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| 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]].
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| 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.
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| == Definition ==
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| The Chandrasekhar number is usually denoted by the letter <math>\ 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]]:
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| :: <math>\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}, </math>
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| where <math>\ \sigma</math> is the [[Prandtl number]], and <math>\ \zeta</math> is the magnetic Prandtl number.
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| The Chandrasekhar number is thus defined as:<ref>N.E. Hurlburt, P.C. Matthews and A.M. Rucklidge, "Solar Magnetoconvection," ''Solar Physics'', 192, p109-118 (2000)</ref>
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| :: <math> {Q}\ =\ \frac{{B_0}^2 d^2}{\mu_0 \rho \nu \lambda} </math>
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| where <math>\ \mu_0</math> is the [[magnetic permeability]], <math>\ \rho</math> is the [[density]] of the fluid, <math>\ \nu</math> is the [[kinematic viscosity]], and <math>\ \lambda</math> is the magnetic [[diffusivity]]. <math>\ B_0</math> and <math>\ d</math> are a characteristic magnetic field and a length scale of the system respectively.
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| It is related to the [[Hartmann number]], <math>\ H</math>, by the relation:
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| :: <math> Q\ {=}\ H^2\ </math>
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| ==References==
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| <references />
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| ==See also==
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| *[[Rayleigh number]]
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| *[[Taylor number]]
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| [[Category:Dimensionless numbers|Chandrasekhar number]]
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| [[Category:Magnetohydrodynamics]]
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I'm Yoshiko Oquendo. Kansas is where her house is but she requirements to move because of her family. Interviewing is how I make a residing and it's some thing I truly appreciate. One of the things I love most is greeting card gathering but I don't have the time recently.
My website; http://vendorportal.citypower.co.za/Activity-Feed/My-Profile/UserId/18066