The Magnetic Prandtl number is a dimensionless quantity

Dimensionless quantity

In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension. It is thus a "pure" number, and as such always has a dimension of 1. Dimensionless quantities are widely used in mathematics, physics, engineering, economics, and...

 occurring in magnetohydrodynamics

Magnetohydrodynamics

Magnetohydrodynamics is an academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water or electrolytes...

 which approximates the ratio of momentum diffusivity (viscosity

Viscosity

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

) and magnetic diffusivity. It is defined as:


where:

• is the magnetic Reynolds number
  Magnetic Reynolds number
  The Magnetic Reynolds number is a dimensionless group thatoccurs in magnetohydrodynamics. It gives an estimate of the effects of magnetic advection to magnetic diffusion, and is typically defined by:where* U is a typical velocity scale of the flow...
  
  
• is the Reynolds number
• is the momentum diffusivity (kinematic viscosity)
• is the magnetic diffusivity

At the base of the Sun

Sun

The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

's convection zone

Convection zone

The convection zone of a star is the range of radii in which energy is transported primarily by convection. In the radiation zone, energy is transported by radiation...

the Magnetic Prandtl number is approximately , and in the interiors of planets and in liquid-metal laboratory dynamos is approximately .