11R45. Introduction to Magnetohydrodynamics. Cambridge Text in Applied Mathematics. - PA Davidson (Univ of Cambridge, UK). Cambridge UP, Cambridge, UK. 2001. 431 pp. (Softcover). ISBN 0-521-79487-0. \$110.00.

Reviewed by K Piechor (Inst of Fund Tech Res, Polish Acad of Sci, ul Swietokrzyska 21, Warsaw, 00-049, Poland).

The reviewed book is a typical textbook on MHD for students in physics, applied mathematics, and engineering. The reader is assumed to be familiar with the classical electrodynamics and quite advanced calculus like surface and curvilinear integrals, Stokes and Gauss theorems.

The book is divided into two parts: Part A, where the fundamentals of MHD are covered, and Part B in which some applications of MHD in engineering and metallurgy are discussed. The division is not very rigorous, so many applications are at least mentioned in Part A, and Part B is not free from theoretical considerations.

Part A, after an introductory Section 1, includes a very brief presentation of the governing equations of electrodynamics (Section 2) and those of fluid mechanics with some discussion of turbulence (Section 3). The main problems of MHD are discussed in Sections 5–7. Roughly speaking, the material of these sections is divided according to the value of the magnetic Reynolds number. Section 5 is devoted to low magnetic Reynolds number. Here the suppression of motion, generation of it, and boundary layers are discussed. The case of moderate magnetic Reynolds number is discussed in Section 6. The last section of Part A, Section 7, contains material on the turbulence at low and high magnetic Reynolds number. Part B, as it was said yet, is written from the point of view of metallurgical application of MHD. Here the magnetic stirring (Section 8), magnetic damping of flows in liquid metals (Section 9), and vacuum-arc remelting (Section 10) are discussed. The role of MHD in production of (mainly) aluminum and the effect of instabilities in reduction cells are presented in Section 11. Some metallurgical processes, where a high-frequency coil is used, are discussed in the last section, 12.

This textbook is written from an interesting viewpoint. Namely, instead of starting from presenting the physical and mathematical problems, equations, and their solutions in an “abstract” form and next looking for possible applications of these results—what is typical for many other textbooks on this subject—the author starts from presenting first natural phenomena or industrial problems, then explains their magnetohydrodynamical nature, and finally he formulates the mathematical formulation (equations). This philosophy causes that almost each section is preceded by (sometimes-long) presentation of the astrophysical or industrial questions. For an impatient reader, who wants to quickly have the equations, the long introductions can be boring and dull. However, in this reviewer’s opinion, a reader omitting these parts of the book loses very much!

The author cares greatly about the student. The language of this book is simple, vivid, yet fully scientific. It is a real pleasure to read it. The most important statements and equations are framed. Many well-thought-out figures help readers to understand the discussed topic. A suitable suggested reading and exercises follow each section.

In this reviewer’s opinion, Introduction to Magnetohydrodynamics is worth recommending, not only to students, but also to everyone who is interested in MHD, particularly to theoreticians who, as a rule, know almost nothing about metallurgical applications of MHD.