# Analytical Heat Diffusion Theory

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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.

## Table of Contents

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

## Product details

- No. of pages: 702
- Language: English
- Copyright: © Academic Press 1968
- Published: January 28, 1968
- Imprint: Academic Press
- eBook ISBN: 9780323143226

## About the Author

### A Luikov

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