Finite element solution of MHD duct flows

Abstract

In the present study a finite element Galerkin method is presented for the solution of MHD duct flows. The electromagnetic theory is used to derive the body force term in the Navier - Stokes equation and the ohmic dissipation term in the energy equation. A computer program is set up to solve the finite element formulation of these equations in the case of steady, incompressible, fully - developed flows in ducts with arbitrary cross-section. In this study, applications to rectangular duct geometries with ideally conducting and insulating boundaries are considered. Comparison of the results provides a good agreement with the other approximate and exact solutions found in the literature. It is observed that in flow of electrically conducting fluids, magnetic field applied in transverse direction retards the flow, inducing electric and magnetic fields in the fluid Recommendations towards improvement of the model and for general MHD flow problems are given for future research.