Fundamental solutions of MHD Stokes flow

Abstract

A simple analytical solution is obtained for the MHD stokeslet in a homogeneous magnetic field. This solution represents the flow past a small particle and can also be interpreted as the flow sufficiently far away from a body of finite size. Fundamental solutions are found in terms of velocity, pressure and scalar potential distributions for the flows due to either a concentrated force or a current source. The former consists of two basic solutions for the force parallel and transverse to the magnetic field, respectively. All fundamental solutions have the characteristic length scale of the Hartmann boundary layer and two parabolic wakes developing along the magnetic field.