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.

## Definition

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:

1σ(∂𝐮∂t + (𝐮⋅∇)𝐮) = −∇p + ∇2𝐮 +σζQ (∇∧𝐁)∧𝐁,

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

The Chandrasekhar number is thus defined as:[1]

Q = B02d2μ0ρνλ

where  μ0 is the magnetic permeability,  ρ is the density of the fluid,  ν is the kinematic viscosity, and  λ is the magnetic diffusivity.  B0 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 = Ha2

## See also

* Rayleigh number
* Taylor number

## References

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

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Dimensionless numbers in fluid mechanics

* Archimedes
* Atwood
* Bagnold
* Bejan
* Biot
* Bond
* Brinkman
* Capillary
* Cauchy
* Chandrasekhar
* Damköhler
* Darcy
* Dean
* Deborah
* Dukhin
* Eckert
* Ekman
* Eötvös
* Euler
* Froude
* Galilei
* Graetz
* Grashof
* Görtler
* Hagen
* Iribarren
* Keulegan–Carpenter
* Knudsen
* Laplace
* Lewis
* Mach
* Marangoni
* Morton
* Nusselt
* Ohnesorge
* Péclet
* Prandtl
* magnetic
* turbulent
* Rayleigh
* Reynolds
* magnetic
* Richardson
* Roshko
* Rossby
* Rouse
* Schmidt
* Scruton
* Sherwood
* Shields
* Stanton
* Stokes
* Strouhal
* Stuart
* Suratman
* Taylor
* Ursell
* Weber
* Weissenberg
* Womersley

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