# 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

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

## References

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