Numerical solution of buoyancy MHD flow with magnetic potential

Abstract

In this study, dual reciprocity boundary element method (DRBEM) is applied for solving the unsteady flow of a viscous, incompressible, electrically conducting fluid in channels under the effect of an externally applied magnetic field and buoyancy force. Magnetohydrodynamics (MHD) equations are coupled with the energy equation due to the heat transfer by means of the Boussinessq approximation. Then, the 2D non-dimensional full MHD equations in terms of stream function, temperature, magnetic potential, current density and vorticity are solved by using DRBEM with implicit backward Euler time integration scheme. Numerical results are obtained utilizing linear boundary elements and linear radial basis functions approximation for the inhomogeneities, in a double lid-driven staggered cavity and in a channel with backward facing step. The results are given for several values of problem parameters as Reynolds number (Re), magnetic Reynolds number (Rem), Hartmann number (Ha) and Rayleigh number (Ra). With the increase in Rem, both magnetic potential and current density circulate near the abrupt changes of the walls. The increase in Ha suppresses this perturbation, and forces the magnetic potential lines to be in the direction of the applied magnetic field. The boundary layer formation through the walls emerge in the flow and current density for larger values of Ha.