Analytical Heat Diffusion Theory is a revised edition of an earlier book by Academician Luikov, which was widely used throughout the Soviet Union and the surrounding socialist countries. This book is divided into 15 chapters that treat heat conduction problems by the classical methods and emphasize the advantages of the transform method, particularly in obtaining short time solutions of many transient problems.
This book starts with a discussion on the physical fundamentals, generalized variables, and solution of boundary value problems of heat transfer. Considerable chapters are devoted to the basic classical heat transfer problems and problems in which the body surface temperature is a specified function of time. Other chapters explore the heat transfer problems under different heat sources, including continuous and pulse-type. The discussion then shifts to the problem of freezing wet ground, two-dimensional temperature field, and heat conduction with variable transfer coefficients. The final chapters deal with the fundamentals of the integral transforms and their application to heat conduction problems. These chapters also look into the application of the theory of analytic functions to the heat conduction theory of mathematical physics.
This book is an invaluable source for advanced undergraduate or graduate in analytical heat transfer.

Contenu

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 Theory
Chapter 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 Coordinate
Chapter 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 Index
Subject Index