Duct flows in a transverse magnetic field

Abstract

The properties of duct flows in the presence of an applied magnetic field are among the basic problems in MHD. In laminar fully established regimes the component of the magnetic field which is perpendicular to the velocity is the only one to be relevant. And, since inertia is zero, the Reynolds number becomes irrelevant. Two particular examples, the Hartmann flow and the Couette MHD flow illustrate the general properties of parallel steady flows (section II). The important dimensionless number in this type of flow is the Hartmann number Ha = (ó/pv)^1/2 B ₀ a, the square of which represents the ratio between Laplace forces and viscous forces. This number is usually quite large in laboratory experiments and because of this, viscosity is not negligible only in thin boundary layers. In particular, along any wall perpendicular to the applied magnetic field, a Hartmann layer develops (section III), which is of primary importance since it controls the core flow. The electrical conductivity of the walls is also vital. It always arises from the condition of closure of electric current streamlines, and it governs the global electromagnetic resistance to this type of flow.