Hartmann Number
The Hartmann number, related to the Chandrasekhar number, is a dimensionless quantity used in magnetic convection to represent the ratio of the Lorentz force to the viscosity.
The Hartmann number equals the product of the magnetic flux density, characteristic length and the square root of the ratio of the electric conductivity to the product of the kinematic viscosity and the mass density.
Formula
![QuantityVariable["Ha", "HartmannNumber"] == QuantityVariable["B", "MagneticFluxDensity"]*QuantityVariable["l", "Length"]*Sqrt[QuantityVariable["σ", "ElectricConductivity"]/(QuantityVariable["ν", "KinematicViscosity"]*QuantityVariable["ρ", "MassDensity"])]](https://www.wolframcloud.com/objects/resourcesystem/marketplacestorage/resources/956/956eca22-398a-4fc8-b31a-39ad203e0adf/Webpage/FormulaImage.png "Copy to Clipboard")
| symbol | description | physical quantity |
|---|---|---|
| Ha | Hartmann number | "HartmannNumber" |
| B | magnetic flux density | "MagneticFluxDensity" |
| l | characteristic length | "Length" |
| ν | kinematic viscosity | "KinematicViscosity" |
| ρ | mass density | "MassDensity" |
| σ | electric conductivity | "ElectricConductivity" |