Hartmann number

Surname

Hartmann number

{\ displaystyle {\ mathit {Ha}}}

dimension

dimensionless

definition

{\ displaystyle {\ mathit {Ha}} = B \ cdot L \ cdot {\ sqrt {\ frac {\ sigma} {\ mu}}}}

${\ displaystyle B}$	Magnetic flux density
${\ displaystyle L}$	Characteristic length
${\ displaystyle \ sigma}$	Electric conductivity
${\ displaystyle \ mu}$	dynamic viscosity

Named after

Julius Hartmann

scope of application

Magnetohydrodynamics

The Hartmann number ( ) is a dimensionless number of fluids , i.e. gases or liquids . It is defined as the ratio between magnetically induced and viscous frictional forces . ${\ displaystyle {\ mathit {Ha}}}$

The Hartmann number ( English Hartmann number ) - named after the Danish physicist Julius Hartmann (1881–1951) - plays an important role in the calculation and characterization of plasmas , such as those found in magnetohydrodynamics .

definition

{\ displaystyle {\ it {Ha}} = B \ cdot L \ cdot {\ sqrt {\ frac {\ sigma} {\ mu}}}}

${\ displaystyle B}$ - Magnetic flux density
${\ displaystyle L}$ - Characteristic length of the system
${\ displaystyle \ sigma}$ - Electrical conductivity
${\ displaystyle \ mu}$ - dynamic viscosity

The square of the Hartmann number gives the Chandrasekhar number : ${\ displaystyle Q}$

{\ displaystyle {\ mathit {Ha}} ^ {2} = Q}

Individual evidence

^ R. Moreau et al .: Julius Hartmann and His Followers: A Review on the Properties of the Hartmann Layer. In: Magnetohydrodynamics Springer Netherlands, 2007, pp. 155–170. ISBN 978-1-4020-4832-6
^ X. Shan, D. Montgomery: On the role of the Hartmann number in magnetohydrodynamic activity . In: Plasma Physics and Controlled Fusion . tape 35 , no. 5 , 1993, p. 619-631 , doi : 10.1088 / 0741-3335 / 35/5/007 .

↑ U. Burr, U. Müller: Rayleigh-Bénard convection in liquid metal layers under the influence of a vertical magnetic field . In: Physics of Fluids . tape 13 , 2001, p. 3247-3257 , doi : 10.1063 / 1.1404385 .

literature

Peter Kurzweil: The Vieweg Formula Lexicon. Vieweg + Teubner, Braunschweig 2002, p. 314 ISBN 3-528-03950-7 .

[1] R. Moreau et al .: Julius Hartmann and His Followers: A Review on the Properties of the Hartmann Layer. In: Magnetohydrodynamics Springer Netherlands, 2007, pp. 155–170. ISBN 978-1-4020-4832-6

[2] X. Shan, D. Montgomery: On the role of the Hartmann number in magnetohydrodynamic activity . In: Plasma Physics and Controlled Fusion . tape 35 , no. 5 , 1993, p. 619-631 , doi : 10.1088 / 0741-3335 / 35/5/007 .

[3] U. Burr, U. Müller: Rayleigh-Bénard convection in liquid metal layers under the influence of a vertical magnetic field . In: Physics of Fluids . tape 13 , 2001, p. 3247-3257 , doi : 10.1063 / 1.1404385 .