The Hartmann number measures the strength of magnetic coupling relative to viscous and resistive effects in a channel:Here is the channel half-width, the kinematic viscosity, the magnetic diffusivity and the electrical conductivity. In Hartmann flow, large produces thin magnetic-viscous wall layers and a flatter, slower core for fixed pressure gradient.
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The Hartmann number (Ha) is a dimensionless quantity used in magnetohydrodynamics (MHD) to characterize the behavior of electrically conducting fluids in the presence of a magnetic field. It is defined as the ratio of the magnetic force to the viscous force acting on the fluid. The Hartmann number is an important parameter in studies involving the flow of liquid metals, plasmas, and other conductive fluids in magnetic fields.