The Magnetic Prandtl number (Pr
m) is a
dimensionless quantity
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that a ...
occurring in
magnetohydrodynamics
In physics and engineering, magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is a model of electrically conducting fluids that treats all interpenetrating particle species together as a single Continuum ...
which approximates the ratio of momentum diffusivity (
viscosity
Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...
) and
magnetic diffusivity
The magnetic diffusivity controls the rate of magnetic field diffusion.
Since its role in the evolution equation for the magnetic field is analogous to that of the viscosity for the velocity field, some authors refer to it as the 'magnetic viscos ...
. It is defined as:
:
where:
* Re
m is the
magnetic Reynolds number
* Re is the
Reynolds number
In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to ...
* ''ν'' is the momentum diffusivity (
kinematic viscosity
Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...
)
* ''η'' is the magnetic diffusivity
At the base of the
Sun
The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light a ...
's
convection zone
A convection zone, convective zone or convective region of a star is a layer which is unstable due to convection. Energy is primarily or partially transported by convection in such a region. In a radiation zone, energy is transported by radiation ...
the Magnetic Prandtl number is approximately 10
−2,
and in the interiors of planets and in liquid-metal laboratory dynamos is approximately 10
−5.
See also
*
Prandtl number
The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as:where:
* \nu : momentum d ...
References
{{NonDimFluMech
Dimensionless numbers of fluid mechanics
Fluid dynamics
Magnetohydrodynamics