The Magnetic Prandtl number (Pr_m) is a dimensionless quantity occurring in

magnetohydrodynamics Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals, ...

which approximates the ratio of momentum diffusivity (

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

) and

magnetic diffusivity The magnetic diffusivity is a parameter in plasma physics which appears in the magnetic Reynolds number. It has SI units of m²/s and is defined as:W. Baumjohann and R. A. Treumann, ''Basic Space Plasma Physics'', Imperial College Press, 1997. :\e ...

. It is defined as: :

\mathrm_\mathrm = \frac = \frac = \frac

where: * Re_m is the

magnetic Reynolds number In magnetohydrodynamics, the magnetic Reynolds number (Rm) is a dimensionless quantity that estimates the relative effects of advection or induction of a magnetic field by the motion of a conducting medium to the magnetic diffusion. It is the ...

* Re is the Reynolds number * ''ν'' is the momentum diffusivity (

kinematic viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the int ...

) * ''η'' is the magnetic diffusivity At the base of the

Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...

convection zone A convection zone, convective zone or convective region of a star is a layer which is unstable due to convection. Energy is primarily or partially transported by convection in such a region. In a radiation zone, energy is transported by radiatio ...

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

{{NonDimFluMech Dimensionless numbers of fluid mechanics Fluid dynamics Magnetohydrodynamics

See also

References