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