Open Access

ARTICLE

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

A. Sellier¹, S. H. Aydin², M. Tezer-Sezgin³

1 LadHyX, École Polytechnique, 91128 Palaiseau cedex. France.
2 Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, TURKEY.
3 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.

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Keywords

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