# Magnetic Prandtl number

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Magnetic Prandtl number

The Magnetic Prandtl number is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity (viscosity) and magnetic diffusivity. It is defined as:

$\mathit{Pr_m} = \frac{\mathit{Re_m}}{\mathit{Re}} = \frac{\nu}{\eta} = \frac{\mbox{viscous diffusion rate}}{\mbox{magnetic diffusion rate}}$

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.

## References

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