For the plane wave of the type exp i(kx - wt) traveling in a uniform magnetic field, the linearized MHD equations are separated into two independent subsystems of equations which define Alfven and magnetoacoustic waves.Īlfven waves are characterized by transversal oscillations of perturbations of velocity In an ideally-conducting fluid (σ = ∞), when there is no dissipation of energy, small perturbations travel as nonattenuating MHD waves. These properties of MHD flows are analogous to those of conventional hydrodynamics derived from theorems on vortex and circulation of velocity. #Define metaimage skin#In this case, magnetic viscosity ν m determines either the characteristic time of magnetic field variation t ~ l 2/υ m at distance l or the characteristic depth of magnetic field penetration l ~ĭuring time t, defined in electrical engineering as the skin layer.Īt Re m = 0 fluid movement does not influence the applied magnetic field, which is induced by currents circulating outside flow volume.Īt Re m = ∞ the effect of magnetic field freezing is observed when magnetic flux through any closed liquid contour is conserved and all liquid particles-initially at the magnetic field line- continue to be on the line. At Re m = 0 diffusion of magnetic field only takes place at finite velocity. The relative role of convection and diffusion is determined by magnetic Reynolds number Re m. The first term in the right hand side of the equation determines the convective transport of magnetic field by fluid particles, the second term describes the diffusion of the magnetic field in the fluid. Where ν m = 1/μσ is the magnetic viscosity. In the case of σ = const and β = 0 the equation of induction can be written as: External conditions represent the paths of electrical current and magnetic field lines outside the flow volume, and in particular, the configuration of external electrical circuit and the type of magnet system.įrom electrodynamic equations leads to an equation containing only one variable Is the Hartmann number and some other parameters.īoundary conditions used in MHD equations are formulated by traditional hydrodynamics and electrodynamics methods. Is the Alfven velocity Re m = μσυL is the magnetic Reynolds number K = E/υB is the parameter of electric field (or load parameter) β = ωτ is the Hall coefficient being the ratio of electron cyclotron frequency and mean frequency of electron collisions with neutrals S = σB 2L/ρυ is the parameter of MHD interaction Ha = BLρ Magnetohydrodynamics is characterized by dimensional parameters which include, in addition to the conventional hydrodynamic parameters (Re, Pr, etc.), new ones containing electromagnetic variables: A = υ/υ a is the Alfven number where υ a = B/ Where j 2/σ is the rate of Joulean dissipation. The MHD equations consist of the mass, momentum and energy conservation laws: MHD applications fall within the conditions of the MHD approximation, according to which nonrelativistic, low frequency movement of an electrically-conducting fluid is considered when displacement and convection currents, electric body force and energy density of electric field can be neglected. Ĭurrently magnetohydrodynamics is applied in astrophysics and geophysics, fission and fusion, metallurgy and direct energy conversion, etc. The discovery of Alfven waves finalized the establishment of magnetohydrodynamics as an individual science. Systematic studies of magnetohydrodynamic (MHD) flows began in the 30s when the first exact solutions of MHD equations were obtained and experiments on liquid metal flows in MHD channels were performed. In the beginning of the 20th century the first proposals for applying electromagnetic induction phenomenon in technical devices with electrically-conducting liquids and gases appeared. Magnetohydrodynamics is a branch of fluid dynamics which studies the movement of an electrically-conducting fluid in a magnetic field.įaraday first pointed out an interaction of sea flows with the Earth is magnetic field (1832).
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