Laminar pipe flow at the entrance into transverse magnetic field

High-resolution numerical simulations are conducted to analyze transformation of a liquid metal flow in a pipe at the entrance into a transverse magnetic field. The case of laminar flow, perfectly insulating pipe walls, and Hartmann number up to 200 is considered. The simulations reveal detailed structure of velocity and electric current fields and distribution of forces with particular attention given to the flow with an M-shaped velocity profile. They also establish criteria for accurate computations of laminar magnetohydrodynamic flows in strong non-uniform magnetic fields.