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 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 ${\displaystyle Q}$, and is motivated by a dimensionless form of the Navier-Stokes equation in the presence of a magnetic force in the equations of magnetohydrodynamics:

${\displaystyle \frac{1}{\sigma }(\frac{{\partial }^{}\mathbf{𝐮}}{\partial t^{}}+(\mathbf{𝐮}\cdot \mathrm{\nabla })\mathbf{𝐮})=-\mathrm{\nabla }p+{\mathrm{\nabla }}^2\mathbf{𝐮}+\frac{\sigma }{\zeta }Q(\mathrm{\nabla }\wedge \mathbf{𝐁})\wedge \mathbf{𝐁},}$

where ${\displaystyle \sigma }$ is the Prandtl number, and ${\displaystyle \zeta }$ is the magnetic Prandtl number.

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

${\displaystyle Q}=\frac{{B_0}^2{d}^2}{{\mu }_0\rho \nu \lambda }$

where ${\displaystyle {\mu }_0}$ is the magnetic permeability, ${\displaystyle \rho }$ is the density of the fluid, ${\displaystyle \nu }$ is the kinematic viscosity, and ${\displaystyle \lambda }$ is the magnetic diffusivity. ${\displaystyle B_0}$ and ${\displaystyle d}$ are a characteristic magnetic field and a length scale of the system respectively.

It is related to the Hartmann number, ${\displaystyle Ha}$, by the relation:

${\displaystyle Q=H{a}^2}$

• Rayleigh number
• Taylor number

0.00 (0 votes) Original source: https://en.wikipedia.org/wiki/Chandrasekhar number. Read more