Analytical Heat Diffusion Theory

Editor's Preface Introduction Chapter 1. Physical Fundamentals of Heat Transfer 1.1 Temperature Field 1.2 The Fundamental Fourier Heat Conduction Law 1.3 Heat Distribution in the High Rate Processes 1.4 Heat Distribution Equation in Liquid and Gas Mixtures 1.5 Differential Heat Conduction Equation 1.6 Hyperbolic Heat Conduction Equation 1.7 A System of Differential Heat and Mass Transfer Equations 1.8 End Conditions 1.9 Methods for Calculating the Heat Flow Chapter 2. Theory of Generalized Variables Introduction 2.1 Dimensionless Quantities 2.2 Operational Calculus and Similarity TheoryChapter 3. Basic Methods for Solution of Boundary Value Problems 3.1 Analysis of a Differential Equation for Heat Conduction 3.2 Solution of the Equation by Classical Methods 3.3 Integral Transform Methods 3.4 Methods of Numerical Solution of Heat Conduction Problems Chapter 4. Nonstationary Temperature Field without Heat Sources: Boundary Condition of the First Kind 4.1 Infinite Body 4.2 Semi-Infinite Body 4.3 Infinite Plate 4.4 Sphere (Symmetrical Problem) 4.5 Infinite Cylinder 4.6 Infinite Hollow Cylinder 4.7 Parallelepiped 4.8 Finite Cylinder 4.9 Heating Problems Chapter 5. Boundary Condition of the Second Kind 5.1 Semi-Infinite Body 5.2 Infinite Plate 5.3 Sphere (Symmetrical Problem) 5.4 Infinite Cylinder 5.5 Hollow Infinite Cylinder Chapter 6. Boundary Condition of the Third Kind 6.1 Semi-Infinite Body 6.2 Semi-Infinite Rod without Thermal Insulation of Its Surface 6.3 Infinite Plate 6.4 Finite Rod without Thermal Insulation of Its Lateral Surface 6.5 Sphere (Symmetrical Problem) 6.6 Infinite Cylinder 6.7 Infinite Hollow Cylinder 6.8 Finite Cylinder 6.9 Finite Plate 6.10 Analysis of the Generalized Solution 6.11 Estimation of Approximation Chapter 7. Temperature Fields without Heat Sources with Variable Temperature of the Surrounding Medium 7.1 Infinite Plate. Ambient Temperature as a Linear Function of Time 7.2 Sphere. Ambient Temperature as a Linear Function of Time 7.3 Infinite Cylinder. Ambient Temperature as a Linear Function of Time 7.4 Infinite Plate, Sphere, and Cylinder. Ambient Temperature as an Exponential Function of Time 7.5 Heating of Moist Bodies (Infinite Plate, Sphere, and Infinite Cylinder) 7.6 Thermal Waves. Infinite Plate, Semi-Infinite Body, Sphere, and Infinite Cylinder. Ambient Temperature as a Simple Harmonic Function of Time 7.7 Semi-Infinite Body. Ambient Temperature as a Function of Time 7.8 Generalized Solution. Duhamel's Theorem 7.9 Hollow Cylinder 7.10 Parallelepiped. Ambient Temperature as a Linear Function of Time Chapter 8. Temperature Field with Continuous Heat Sources 8.1 Semi-Infinite Body 8.2 Infinite Plate 8.3 Sphere (Symmetrical Problem) 8.4 Infinite Cylinder Chapter 9. Temperature Field with Pulse-Type Heat Sources Introduction 9.1 Semi-Infinite Body 9.2 Infinite Plate 9.3 Sphere (Symmetrical Problem) 9.4 Infinite Cylinder 9.5 Regular Thermal Regime Chapter 10. Boundary Conditions of the Fourth Kind 10.1 System of Two Bodies (Two Semi-Infinite Rods) 10.2 System of Two Bodies (Finite and Semi-Infinite Rods) 10.3 System of Two Bodies (Two Infinite Plates) 10.4 System of Two Spherical Bodies (Sphere inside Sphere) 10.5 System of Two Cylindrical Bodies 10.6 Infinite Plate 10.7 Sphere (Symmetrical Problem) 10.8 Infinite Cylinder 10.9 Heat Transfer between a Body and a Liquid Flow 10.10 Symmetrical System of Bodies Consisting of Three Infinite Plates Chapter 11. Temperature Field of Body with Changing State of Aggregation 11.1 Freezing of Wet Ground 11.2 Approximate Solutions of Problems of Solidification of a Semi-Infinite Body, an Infinite Plate, a Sphere, and an Infinite Cylinder 11.3 Metal Solidification with the Heat Conduction Coefficient and Heat Capacity as Functions of Temperature Chapter 12. Two-Dimensional Temperature Field: Particular Problems 12.1 Semi-Infinite Plate 12.2 Two-Dimensional Plate 12.3 Semi-Infinite Cylinder 12.4 Heat Transfer in Cylindrical Regions Chapter 13. Heat Conduction with Variable Transfer Coefficients 13.1 Semi-Infinite Body, Heat Conductivity, and Heat Capacity as Power Functions of Coordinates 13.2 Finite Plate. Thermal Conductivity as an Exponential Function of the Coordinate 13.3 Nonstationary Temperature Fields in Nonlinear Temperature Processes 13.4 Boundary-Value Problems for the Heat Conduction Equation with the Coefficients Dependent upon the CoordinateChapter 14. Fundamentals of the Integral Transforms 14.1 Definitions 14.2 Laplace Transformation Properties 14.3 Method of Solution for Simplest Differential Equations 14.4 Other Properties of the Laplace Transformation 14.5 Solution of the Linear Differential Equation with Constant Coefficients by Operational Methods 14.6 Expansion Theorems 14.7 Solution of Some Differential Equations with Variable Coefficients 14.8 Integral Transformations and Operational Methods 14.9 Inversion of the Transform 14.10 Integral Fourier and Hankel Transforms 14.11 Finite Integral Fourier and Hankel Transforms 14.12 Kernels of Finite Integral Transforms Chapter 15. Elements of the Theory of Analytic Functions and Its Applications 15.1 Analytic Functions 15.2 Contour Integration of Complex Variable Functions 15.3 Representation of Analytic Functions by Series 15.4 Classification of Analytic Functions by Their Singularities. The Concept of Analytical Continuation 15.5 Residue Theory and Its Application to Calculating Integrals and Summing Up Series 15.6 Some Analytical Properties of Laplace Transforms and Asymptotic Estimates Appendix 1. Some Reference Formulas Appendix 2. The Uniqueness Theorem Appendix 3. Differential Heat Conduction Equation in Various Coordinate Systems Appendix 4. Main Rules and Theorems of the Laplace Transformation Appendix 5. Transforms of Some Functions Appendix 6. Values of Functions in erfc x References Author IndexSubject Index