An Introduction to Magnetohydrodynamics

Cambridge Texts in Applied Mathematics #25

by Peter A. Davidson

Magnetic fields are routinely used in industry to heat, pump, stir and levitate liquid metals. There is the terrestrial magnetic field that is maintained by fluid motion in the earth's core, the solar magnetic field, which generates sunspots and solar flares, and the galactic field that influences the formation of stars. This introductory text on magnetohydrodynamics (MHD) (the study of the interaction of magnetic fields and conducting fluids) is intended to serve as an introductory text for advanced undergraduates and graduate students in physics, applied mathematics and engineering. The material in the text is heavily weighted toward incompressible flows and to terrestrial (as distinct from astrophysical) applications. The final sections of the text, which outline the latest advances in the metallurgical applications of MHD, make the book of interest to professional researchers in applied mathematics, engineering and metallurgy.

Genres: Physics

452 pages, Paperback

First published January 28, 2001

Reviews

[Robert · Rating 1 out of 5]

So magnetohydrodynamics (MHD) is the (classical) theory of electrically conducting fluids, which divide neatly into liquid metals and plasmas. I'm not professionally interested in liquid metals so I skipped all the material that was solely applicable to them, which is possibly as much as half of it. It's also a microcosm of one of the many problems with the book -it's scope is way too large for it's size. To get anywhere with a topic that is defined as the merging of fluid mechanics and classical electrodynamics, one must have a thorough grounding in both those separate topics first. This book tries to cover that and does it badly because they need a book each. The physics of plasmas is very different from that of liquid metals but this book tries to cover both. So really we have four books' worth of material crammed into the space of only one. That's one problem.

Next there's the mathematical treatment, which is really poor. The subject requires a strong grasp of vector calculus. This is unavoidable. The fundamental equations of the theory are non-linear and form a large set that must be solved "self-consistently" whilst describing a dynamic (i.e. time varying) system. This also, is unavoidable. In other words this ain't no easy subject. That's no excuse for lax derivations, poor or absent definitions, or equations that are actually useless because one of the parameters in them has to be "chosen appropriately" (i.e. fudged) in every specific case, with no means of doing so so much as hinted at.

Finally, the verbal description of the physics is on occasions horrendously bad (and plain wrong). This is particularly so with regard to energy, which is repeatly "destroyed" throughout the book - a task nobody else has been able to accomplish in the history of physics. The author seems simply not to know what happens to the kinetic energy of the fluids he describes when it stops being obviously visible. Heat, man! Heat! Conservation of angular momentum is similarly and even more cavalierly treated.

I can't recommend this book to anybody, unfortunately. I have a number of other books that treat MHD. In some it's an introductory chapter, in others it's in relation to a specific context (naturally occurring plasmas). Whether these will prove better remains to be seen.

[Taha0527 · Rating 4 out of 5]

You asked, 'What is this transient pattern?'
If we tell the truth of it, it will be a long story;
It is a pattern that came up out of an ocean
And in a moment returned to that ocean's depth
(Omar Khayyam)
Page 222

[Omran Embahbah · Rating 3 out of 5]

it is very good book