Heat Conduction 3e

Preface xiii Preface to Second Edition xvii 1 Heat Conduction Fundamentals 1 1-1 The Heat Flux, 2 1-2 Thermal Conductivity, 4 1-3 Differential Equation of Heat Conduction, 6 1-4 Fourier's Law and the Heat Equation in Cylindrical and Spherical Coordinate Systems, 14 1-5 General Boundary Conditions and Initial Condition for the Heat Equation, 16 1-6 Nondimensional Analysis of the Heat Conduction Equation, 25 1-7 Heat Conduction Equation for Anisotropic Medium, 27 1-8 Lumped and Partially Lumped Formulation, 29 References, 36 Problems, 37 2 Orthogonal Functions, Boundary Value Problems, and the Fourier Series 40 2-1 Orthogonal Functions, 40 2-2 Boundary Value Problems, 41 2-3 The Fourier Series, 60 2-4 Computation of Eigenvalues, 63 2-5 Fourier Integrals, 67 References, 73 Problems, 73 3 Separation of Variables in the Rectangular Coordinate System 75 3-1 Basic Concepts in the Separation of Variables Method, 75 3-2 Generalization to Multidimensional Problems, 85 3-3 Solution of Multidimensional Homogenous Problems, 86 3-4 Multidimensional Nonhomogeneous Problems: Method of Superposition, 98 3-5 Product Solution, 112 3-6 Capstone Problem, 116 References, 123 Problems, 124 4 Separation of Variables in the Cylindrical Coordinate System 128 4-1 Separation of Heat Conduction Equation in the Cylindrical Coordinate System, 128 4-2 Solution of Steady-State Problems, 131 4-3 Solution of Transient Problems, 151 4-4 Capstone Problem, 167 References, 179 Problems, 179 5 Separation of Variables in the Spherical Coordinate System 183 5-1 Separation of Heat Conduction Equation in the Spherical Coordinate System, 183 5-2 Solution of Steady-State Problems, 188 5-3 Solution of Transient Problems, 194 5-4 Capstone Problem, 221 References, 233 Problems, 233 Notes, 235 6 Solution of the Heat Equation for Semi-Infinite and Infinite Domains 236 6-1 One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System, 236 6-2 Multidimensional Homogeneous Problems in a Semi-Infinite Medium for the Cartesian Coordinate System, 247 6-3 One-Dimensional Homogeneous Problems in An Infinite Medium for the Cartesian Coordinate System, 255 6-4 One-Dimensional homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System, 260 6-5 Two-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Cylindrical Coordinate System, 265 6-6 One-Dimensional Homogeneous Problems in a Semi-Infinite Medium for the Spherical Coordinate System, 268 References, 271 Problems, 271 7 Use of Duhamel's Theorem 273 7-1 Development of Duhamel's Theorem for Continuous Time-Dependent Boundary Conditions, 273 7-2 Treatment of Discontinuities, 276 7-3 General Statement of Duhamel's Theorem, 278 7-4 Applications of Duhamel's Theorem, 281 7-5 Applications of Duhamel's Theorem for Internal Energy Generation, 294 References, 296 Problems, 297 8 Use of Green's Function for Solution of Heat Conduction Problems 300 8-1 Green's Function Approach for Solving Nonhomogeneous Transient Heat Conduction, 300 8-2 Determination of Green's Functions, 306 8-3 Representation of Point, Line, and Surface Heat Sources with Delta Functions, 312 8-4 Applications of Green's Function in the Rectangular Coordinate System, 317 8-5 Applications of Green's Function in the Cylindrical Coordinate System, 329 8-6 Applications of Green's Function in the Spherical Coordinate System, 335 8-7 Products of Green's Functions, 344 References, 349 Problems, 349 9 Use of the Laplace Transform 355 9-1 Definition of Laplace Transformation, 356 9-2 Properties of Laplace Transform, 357 9-3 Inversion of Laplace Transform Using the Inversion Tables, 365 9-4 Application of the Laplace Transform in the Solution of Time-Dependent Heat Conduction Problems, 372 9-5 Approximations for Small Times, 382 References, 390 Problems, 390 10 One-Dimensional Composite Medium 393 10-1 Mathematical Formulation of One-Dimensional Transient Heat Conduction in a Composite Medium, 393 10-2 Transformation of Nonhomogeneous Boundary Conditions into Homogeneous Ones, 395 10-3 Orthogonal Expansion Technique for Solving M-Layer Homogeneous Problems, 401 10-4 Determination of Eigenfunctions and Eigenvalues, 407 10-5 Applications of Orthogonal Expansion Technique, 410 10-6 Green's Function Approach for Solving Nonhomogeneous Problems, 418 10-7 Use of Laplace Transform for Solving Semi-Infinite and Infinite Medium Problems, 424 References, 429 Problems, 430 11 Moving Heat Source Problems 433 11-1 Mathematical Modeling of Moving Heat Source Problems, 434 11-2 One-Dimensional Quasi-Stationary Plane Heat Source Problem, 439 11-3 Two-Dimensional Quasi-Stationary Line Heat Source Problem, 443 11-4 Two-Dimensional Quasi-Stationary Ring Heat Source Problem, 445 References, 449 Problems, 450 12 Phase-Change Problems 452 12-1 Mathematical Formulation of Phase-Change Problems, 454 12-2 Exact Solution of Phase-Change Problems, 461 12-3 Integral Method of Solution of Phase-Change Problems, 474 12-4 Variable Time Step Method for Solving Phase-Change Problems: A Numerical Solution, 478 12-5 Enthalpy Method for Solution of Phase-Change Problems: A Numerical Solution, 484 References, 490 Problems, 493 Note, 495 13 Approximate Analytic Methods 496 13-1 Integral Method: Basic Concepts, 496 13-2 Integral Method: Application to Linear Transient Heat Conduction in a Semi-Infinite Medium, 498 13-3 Integral Method: Application to Nonlinear Transient Heat Conduction, 508 13-4 Integral Method: Application to a Finite Region, 512 13-5 Approximate Analytic Methods of Residuals, 516 13-6 The Galerkin Method, 521 13-7 Partial Integration, 533 13-8 Application to Transient Problems, 538 References, 542 Problems, 544 14 Integral Transform Technique 547 14-1 Use of Integral Transform in the Solution of Heat Conduction Problems, 548 14-2 Applications in the Rectangular Coordinate System, 556 14-3 Applications in the Cylindrical Coordinate System, 572 14-4 Applications in the Spherical Coordinate System, 589 14-5 Applications in the Solution of Steady-state problems, 599 References, 602 Problems, 603 Notes, 607 15 Heat Conduction in Anisotropic Solids 614 15-1 Heat Flux for Anisotropic Solids, 615 15-2 Heat Conduction Equation for Anisotropic Solids, 617 15-3 Boundary Conditions, 618 15-4 Thermal Resistivity Coefficients, 620 15-5 Determination of Principal Conductivities and Principal Axes, 621 15-6 Conductivity Matrix for Crystal Systems, 623 15-7 Transformation of Heat Conduction Equation for Orthotropic Medium, 624 15-8 Some Special Cases, 625 15-9 Heat Conduction in an Orthotropic Medium, 628 15-10 Multidimensional Heat Conduction in an Anisotropic Medium, 637 References, 645 Problems, 647 Notes, 649 16 Introduction to Microscale Heat Conduction 651 16-1 Microstructure and Relevant Length Scales, 652 16-2 Physics of Energy Carriers, 656 16-3 Energy Storage and Transport, 661 16-4 Limitations of Fourier's Law and the First Regime of Microscale Heat Transfer, 667 16-5 Solutions and Approximations for the First Regime of Microscale Heat Transfer, 672 16-6 Second and Third Regimes of Microscale Heat Transfer, 676 16-7 Summary Remarks, 676 References, 676 APPENDIXES 679 Appendix I Physical Properties 681 Table I-1 Physical Properties of Metals, 681 Table I-2 Physical Properties of Nonmetals, 683 Table I-3 Physical Properties of Insulating Materials, 684 Appendix II Roots of Transcendental Equations 685 Appendix III Error Functions 688 Appendix IV Bessel Functions 691 Table IV-1 Numerical Values of Bessel Functions, 696 Table IV-2 First 10 Roots of Jn(z) = 0, n = 0, 1, 2, 3, 4, 5, 704 Table IV-3 First Six Roots of betaJ1(beta) - cJ0(beta) = 0, 705 Table IV-4 First Five Roots of J0(beta)Y0(cbeta) - Y0(beta)J0(cbeta) = 0, 706 Appendix V Numerical Values of Legendre Polynomials of the First Kind 707 Appendix VI Properties of Delta Functions 710 Index 713