The Stuart number (N), also known as magnetic interaction parameter, is a
dimensionless number
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
of
fluid
In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
s, 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
:
* ''B'' –
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
* ''L
c'' –
characteristic length
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by ...
* ''σ'' –
electric conductivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allow ...
* ''U'' – characteristic velocity scale
* ''ρ'' –
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
* Ha –
Hartmann number The Hartmann number (Ha) is the ratio of electromagnetic force to the viscous force, first introduced by Julius Hartmann (18811951) of Denmark. It is frequently encountered in fluid flows through magnetic fields. It is defined by:
: \mathrm = B L\s ...
* Re –
Reynolds number
In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be domi ...
References
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.
{{NonDimFluMech
Dimensionless numbers of thermodynamics
Fluid dynamics
Magnetohydrodynamics