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Free-Space Fundamental Solution of a 2D Steady Slow Viscous MHD Flow

A. Sellier1, S. H. Aydin2, M. Tezer-Sezgin3
LadHyX, École Polytechnique, 91128 Palaiseau cedex. France.
Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, TURKEY.
Department of Mathematics, Middle East Technical University, 06531, Ankara, TURKEY.

Computer Modeling in Engineering & Sciences 2014, 102(5), 393-406. https://doi.org/10.3970/cmes.2014.102.393

Abstract

The fundamental free-space 2D steady creeping MHD flow produced by a concentrated point force of strength g located at a so-called source point x0 in an unbounded conducting Newtonian liquid with uniform viscosity µ and conductivity σ > 0 subject to a prescribed uniform ambient magnetic field B = Be1 is analytically obtained. More precisely, not only the produced flow pressure p and velocity u but also the resulting stress tensor field σ are expressed at any observation point x ≠ x0 in terms of usual modified Bessel functions, the vectors g, x-x0 and the so-called Hartmann layer thickness d = (√µ/σ)/B (see Hartmann (1937)). The resulting basic flows obtained for g either parallel with or normal to the magnetic field B are examined and found to exhibit quite different properties.

Keywords

MagnetoHydroDynamics, Two-dimensional flow, Stokes flow, Fundamental solution, Green tensor, Hartmann layer thickness, modified Bessel functions.

Cite This Article

Sellier, A., Aydin, S. H., Tezer-Sezgin, M. (2014). Free-Space Fundamental Solution of a 2D Steady Slow Viscous MHD Flow. CMES-Computer Modeling in Engineering & Sciences, 102(5), 393–406.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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