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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 | |