# Hartmann Number

on . Posted in Dimensionless Numbers

Hartmann number, abbreviated as Ha, a dimensionless number, is used to characterize the behavior of a conducting fluid (such as a plasma or a liquid metal) flowing through a magnetic field.  The Hartmann number helps quantify the relative importance of magnetic forces compared to viscous forces and inertia in the fluid flow.

### Hartmann number Interpretation

• High Ha  -  Magnetic effects dominate, causing the fluid to be strongly influenced by the magnetic field.  This can lead to phenomena like suppression of turbulence, stabilization of flow.
• Low Ha  -  Magnetic effects are less pronounced compared to viscous and inertial effects, and the fluid behavior resembles that of a non-conducting fluid.

The Hartmann number is a crucial parameter in various applications, including the study of plasma behavior in fusion reactors, liquid metal cooling systems, and astrophysical phenomena like the behavior of ionized gases in the presence of strong magnetic fields.

### Hartmann Number formula

$$Ma \;=\; B \; l \; \sqrt{ \sigma \;/\; \rho \; \mu }$$
Symbol English Metric
$$Ha$$ = Hartmann number $$dimensionless$$
$$B$$ = magnetic field strength $$T$$ $$kg\;/\;s^2-A$$
$$l$$ = characteristic length $$ft$$ $$m$$
$$\sigma$$  (Greek symbol sigma) = electrical conductivity of fluid - $$S\;/\;m$$
$$\rho$$  (Greek symbol rho) = density of fluid $$lbm\;/\;ft^3$$ $$kg\;/\;m^3$$
$$\mu$$  (Greek symbol mu) = kinematic viscosity of fluid $$ft^2\;/\;sec$$ $$m^2\;/\;s$$

Tags: Fluid Magnetic