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

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 x(0) in an unbounded conducting Newtonian liquid with uniform viscosity mu and conductivity sigma > 0 subject to a prescribed uniform ambient magnetic field B = Be-1 is analytically obtained. More precisely, not only the produced flow pressure p and velocity u but also the resulting stress tensor field sigma are expressed at any observation point x not equal x(0) in terms of usual modified Bessel functions, the vectors g, x - x(0) and the so-called Hartmann layer thickness d = (root mu/sigma)/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.