## An Introduction to MagnetohydrodynamicsMagnetic 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. |

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### Contents

The Governing Equations of Electrodynamics | 27 |

The Governing Equations of Fluid Mechanics | 47 |

Incorporating the Lorentz Force | 95 |

Advection and Diffusion | 102 |

Dynamics at Low Magnetic Reynolds Numbers | 117 |

Generation of Motion | 139 |

Boundary Layers | 151 |

Dynamics at Moderate to High Magnetic | 159 |

Magnetic Stirring Using Rotating Fields | 285 |

Magnetic Damping Using Static Fields | 301 |

Axisymmetric Flows Driven by the Injection | 332 |

MUD Instabilities in Reduction Cells | 363 |

Magnetic Levitation | 387 |

Appendices | 405 |

Physical Properties of Liquid Metals | 417 |

423 | |

MHD Turbulence at Low and High Magnetic | 222 |

Applications in Engineering and Metallurgy | 273 |

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### Common terms and phrases

a-effect advection Alfven waves aluminium angular momentum axis axisymmetric azimuthal field boundary layer buoyancy Chapter component conductor conservation consider constant cryolite decay differential rotation diffusion dipole domain dynamo dynamo theory eddies Ekman layer Ekman pumping electrode electromagnetic equation of motion estimate example Faraday's law finite fluid elements fluid mechanics fluid particle flux tube gradient heat induced induction equation inertial inertial waves ingot initial instability integral inviscid isotropic Joule Joule dissipation kinetic energy laminar length scale liquid metal Lorentz force magnetic damping magnetic field lines magnetic pressure Navier-Stokes equation Note Ohm's law perturbation plasma poloidal motion pool problem radial radius result Reynolds number Section shown in Figure small-scale solar solution stability stirring streamlines sunspots Suppose surface swirl theorem theory thermal tion torque turbulent flow two-dimensional vector velocity field viscous vortex vortex tube vorticity yields zero