Hartmann number

The Hartmann number (Ha) is the ratio of electromagnetic force to the viscous force, first introduced by Julius Hartmann (1881 – 1951) of Denmark.^[1][2] It is frequently encountered in fluid flows through magnetic fields.^[3] It is defined by:

${\displaystyle \mathrm {Ha} =BL{\sqrt {\frac {\sigma }{\mu }}}}$

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

References

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

Further reading

• Jackson, J.D. (1975). "Magnetohydrodynamics and Plasma Physics". Classical Electrodynamics (Second ed.). John Wiley & Sons. ISBN 0-471-43132-X. LCCN 75009962. Retrieved 2020-05-16. Hartmann number is indicated by letter M in analogy with Mach number for aerodynamics.