flows at moderate and high magnetic Reynolds number
An introduction to magnetohydrodynamics
This book written by an experienced teacher is divided into two main parts A and B, where the theoretical part A is subdivided into 7 chapters, and part B devoted to applications is subdivided into 5 chapters.NEWLINENEWLINENEWLINEIn part A, the author discusses different aspects of magnetohydrodynamics from theoretical as well as from physical point of view, which is especially important for understanding the basics of the subject. More precisely, chapter 1 presents the interesting history of MHD starting from 1930, without much mathematical rigor. The author includes some simple applications which promoted the development of MHD, like 1) sunspot formation; 2) the study of terrestrial magnetic field; 3) controlled thermonuclear fusion; 4) the theory of electromagnetic pumps; 5) magnetic stirring of an ingot; 6) magnetic damping of motion during casting process; 7) the theory of electromagnetic valve; 8) interfacial gravity waves in magnetic fluids; 9) applications in military operations. Chapter 2 contains a detailed discussion of basic equations of electrodynamics (Maxwell equations. Ohm's law, formula for Lorentz force, Ampère's law, Faraday's laws). Chapter 3 does not involve MHD but is very important as it describes the fundamentals of fluid mechanics: viscous flow theory, boundary-layer concept, a short derivation of non-MHD Navier-Stokes equations, vorticity, angular momentum, a brief sketch of nonviscous flow theory (Kelvin theorem, Helmholtz laws and helicity), and an introduction to turbulence. As applications, the author discusses von Kármán and Bödewadt problems. Finally, the author derives the MHD form of Navier-Stokes equations. Chapter 4 describes advection and diffusion in magnetic fields.NEWLINENEWLINENEWLINEFrom chapter 5, the author starts with the presentation of genuinely MHD topics. First, the author subdivides the MHD theory into two main parts: flows at low magnetic Reynolds number \(R_m\), and flows at moderate and high magnetic Reynolds number \(R_m\). For \(R_m\ll 1\), the MHD flows are examined in chapter 5. Together with the discussion of magnetic damping and Rayleigh-Bénard instability, the author describes engineering application of these flows: flows between two parallel plates induced by rotating magnetic field, Hartmann boundary layers, Hartmann flows between two plates, flow-meters and MHD-generators, pumps, propulsion and projectiles. Unfortunately, some important from reviewer's viewpoint flows are not included in the book: MHD flows past semi-infinite plates in transverse magnetic fields, MHD Couette flow, MHD combined convection etc. The moderate and high magnetic Reynolds number flows are topics of chapter 6. The author discusses here Alfvén waves, magnetostrophic waves, MHD dynamo theory and elements of geo-dynamo theory, solar MHD flows, and energy method for the study of MHD stability. The last theoretical chapter 7 deals with turbulent flows with and without MHD. NEWLINENEWLINENEWLINEPart B contains the following applications of MHD in engineering and metallurgy: 1) magnetic stirring induced by rotating magnetic field; 2) magnetic damping of jets, vortices and natural convection; 3) flows arising from the injection of current into a liquid-metal pool; 4) interfacial instabilities due to a current between two conducting fluids; 5) magnetic levitation and heating induced by high-frequency magnetic fields. At the end, the author gives journal references for part B which could be very helpful for practitioners carrying out research in applied MHD. Hence the importance of this text-book to graduate and post-graduate level students, and hence the book can be highly recommended for all institute libraries.
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