Electrically Induced Vortical Flows

1/Basic Properties of Axially Symmetric Motions in Magnetohydrodynamics.- 1.1. Magnetohydrodynamic Equations.- 1.2. Some Facts about Orthogonal Curvilinear Coordinates.- 1.3. Differential Operators in Orthogonal Curvilinear Coordinates.- 1.4. The Most Commonly Used Rotational Coordinate Systems.- 1.5. Axisymmetric Motions.- 1.6. Relation between Stokes Stream Function and Self-Magnetic Field of an Electric Current in Problems with Axial Symmetry.- 1.7. Feasible Schemes for Axially Symmetric Electric Current Distributions.- 1.8. Magnetic Field in Axisymmetric Flow.- 1.9. Electric Field in Axisymmetric Flow.- 1.10. Full Set of Equations for Axisymmetric Motion.- 2/Solutions in Spherical Coordinates.- 2.1. Definition of the Class of Exact Solutions.- 2.2. Low Magnetic Reynolds Number Approximation. Electric Current and External Magnetic Fields.- 2.3. Integral Flow Characteristics and Dimensionless Criteria.- 2.4. Review of the Class of Exact Solutions in Spherical Coordinates.- 2.5. Electrically Induced Vortex Flow in a Cone.- 2.6. Gas Flow in an Electrical Arc.- 2.7. Problems of the Nonlinear Solution.- 2.8. Landau-Squire Flows in the Presence of a Radially Diverging Electric Current.- 2.9. Effect of the Induced Electric Current on the Flow at a Point Current Source.- 2.10. Electrically Induced Flows at Finite Size Electrodes.- 3/Electrically Induced Vortex Flow at a Point Electrode and Azimuthal Rotation.- 3.1. Integral Properties of the Flows Driven by Rotational Electromagnetic Forces.- 3.2. A Model Demonstrating the Effect of Viscosity.- 3.3. Flow at an Immersed Electrode.- 3.4. Asymptotic Solution for High S.- 3.5. Electrically Induced Flow with Differential Rotation.- 3.6. Growth of Azimuthal Disturbance in the Electrically Induced Flow at a Point Electrode.- 3.7. Intensification of Rotation in a Closed Volume.- 3.8. Mechanism of Rotation Intensification in an Axisymmetric Vortex.- 4/Flows with Cylindrical Symmetry.- 4.1. External Electric Current and Magnetic Field in Cylindrical Coordinates.- 4.2. Similarity Solutions.- 4.3. Electrically Induced Flow between Two Parallel Walls.- 4.4. Flow with Line Source in a Circular Cone.- 4.5. Magnetohydrodynamic Model of Tornado.- 4.6. EVF in a Cylindrical Container.- 4.7. Effect of Electric Current Configuration on Flow in a Cylindrical Container.- 5/Periodic Electrically Induced Flows.- 5.1. Periodic Distributions of Current and Magnetic Field in Cylindrical Coordinates.- 5.2. Integral Action of Electromagnetic Force.- 5.3. A Method Used to Construct Linear Solution of Periodic EVF in Tubes.- 5.4. EVF in a Tube with Radial Current Supply.- 5.5. EVF in a Tube with Longitudinal Electric Current.- 5.6. EVF in an Annular Tube.- 5.7. Periodic EVF in a Longitudinal Magnetic Field.- 5.8. Longitudinal Magnetic Field Effect on Integral Features of EVF.- 5.9. Nonlinear Interaction of Periodic EVF with Through-Flow.- 5.10. Electrically Induced Flow in a Loosely Coiled Tube.- 6/Bodies in a Current-Carrying Fluid.- 6.1. Effect of Potential Forces on a Body in a Current-Carrying Fluid.- 6.2. Effect of the Rotational Electromagnetic Forces on Axisymmetric Bodies.- 6.3. Flow at a Stationary Sphere.- 6.4. Drag of a Sphere in the Flow of Current-Carrying Fluid.- 6.5. Flows at Spheroids.- 6.6. Discharge between Electrodes of Hyperboloidal Form.- 6.7. Flow at a Cone with an Electric Current Source in the Apex.- 6.8. Motion of a Sphere with a Current-Source.- 7/Heat and Mass Transfer in Electrically Induced Vortical Flows.- 7.1. Equations of Heat and Mass Transfer, and the Nondimensional Numbers.- 7.2. Mass Transfer from a Stationary Spherical Particle in Current-Carrying Fluid.- 7.3. Mass Transfer from a Translating Spherical Particle in a Current-Carrying Fluid.- 7.4. Mass Transfer from a Stationary Sphere in a Longitudinal Magnetic Field.- 7.5. Heat and Mass Transfer in a Cylindrical Container.- 7.6. Thermal Convection in Electrically Induced Flows.- 8/Experimental Investigations of EVF and Applications.- 8.1. Electroslag Welding.- 8.2. Electroslag Remelting.- 8.3. Electric-Arc Furnaces.- 8.4. Hydrodynamics of Furnaces with Multiple Electrodes.- 8.5. Electrical Jet Thrusters.- 8.6. Induction Channel Furnaces.- 8.7. Electrically Induced Flows in a Flat Layer between Ferromagnetic Masses.- 8.8. Electrolytic Aluminium Production.- References.