Hartmann number explained

The Hartmann number (Ha) is the ratio of electromagnetic force to the viscous force, first introduced by Julius Hartmann (18811951) of Denmark.^{[1] [2]} It is frequently encountered in fluid flows through magnetic fields.^[3] It is defined by:

Ha = B L\sqrt{ (\sigma)/(\mu) }where

• B is the magnetic field intensity
• L is the characteristic length scale
• σ is the electrical conductivity
• μ is the dynamic viscosity

See also

• Magnetohydrodynamics

Further reading

• Book: Jackson, J.D.. Classical Electrodynamics. John Wiley & Sons. 1975. 0-471-43132-X. Second. Magnetohydrodynamics and Plasma Physics. 75009962. 2020-05-16. https://archive.org/stream/ClassicalElectrodynamics2nd#page/n495/mode/2up. Hartmann number is indicated by letter M in analogy with Mach number for aerodynamics.

Notes and References

1. Book: Moreau. René. Magnetohydrodynamics: Historical Evolution and Trends. Molokov. Sergei S.. Springer. 2007. 978-1-4020-4833-3. Molokov. Sergei S.. Fluid Mechanics and Its Applications. 80. 155–156. Julius Hartmann and His Followers: A Review on the Properties of the Hartmann Layer. 10.1007/978-1-4020-4833-3_9. René Moreau. Moreau. René. Moffatt. H. Keith. Keith Moffatt.
2. Hunt. J.C.R.. Shercliff. J.A.. January 1971. Magnetohydrodynamics at High Hartmann Number. Annual Review of Fluid Mechanics. 3. 37–62. 1971AnRFM...3...37H. 10.1146/annurev.fl.03.010171.000345.
3. Book: Cramer. Magnetofluid Dynamics for Engineers and Applied Physicists. Pai. Shih-i. Scripta Publishing Company. 1973. 0-07-013425-1. 73009936.