Hartmann Number formula |
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\( Ma \;=\; B \cdot l \cdot \sqrt{ \dfrac{\sigma }{ \rho \cdot \mu } }\) (Hartman Number) \( B \;=\; \dfrac{ Ma \cdot \sqrt{ \rho \cdot \mu } }{ l \cdot \sqrt{ \sigma } }\) \( l \;=\; \dfrac{ Ma \cdot \sqrt{ \rho \cdot \mu } }{ B \cdot \sqrt{ \sigma } }\) \( \sigma \;=\; \dfrac{ \rho \cdot \mu \cdot Ma^2 }{ B^2 \cdot l^2 }\) \( \rho \;=\; \dfrac{ \sigma \cdot B^2 \cdot l^2 }{ \mu \cdot Ma^2 }\) \( \mu \;=\; \dfrac{ \sigma \cdot B^2 \cdot l^2 }{ \rho \cdot Ma^2 }\) |
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| 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.
