Analytical Solution of the Problem of the Electrovortex Flow in the Hemisphere with Finite Size Electrodes in the Stokes Approximation
An analytical solution was obtained for a stationary axisymmetric motion equation for a flow caused by an inhomogeneous electric current propagating through an electrically conducting liquid. The problem was solved in the variables for vorticity and velocity vector potential in hemispherical geometry with the finite size electrodes. Stokes and electrodynamic approximations were used.
Keywordsvelocity conductive medium electric current magnetic field vector potential vorticity
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- 1.V. V. Boyarevich, Ya. Zh. Freiberg, E. I. Shilova, et al., Electrical Eddy Flows, Ed. by E.V. Shcherbinin (Zinatne, Riga, 1985).Google Scholar
- 4.V. G. Zhilin, Yu. P. Ivochkin, V. S. Igumnov, and A. A. Oksman, Teplofiz. Vys. Temp. 33, 5 (1995).Google Scholar
- 6.Yu. P. Ivochkin, I. O. Teplyakov, and D. A. Vinogradov, Magnetohydrodynamics 52, 277 (2016).Google Scholar
- 7.I. M. Yachikov, O. I. Karandaeva, and T. P. Larina, Simulation of Electrical Eddy Flows in the Bath of a DC Electric Arc Furnace (Magnitogorsk. Gos. Tekh. Univ., Magnitogorsk, 2008).Google Scholar
- 8.S. Yu. Khripchenko, Doctoral Dissertation in Engineering (Perm State Univ., Perm, 2007).Google Scholar
- 9.V. Shatrov and G. Gerbeth, Magnetohydrodynamics 48, 469 (2012).Google Scholar
- 13.H. Bateman and A. Erdélyi, Higher Transcendental Functions (McGraw-Hill, New York, 1953), Vol.1.Google Scholar
- 14.I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Fizmatgiz, Moscow, 1963).Google Scholar