The magnetic Prandtl number compares kinematic viscosity with magnetic diffusivity. It is the ratio of the viscous and magnetic diffusion coefficients; equivalently it is the magnetic Reynolds number divided by the Reynolds number when the same speed and length scale are used.
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The Magnetic Prandtl number (Pm) is a dimensionless quantity in magnetohydrodynamics (MHD) that characterizes the relative importance of magnetic diffusion to momentum diffusion in a conducting fluid.