Magnetic Prandtl number

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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}}


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.

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