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

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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Antoine Sellier, S. H. Aydin, M. Tezer-Sezgin. Free-Space Fundamental Solution of a 2D Steady Slow Viscous MHD Flow. Computer Modeling in Engineering and Sciences, Tech Science Press, 2014, 102 (5), pp.393-406. ⟨10.3970/cmes.2014.102.393⟩. ⟨hal-01178417⟩



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