Hartmann number

Summary

The Hartmann number $\mathrm{Ha} = B_0 L \sqrt{\sigma / \mu}$ is the dimensionless number of magnetohydrodynamics that compares magnetic braking with viscous friction. Its square is the ratio of the Lorentz force to the viscous force. At large Hartmann number, flows of liquid metals across a magnetic field become flat in the core. They have thin boundary layers, the Hartmann layers, of thickness about $L / \mathrm{Ha}$.