Hartmann layer ($\delta \sim L/H$)

A Hartmann layer is the thin viscous-magnetic boundary layer next to a wall crossed by the applied magnetic field. For channel half-width $L$ and large Hartmann number $H$, its thickness is $\delta \sim L/H=\sqrt{{\mu }_0\rho \nu \eta }/|B_0|$. It restores the no-slip boundary condition and the specified magnetic wall condition outside the nearly uniform Hartmann flow core.