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 India n 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.
The Chandrasekhar number is usually denoted by the letter [math]\displaystyle{ \ Q }[/math], 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 [math]\displaystyle{ \ \sigma }[/math] is the Prandtl number, and [math]\displaystyle{ \ \zeta }[/math] is the magnetic Prandtl number.
The Chandrasekhar number is thus defined as:[1]
where [math]\displaystyle{ \ \mu_0 }[/math] is the magnetic permeability, [math]\displaystyle{ \ \rho }[/math] is the density of the fluid, [math]\displaystyle{ \ \nu }[/math] is the kinematic viscosity, and [math]\displaystyle{ \ \lambda }[/math] is the magnetic diffusivity. [math]\displaystyle{ \ B_0 }[/math] and [math]\displaystyle{ \ d }[/math] are a characteristic magnetic field and a length scale of the system respectively.
It is related to the Hartmann number, [math]\displaystyle{ \ Ha }[/math], by the relation:
![]() | Original source: https://en.wikipedia.org/wiki/Chandrasekhar number.
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