# Magnetic Prandtl number

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

where:

- Re
_{m}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

## References

*Critical Magnetic Prandtl Number for Small Scale Dynamo*, Schekochihin, A.A.,*et al.*2004, Physical Review Letters, 92, 5

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