Stuart number explained

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.

Definition

N = (B ^{2} L _{c} \sigma)/(\rho U) = (Ha ^{2})/(Re)

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

Further reading

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