Hartmann Number formula |
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| \( Ma \;=\; B \cdot l \cdot \sqrt{ \dfrac{\sigma }{ \rho \cdot \mu } }\) | ||
| Symbol | English | Metric |
| \( Ha \) = Hartmann Number | \(dimensionless\) | \(dimensionless\) |
| \( B \) = Magnetic Field Strength | \( T \) | \(kg\;/\;s^2-A\) |
| \( l \) = Characteristic Length | \(ft\) | \(m\) |
| \( \sigma \) (Greek symbol sigma) = Conductivity | - | \(S\;/\;m\) |
| \( \rho \) (Greek symbol rho) = Density | \(lbm\;/\;ft^3\) | \(kg\;/\;m^3\) |
| \( \mu \) (Greek symbol mu) = Kinematic Viscosity | \(ft^2\;/\;sec\) | \(m^2\;/\;s\) |
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
- Low Hartmann Number (Ha << 1) - Viscous forces dominate, and the magnetic field has a negligible effect on the flow. The fluid behaves similarly to a non-magnetic flow.
- High Hartmann Number (Ha >> 1) - Magnetic forces dominate, often leading to the suppression of turbulence and the formation of a Hartmann layer, a thin boundary layer near solid walls where the velocity gradient is steep due to the magnetic field's damping effect.
In high Ha regimes, the thickness of the Hartmann layer scales inversely with the Hartmann number: δ ≈ L/Ha. This layer is where the transition from the bulk flow to the no-slip condition at the wall occurs.
The Hartmann number quantifies the competition between the Lorentz force (induced by the interaction of the magnetic field and the fluid’s motion) and the viscous forces that resist fluid motion. Think of the Hartmann number as a "magnetic dominance indicator." If Ha is small, the fluid "ignores" the magnetic field and flows freely. If Ha is large, the magnetic field "grabs" the fluid, restricting its motion and enforcing a more rigid structure.
