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:
P r m = R e m R e = ν η = viscous diffusion rate magnetic diffusion rate {\displaystyle \mathrm {{Pr}_{m}} ={\frac {\mathrm {{Re}_{m}} }{\mathrm {Re} }}={\frac {\nu }{\eta }}={\frac {\text{viscous diffusion rate}}{\text{magnetic diffusion rate}}}}
where:
Rem 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.
See also Prandtl number
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