Magnetic Prandtl number (diffusion rate)

Description

The Magnetic Prandtl number is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity (viscosity) and magnetic diffusivity. At the base of the Sun’s convection zone the Magnetic Prandtl number is approximately 10−2, and in the interiors of planets and in liquid-metal laboratory dynamos is approximately 10−5.<br />As another example, a magnetic Prandtl number of order unity is a widely accepted value for the thin accretion discs. Nevertheless this complicates the problem of launching jets: strong concentrations of magnetic field are required at the inner regions of the disc in order to launch jets, but a magnetic Prandtl number of order unity causes the field to diffuse away faster than it accretes inward.

Related formulas

Variables

PrmMagnetic Prandtl number (dimensionless) (dimensionless)
νmomentum diffusivity (kinematic viscosity) (m^2/s) (dimensionless)
ηmagnetic diffusivity (m^2/s) (dimensionless)