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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.[1] 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:

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.

Prandtl number

References

Schekochihin, Alexander A.; Cowley, Steven C.; Maron, Jason L.; McWilliams, James C. (2004-02-03). "Critical Magnetic Prandtl Number for Small-Scale Dynamo". Physical Review Letters. American Physical Society (APS). 92 (5): 054502. arXiv:astro-ph/0308336. doi:10.1103/physrevlett.92.054502. ISSN 0031-9007.

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