Magnetohydrodynamics in Materials Processing

Abstract

Magnetohydrodynamics was established by Alfvén in 1942. When we solve problems concerning a flow of highly conductive fluids such as molten metals or salts under an electric and/or magnetic fields, an electromagnetic force term induced by electric and magnetic fields appears in a force term in the equation of motion. Therefore, it is necessary to know the directions and magnitudes of the existing electric and magnetic fields. On the other hand, to obtain those parameters in electric and magnetic fields in the highly conductive fluid by solving Maxwell's equation, we have to know the fluid velocity in a generalized Ohm’s law. In this way, magnetohydrodynamics describes problems where the electric and magnetic fields couple with the velocity field. Magnetohydrodynamics covers not only plasma physics, geophysics and astrophysics but also EPM (Electromagnetic Processing of Materials), which is the main subject of this book. The mutual interaction between the electric and magnetic fields and the velocity field depends on the problems we have to solve. In most cases of EPM, it is generally to be considered that the electric and magnetic fields influence the velocity field, while the velocity field scarcely influences the electric and magnetic fields. Therefore, we first solve the equation of electric and magnetic fields without considering the influence of the velocity field, and then get the velocity field by substituting the obtained electric and magnetic fields into the driving force term in the equation of motion. That is, the coupling will be one-sided in many cases.