The Chandrasekhar number is usually denoted by the letter \ 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: :: \frac{1}{\sigma}\left(\frac{\partial^{}\mathbf{u}}{\partial t^{}}\ +\ (\mathbf{u} \cdot \nabla) \mathbf{u}\right)\ =\ - {\mathbf \nabla }p\ +\ \nabla^2 \mathbf{u}\ +\frac {\sigma}{\zeta} {Q}\ ({\mathbf \nabla} \wedge \mathbf{B}) \wedge\mathbf{B}, where \ \sigma is the
Prandtl number, and \ \zeta is the magnetic Prandtl number. The Chandrasekhar number is thus defined as: :: {Q}\ =\ \frac{{B_0}^2 d^2}{\mu_0 \rho \nu \lambda} where \ \mu_0 is the
magnetic permeability, \ \rho is the
density of the fluid, \ \nu is the
kinematic viscosity, and \ \lambda is the
magnetic diffusivity. \ B_0 and \ d are a characteristic magnetic field and a length scale of the system, respectively. It is related to the
Hartmann number, \ Ha, by the relation: :: Q\ {=}\ Ha^2\ ==See also==