Weight-of-conflict conjecture

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

$\mathrm{N}=\frac{B^2{L}_c\sigma }{\rho U}=\frac{{\mathrm{H}\mathrm{a}}^2}{\mathrm{R}\mathrm{e}}$

• B – magnetic flux density
• L_c – characteristic length
• σ – electric conductivity
• μ – dynamic viscosity, sometimes denoted as η
• Ha – Hartmann number
• Re – Reynolds number

References

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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.