Magnetic Prandtl number
# Magnetic Prandtl number

The Magnetic Prandtl number $(Pr_m)$ 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:

* $Re_m$ is the magnetic Reynolds number
* Re is the Reynolds number
* ν is the momentum diffusivity (kinematic viscosity)
* η 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 $10^{−5}.$

