Fundamental MHD creeping flow bounded by a motionless plane solid wall

This work determines the three-dimensional (3D) fundamental MHD creeping flow and associated electric potential produced by a concentrated source point, with given unit strength e, located in a conducting Newtonian liquid bounded by a plane solid and motionless wall and subject to a given uniform magnetic field normal to the wall. The wall is no-slip but may be either perfectly conducting or insulating. By linearity, the analysis is confined to the cases of e either normal or parallel to the wall. Such different wall natures and force orientations result in different flows and electric potential functions which are obtained using direct and inverse two-dimensional Fourier transforms. As a result, it has been possible to analytically express in closed-form each resulting fundamental flow and potential.