Magnetic Prandtl number

The Magnetic Prandtl number (Prm) is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity (viscosity) and magnetic diffusivity. It is defined as:


 * $$\mathrm{Pr}_\mathrm{m} = \frac{\mathrm{Re_m}}{\mathrm{Re}} = \frac{\nu}{\eta} = \frac{\mbox{viscous diffusion rate}}{\mbox{magnetic diffusion rate}}$$

where:
 * Rem is the magnetic Reynolds number
 * Re is the Reynolds number
 * &nu; is the momentum diffusivity (kinematic viscosity)
 * &eta; is the 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.