Heat Conduction

HEAT CONDUCTION Mechanical Engineering THE LONG-AWAITED REVISION OF THE BESTSELLER ON HEAT CONDUCTION Heat Conduction, Third Edition is an update of the classic text on heat conduction, replacing some of the coverage of numerical methods with content on micro- and nanoscale heat transfer. With an emphasis on the mathematics and underlying physics, this new edition has considerable depth and analytical rigor, providing a systematic framework for each solution scheme with attention to boundary conditions and energy conservation. Chapter coverage includes: Heat conduction fundamentals Orthogonal functions, boundary value problems, and the Fourier Series The separation of variables in the rectangular coordinate system The separation of variables in the cylindrical coordinate system The separation of variables in the spherical coordinate system Solution of the heat equation for semi-infinite and infinite domains The use of Duhamel’s theorem The use of Green’s function for solution of heat conduction The use of the Laplace transform One-dimensional composite medium Moving heat source problems Phase-change problems Approximate analytic methods Integral-transform technique Heat conduction in anisotropic solids Introduction to microscale heat conduction In addition, new capstone examples are included in this edition and extensive problems, cases, and examples have been thoroughly updated. A solutions manual is also available. Heat Conduction is appropriate reading for students in mainstream courses of conduction heat transfer, students in mechanical engineering, and engineers in research and design functions throughout industry.

Table of Contents:
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 βJ1(β) − cJ0(β) = 0 705 Table IV-4 First Five Roots of J0(β)Y0(cβ) − Y0(β)J0(cβ) = 0 706 Appendix V Numerical Values of Legendre Polynomials of the First Kind 707 Appendix VI Properties of Delta Functions 710 Index 713

About the Author :
DAVID W. HAHN is the Knox T. Millsaps Professor of Mechanical and Aerospace Engineering at the University of Florida, Gainesville. His areas of specialization include both thermal sciences and biomedical engineering, including the development and application of laser-based diagnostic techniques and general laser-material interactions. The late M. NECATI ÖZISIK retired as Professor Emeritus of North Carolina State University’s Mechanical and Aerospace Engineering Department, where he spent most of his academic career. Professor ÖziŞik dedicated his life to education and research in heat transfer. His outstanding contributions earned him several awards, including the Outstanding Engineering Educator Award from the American Society for Engineering Education in 1992.