Fundamental solutions of MHD Stokes flow

TL;DR

This paper derives analytical fundamental solutions for magnetohydrodynamic Stokes flow in a magnetic field, describing flow past small particles and far from finite bodies, highlighting boundary layer effects and wake formations.

Contribution

It provides the first explicit analytical solutions for MHD Stokes flow, including velocity, pressure, and scalar potential distributions for force and current sources.

Findings

Solutions feature Hartmann boundary layer scale

Flow exhibits two parabolic wakes along magnetic field

Analytical solutions applicable to small particles and distant flows

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.