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 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/σB (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.