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 named after mathematician John Trevor Stuart.^[1]

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.^[2]

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

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

• 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.