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

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

• B – magnetic induction
• L_c – characteristic length
• σ – electric conductivity
• U – characteristic velocity scale
• ρ – density
• Ha – Hartmann number
• Re – Reynolds number

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 

Further reading

• R. Moreau: Magnetohydrodynamics (= Fluid Mechanics and its Applications. Vol. 3). Kluwer Academic Publishers, Dordrecht u. a. 1990, ISBN 0-7923-0937-5, S. 127.
• P. A. Davidson: An Introduction to Magnetohydrodynamics. Cambridge University Press, Cambridge 2001, ISBN 0-521-79149-9, S. 97.