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| Preface | |
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| Preface to Second Edition | |
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| Heat Conduction Fundamentals | |
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| The Heat Flux | |
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| Thermal Conductivity | |
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| Differential Equation of Heat Conduction | |
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| Fourier's Law and the Heat Equation in Cylindrical and Spherical Coordinate Systems | |
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| General Boundary Conditions and Initial Condition for the Heat Equation | |
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| Nondimensional Analysis of the Heat Conduction Equation | |
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| Heat Conduction Equation for Anisotropic Medium | |
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| Lumped and Partially Lumped Formulation | |
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| References | |
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| Problems | |
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| Orthogonal Functions, Boundary Value Problems, and the Fourier Series | |
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| Orthogonal Functions | |
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| Boundary Value, Problems | |
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| The Fourier Series | |
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| Computation of Eigenvalues | |
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| Fourier Integrals | |
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| References | |
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| Problems | |
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| Separation of Variables in the Rectangular Coordinate System | |
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| Basic Concepts in the Separation of Variables Method | |
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| Generalization to Multidimensional Problems | |
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| Solution of Multidimensional Homogenous Problems | |
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| Multidimensional Nonhomogeneous Problems: Method of Superposition | |
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| Product Solution | |
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| Capstone Problem | |
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| References | |
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| Problems | |
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| Separation of Variables in the Cylindrical Coordinate System | |
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| Separation of Heat Conduction Equation in the Cylindrical Coordinate System | |
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| Solution of Steady-State Problems | |
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| Solution of Transient Problems | |
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| Capstone Problem | |
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| References | |
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| Problems | |
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| Separation of Variables in the Spherical Coordinate System | |
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| Separation of Heat Conduction Equation in the Spherical Coordinate System | |
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| Solution of Steady-State Problems | |
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| Solution of Transient Problems | |
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| Capstone Problem | |
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| References | |
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| Problems | |
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| Notes | |
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| Solution of the Heat Equation for Semi-Infinite and Infinite Domains | |
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| One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System | |
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| Multidimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System | |
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| One-Dimensional Homogeneous Problems in an Infinite Medium for the Cartesian Coordinate System | |
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| One-Dimensional homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System | |
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| Two-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System | |
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| One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Spherical Coordinate System | |
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| References | |
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| Problems | |
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| Use of Duhamel's Theorem | |
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| Development of Duhamel's Theorem for Continuous Time-Dependent Boundary Conditions | |
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| Treatment of Discontinuities | |
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| General Statement of Duhamel's Theorem | |
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| Applications of Duhamel's Theorem | |
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| Applications of Duhamel's Theorem for Internal Energy Generation | |
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| References | |
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| Problems | |
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| Use of Green's Function for Solution of Heat Conduction Problems | |
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| Green's Function Approach for Solving Nonhomogeneous Transient Heat Conduction | |
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| Determination of Green's Functions | |
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| Representation of Point, Line, and Surface Heat Sources with Delta Functions | |
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| Applications of Green's Function in the Rectangular Coordinate System | |
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| Applications of Green's Function in the Cylindrical Coordinate System | |
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| Applications of Green's Function in the Spherical Coordinate System | |
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| Products of Green's Functions | |
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| References | |
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| Problems | |
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| Use of the Laplace Transform | |
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| Definition of Laplace Transformation | |
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| Properties of Laplace Transform | |
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| Inversion of Laplace Transform Using the Inversion Tables | |
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| Application of the Laplace Transform in the Solution of Time-Dependent Heat Conduction Problems | |
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| Approximations for Small Times | |
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| References | |
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| Problems | |
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| One-Dimensional Composite Medium | |
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| Mathematical Formulation of One-Dimensional Transient Heat Conduction in a Composite Medium | |
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| Transformation of Nonhomogeneous Boundary Conditions into Homogeneous Ones | |
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| Orthogonal Expansion Technique for Solving M-Layer Homogeneous Problems | |
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| Determination of Eigenfunctions and Eigenvalues | |
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| Applications of Orthogonal Expansion Technique | |
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| Green's Function Approach for Solving Nonhomogeneous Problems | |
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| Use of Laplace Transform for Solving Semi-Infinite and Infinite Medium Problems | |
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| References | |
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| Problems | |
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| Moving Heat Source Problems | |
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| Mathematical Modeling of Moving Heat Source Problems | |
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| One-Dimensional Quasi-Stationary Plane Heat Source Problem | |
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| Two-Dimensional Quasi-Stationary Line Heat Source Problem | |
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| Two-Dimensional Quasi-Stationary Ring Heat Source Problem | |
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| References | |
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| Problems | |
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| Phase-Change Problems | |
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| Mathematical Formulation of Phase-Change Problems | |
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| Exact Solution of Phase-Change Problems | |
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| Integral Method of Solution of Phase-Change Problems | |
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| Variable Time Step Method for Solving Phase-Change Problems: A Numerical Solution | |
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| Enthalpy Method for Solution of Phase-Change Problems: A Numerical Solution | |
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| References | |
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| Problems | |
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| Note | |
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| Approximate Analytic Methods | |
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| Integral Method: Basic Concepts | |
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| Integral Method: Application to Linear Transient Heat Conduction in a Semi-Infinite Medium | |
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| Integral Method: Application to Nonlinear Transient Heat Conduction | |
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| Integral Method: Application to a Finite Region | |
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| Approximate Analytic Methods of Residuals | |
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| The Galerkin Method | |
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| Partial Integration | |
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| Application to Transient Problems | |
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| References | |
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| Problems | |
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| Integral Transform Technique | |
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| Use of Integral Transform in the Solution of Heat Conduction Problems | |
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| Applications in the Rectangular Coordinate System | |
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| Applications in the Cylindrical Coordinate System | |
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| Applications in the Spherical Coordinate System | |
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| Applications in the Solution of Steady-state problems | |
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| References | |
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| Problems | |
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| Notes | |
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| Heat Conduction in Anisotropic Solids | |
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| Heat Flux for Anisotropic Solids | |
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| Heat Conduction Equation for Anisotropic Solids | |
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| Boundary Conditions | |
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| Thermal Resistivity Coefficients | |
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| Determination of Principal Conductivities and Principal Axes | |
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| Conductivity Matrix for Crystal Systems | |
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| Transformation of Heat Conduction Equation for Orthotropic Medium | |
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| Some Special Cases | |
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| Heat Conduction in an Orthotropic Medium | |
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| Multidimensional Heat Conduction in an Anisotropic Medium | |
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| References | |
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| Problems | |
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| Notes | |
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| Introduction to Microscale Heat Conduction | |
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| Microstructure and Relevant Length Scales | |
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| Physics of Energy Carriers | |
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| Energy Storage and Transport | |
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| Limitations of Fourier's Law and the First Regime of Microscale Heat Transfer | |
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| Solutions and Approximations for the First Regime of Microscale Heat Transfer | |
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| Second and Third Regimes of Microscale Heat Transfer | |
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| Summary Remarks | |
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| References | |
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| Appendixes | |
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| Physical Properties | |
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| Physical Properties of Metals | |
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| Physical Properties of Nonmetals | |
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| Physical Properties of Insulating Materials | |
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| Roots of Transcendental Equations | |
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| Error Functions | |
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| Bessel Functions | |
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| Numerical Values of Bessel Functions | |
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| First 10 Roots of J<sub>n</sub>(Z)=0, n=0,1,2,3,4,5 | |
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| First Six Roots of �J<sub>1</sub>(�)-cJ<sub>0</sub>(�)=0 | |
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| First Five Roots of J<sub>0</sub>(�)Y<sub>0</sub>(c�)-Y<sub>0</sub>(�)J<sub>0</sub>(c�)=0 | |
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| Numerical Values of Legendre Polynomials of the First Kind | |
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| Properties of Delta Functions | |
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| Index | |