |

| |

Representation of Point, Line, and Surface Heat Sources with Delta Functions | |

| |

| |

| |

Applications of Green's Function in the Rectangular Coordinate System | |

| |

| |

| |

Applications of Green's Function in the Cylindrical Coordinate System | |

| |

| |

| |

Applications of Green's Function in the Spherical Coordinate System | |

| |

| |

| |

Products of Green's Functions | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Use of the Laplace Transform | |

| |

| |

| |

Definition of Laplace Transformation | |

| |

| |

| |

Properties of Laplace Transform | |

| |

| |

| |

Inversion of Laplace Transform Using the Inversion Tables | |

| |

| |

| |

Application of the Laplace Transform in the Solution of Time-Dependent Heat Conduction Problems | |

| |

| |

| |

Approximations for Small Times | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

One-Dimensional Composite Medium | |

| |

| |

| |

Mathematical Formulation of One-Dimensional Transient Heat Conduction in a Composite Medium | |

| |

| |

| |

Transformation of Nonhomogeneous Boundary Conditions into Homogeneous Ones | |

| |

| |

| |

Orthogonal Expansion Technique for Solving M-Layer Homogeneous Problems | |

| |

| |

| |

Determination of Eigenfunctions and Eigenvalues | |

| |

| |

| |

Applications of Orthogonal Expansion Technique | |

| |

| |

| |

Green's Function Approach for Solving Nonhomogeneous Problems | |

| |

| |

| |

Use of Laplace Transform for Solving Semi-Infinite and Infinite Medium Problems | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Moving Heat Source Problems | |

| |

| |

| |

Mathematical Modeling of Moving Heat Source Problems | |

| |

| |

| |

One-Dimensional Quasi-Stationary Plane Heat Source Problem | |

| |

| |

| |

Two-Dimensional Quasi-Stationary Line Heat Source Problem | |

| |

| |

| |

Two-Dimensional Quasi-Stationary Ring Heat Source Problem | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Phase-Change Problems | |

| |

| |

| |

Mathematical Formulation of Phase-Change Problems | |

| |

| |

| |

Exact Solution of Phase-Change Problems | |

| |

| |

| |

Integral Method of Solution of Phase-Change Problems | |

| |

| |

| |

Variable Time Step Method for Solving Phase-Change Problems: A Numerical Solution | |

| |

| |

| |

Enthalpy Method for Solution of Phase-Change Problems: A Numerical Solution | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

Note | |

| |

| |

| |

Approximate Analytic Methods | |

| |

| |

| |

Integral Method: Basic Concepts | |

| |

| |

| |

Integral Method: Application to Linear Transient Heat Conduction in a Semi-Infinite Medium | |

| |

| |

| |

Integral Method: Application to Nonlinear Transient Heat Conduction | |

| |

| |

| |

Integral Method: Application to a Finite Region | |

| |

| |

| |

Approximate Analytic Methods of Residuals | |

| |

| |

| |

The Galerkin Method | |

| |

| |

| |

Partial Integration | |

| |

| |

| |

Application to Transient Problems | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

| |

Integral Transform Technique | |

| |

| |

| |

Use of Integral Transform in the Solution of Heat Conduction Problems | |

| |

| |

| |

Applications in the Rectangular Coordinate System | |

| |

| |

| |

Applications in the Cylindrical Coordinate System | |

| |

| |

| |

Applications in the Spherical Coordinate System | |

| |

| |

| |

Applications in the Solution of Steady-state problems | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

Notes | |

| |

| |

| |

Heat Conduction in Anisotropic Solids | |

| |

| |

| |

Heat Flux for Anisotropic Solids | |

| |

| |

| |

Heat Conduction Equation for Anisotropic Solids | |

| |

| |

| |

Boundary Conditions | |

| |

| |

| |

Thermal Resistivity Coefficients | |

| |

| |

| |

Determination of Principal Conductivities and Principal Axes | |

| |

| |

| |

Conductivity Matrix for Crystal Systems | |

| |

| |

| |

Transformation of Heat Conduction Equation for Orthotropic Medium | |

| |

| |

| |

Some Special Cases | |

| |

| |

| |

Heat Conduction in an Orthotropic Medium | |

| |

| |

| |

Multidimensional Heat Conduction in an Anisotropic Medium | |

| |

| |

References | |

| |

| |

Problems | |

| |

| |

Notes | |

| |

| |

| |

Introduction to Microscale Heat Conduction | |

| |

| |

| |

Microstructure and Relevant Length Scales | |

| |

| |

| |

Physics of Energy Carriers | |

| |

| |

| |

Energy Storage and Transport | |

| |

| |

| |

Limitations of Fourier's Law and the First Regime of Microscale Heat Transfer | |

| |

| |

| |

Solutions and Approximations for the First Regime of Microscale Heat Transfer | |

| |

| |

| |

Second and Third Regimes of Microscale Heat Transfer | |

| |

| |

| |

Summary Remarks | |

| |

| |

References | |

| |

| |

Appendixes | |

| |

| |

| |

Physical Properties | |

| |

| |

| |

Physical Properties of Metals | |

| |

| |

| |

Physical Properties of Nonmetals | |

| |

| |

| |

Physical Properties of Insulating Materials | |

| |

| |

| |

Roots of Transcendental Equations | |

| |

| |

| |

Error Functions | |

| |

| |

| |

Bessel Functions | |

| |

| |

| |

Numerical Values of Bessel Functions | |

| |

| |

| |

First 10 Roots of J<sub>n</sub>(Z)=0, n=0,1,2,3,4,5 | |

| |

| |

| |

First Six Roots of ï¿½J<sub>1</sub>(ï¿½)-cJ<sub>0</sub>(ï¿½)=0 | |

| |

| |

| |

First Five Roots of J<sub>0</sub>(ï¿½)Y<sub>0</sub>(cï¿½)-Y<sub>0</sub>(ï¿½)J<sub>0</sub>(cï¿½)=0 | |

| |

| |

| |

Numerical Values of Legendre Polynomials of the First Kind | |

| |

| |

| |

Properties of Delta Functions | |

| |

| |

Index | |