# 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:

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

where:

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.