# Chandrasekhar number

The **Chandrasekhar number** is a dimensionless quantity used in magnetic convection to represent ratio of the Lorentz force to the viscosity. It is named after the Indian astrophysicist Subrahmanyan Chandrasekhar.

The number's main function is as a measure of the magnetic field, being proportional to the square of a characteristic magnetic field in a system.

## Definition[edit]

The Chandrasekhar number is usually denoted by the letter , and is motivated by a dimensionless form of the Navier-Stokes equation in the presence of a magnetic force in the equations of magnetohydrodynamics:

where is the Prandtl number, and is the magnetic Prandtl number.

The Chandrasekhar number is thus defined as:^{[1]}

where is the magnetic permeability, is the density of the fluid, is the kinematic viscosity, and is the magnetic diffusivity. and are a characteristic magnetic field and a length scale of the system respectively.

It is related to the Hartmann number, , by the relation:

## References[edit]

**^**N.E. Hurlburt, P.C. Matthews and A.M. Rucklidge, "Solar Magnetoconvection,"*Solar Physics*, 192, p109-118 (2000)