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| | The '''Magnetic Prandtl number''' ('''Pr<sub>m</sub>''') is a [[dimensionless quantity]] occurring in [[magnetohydrodynamics]] which approximates the ratio of momentum diffusivity ([[viscosity]]) and magnetic diffusivity. It is defined as: |
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| | :<math>\mathrm{Pr}_\mathrm{m} = \frac{\mathrm{Re_m}}{\mathrm{Re}} = \frac{\nu}{\eta} = \frac{\mbox{viscous diffusion rate}}{\mbox{magnetic diffusion rate}}</math> |
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| | where: |
| | * Re<sub>m</sub> is the [[magnetic Reynolds number]] |
| | * Re is the [[Reynolds number]] |
| | * ''ν'' is the momentum diffusivity ([[Viscosity#Kinematic_viscosity|kinematic viscosity]]) |
| | * ''η'' is the magnetic diffusivity |
| | |
| | At the base of the [[Sun]]'s [[convection zone]] the Magnetic Prandtl number is approximately 10<sup>–2</sup>, and in the interiors of planets and in liquid-metal laboratory dynamos is approximately 10<sup>–5</sup>. |
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| | ==See also== |
| | {{NonDimFluMech}} |
| | |
| | ==References== |
| | *''[http://prola.aps.org/abstract/PRL/v92/i5/e054502 Critical Magnetic Prandtl Number for Small Scale Dynamo]'', Schekochihin, A.A., ''et al.'' 2004, Physical Review Letters, 92, 5 |
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| | [[Category:Dimensionless numbers of fluid mechanics]] |
| | [[Category:Fluid dynamics]] |
| | [[Category:Magnetohydrodynamics]] |
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:
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.
See also
Template:NonDimFluMech
References