Conduction of heat in solids. 2nd ed. (paperback). (English) Zbl 0584.73001

Carslaw, H. S.; Jaeger, J. C.

Oxford: Science Publications. Oxford: Clarendon Press. X, 510 p. £24.00 (1986).

[For the first (1947) and second (1960) editions see Zbl 0029.37801 and Zbl 0095.30201]
This paperback edition presents the theory of the conduction of heat in solids setting out the foundations in careful mathematical details. The aim of this book is to give an account as complete as possible of the exact solutions and soluble problems of the heat flow. Many classical results have been analysed, for example, heat generation, surface heating, melting and freezing, geophysical applications, anisotropic media, moving media, and materials with variable thermal properties. The book covers a great variety of standard boundary value problems in the area of heat flow. The solutions of the boundary value problems are presented in adequate details with the help of classical methods. The method of separation of variables, the use of Green’s function, the Laplace and other integral transformations are applied to get the exact solutions of the problems of heat flow. Explicit solutions of many problems of practical interest are included and numerical informations are given in the form of tables and text figures.
More than four hundred selected references to the mathematical and physical aspects of the various topics are discussed in the text. An adequate introduction to the literature of the subject is given. Excellent physical interpretations of the equations and of each of the solutions are given. The book is written in a very nice and smooth style. Throughout, the discussion is very clear and lucid, and well organized. This is a superb book, encyclopedic in scope, lucid in its presentation, showing throughout the efforts of brillant scientists. This is an ideal book for self-study.
The book consists of the following chapters: 1. General theory; 2. Linear flow of heat: The infinite and semi-infinite solid; 3. Linear flow of heat in the solid bounded by two parallel planes; 4. Linear flow of heat in the rod; 5. Flow of heat in a rectangle; 6. The flow of heat in a rectangular parallelepiped; 7. The flow of heat in an infinite circular cylinder; 8. The flow of heat in regions bounded by surfaces of the cylindrical coordinate system; 9. The flow of heat in a sphere and cone; 10. The use of sources and sinks in cases of variable temperature; 11. Change of state; 12. The Laplace transformation: Problems in linear flow; 13. The Laplace transformation: Problems on the cylinder and sphere; 14. The use of Green’s functions in the solution of the equation of conduction; 15. Further applications of the Laplace transformation; 16. Steady temperature; 17. Integral transforms; 18. Numerical methods. The appendixes contain the following topics: 1. Contour integrals and the verification of solutions obtained by the Laplace transformation; 2. The error function and related functions; 3. Note on Bessel functions; 4. The roots of certain transcendental equations; 5. Table of Laplace transforms; 6. Thermal properties of some common substances.

Reviewer: I.Ecsedi

MSC:

74A15	Thermodynamics in solid mechanics
80A20	Heat and mass transfer, heat flow (MSC2010)
74-02	Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
35K05	Heat equation
80-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to classical thermodynamics
74-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
80A17	Thermodynamics of continua

Keywords:

exact solutions; heat generation; surface heating; melting; freezing; geophysical applications; anisotropic media; moving media; variable thermal properties; standard boundary value problems; separation of variables; Green’s function; integral transformations

Citations:

Zbl 0029.37801; Zbl 0095.30201