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       magnetic fields influence many natural and man-made flows. they are routinely used in industry to heat, pump, stir and levitate liquid metals.there is the terrestrial magnetic field which is maintained by fluid motion in the earth's core, the solar magnetic field which generates sunspots and solar flares, and the galactic field which influences the formation of stars.this is an introductory text on magnetohydrodynamics (mhd) - the study of the interaction of magnetic fields and conducting fluids.
　　this book is intended to serve as an introductory text for advanced undergraduate and postgraduate students in physics, applied mathematics and engineering. the material in the text is heavily weighted towards incompressible flows and to terrestrial (as distinct from astrophysical) applications. the final sections of the text also contain an outline of the latest advances in the metallurgical applications of mhd and so are relevant to professional researchers in applied mathematics, engineering and metallurgy.

preface
part a: the fundamentals of mhd
　introduction: the aims of part a
　1 a qualitative overview of mhd
　　1.1 what is mhd?
　　1.2 a brief history of mhd
　　1.3 from electrodynamics to mhd: a simple experiment
　　　1.3.1 some important parameters in electrodynamics and mhd
　　　1.3.2 a brief reminder of the laws of electrodynamics
　　　1.3.3 a familiar high-school experiment
　　　1.3.4 a summary of the key results for mhd
　　1.4 some simple applications of mhd
　2 the governing equations of eiectrodynamics
　　2.1 the electric field and the lorentz force
　　2.2 ohm's law and the volumetric lorentz force
　　2.3 ampere's law
　　2.4 faraday's law in differential form
　　2.5 the reduced form of maxwell's equations for mhd
　　2.6 a transport equation for b
　　2.7 on the remarkable nature of faraday and of faraday's law
　　　2.7.1 an historical footnote
　　　2.7.2 an important kinematic equation
　　　2.7.3 the full significance of faraday's law
　　　2.7.4 faraday's law in ideal conductors: alfvtn's theorem
　3 the governing equations of fluid mechanics
　　part 1: fluid flow in the absence of lorentz forces
　　　3.1 elementary concepts
　　　　3.1.1 different categories of fluid flow
　　　　3.1.2 the navier-stokes equation
　　　3.2 vorticity, angular momentum and the biot-savart law
　　　3.3 advection and diffusion of vorticity
　　　　3.3.1 the vorticity equation
　　　　3.3.2 advection and diffusion of vorticity: temperature as a prototype
　　　　3.3.3 vortex line stretching
　　　3.4 kelvin's theorem, helmholtz's laws and helieity
　　　　3.4.1 kelvin's theorem and helmholtz's laws
　　　　3.4.2 helicity
　　　3.5 the prandti-batchelor theorem
　　　3.6 boundary layers, reynolds stresses and turbulence models
　　　　3.6.1 boundary layers
　　　　3.6.2 reynolds stresses and turbulence models
　　　3.7 ekman pumping in rotating flows
　　part 2: incorporating the lorentz force
　　　3.8 the full equations of mhd and key dimensionless groups
　　　3.9 maxwell stresses
　4 kinematics of mhd: advection and diffusion of a magnetic field
　5 dynamics at low magnetic reynolds numbers
　6 dynamics at moderate to high magnetic reynolds' number
　7 mhd turbulence at low and high magnetic reynolds number
Part b: applications in engineering and metallrugy
　8 introduction: an overview of metallurgical applications
　9 magnetic damping using static fields
　10 axisymmetric flows driven by the injection of current
　11 mhd instabilities in reduction cells
　12 high-frequency fields: magnetic levitation and induction heating
appendices
bibliography
subject index