MHD formulations for the liquid metal flow in a curved pipe of circular cross section

•A computational model is developed for the MFD flow in a curved channel.•The balance between the centrifugal and the electromagnetic forces is examined.•A secondary flow is generated due to the curvature of the duct.•The secondary flow is strongly suppressed as the Hartmann number increases.

The laminar fully developed magnetohydrodynamic (MHD) flow of a liquid metal into a curved pipe of circular cross section, subjected to a transverse external magnetic field, is studied. Three different formulations are used for the implementation of the electromagnetic variables. The extended Continuity Vorticity Pressure (CVP) numerical variational method for MHD flows is used for the coupling of the momentum and the continuity equation. Results are obtained for different values of the curvature (0–0.2) and of the Hartmann number (0–1000). The magnitude of the axial velocity is determined by the balance of the centrifugal and the electromagnetic forces. The results reveal the limits of applicability of the used electromagnetic models as the Hartmann number increases.