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