# Stuart number

The Stuart number (N), also known as magnetic interaction parameter, is a dimensionless number of fluids, i.e. gases or liquids.

It is defined as the ratio of electromagnetic to inertial forces, which gives an estimate of the relative importance of a magnetic field on a flow. The Stuart number is relevant for flows of conducting fluids, e.g. in fusion reactors, steel casters or plasmas.[1]

## Definition

${\displaystyle \mathrm {N} ={\frac {B^{2}L_{c}\sigma }{\rho U}}={\frac {\mathrm {Ha} ^{2}}{\mathrm {Re} }}}$

## References

1. ^ D. Lee; H. Choi (2001), "Magnetohydrodynamic turbulent flow in a channel at low magnetic Reynolds number", Journal of Fluid Mechanics, 439, pp. 367–394, doi:10.1017/S0022112001004621