effects of magnetic field direction and strength on square lid-driven cavity flow

in this study, the effects of strength and direction of the magnetic field on lid-driven cavity flow in the whole range of magnetic field strength variations, which already used in practice up to present (0 to 10 tesla), are studied. the governing equations, including conservative equations of momentum, continuity and magnetic field equations were solved numerically. momentum and continuity equations were solved by the finite volume method, using simple algorithm where the finite difference method was used for solving of magnetic field equation. in this research the effects of magnetic field on the velocity distribution, stream lines and vortex flow shows, the vortices of the cavity shrink up to 0.01 tesla where the uniform and vertical magnetic field applied from the bottom surface. for the magnetic field of 0.01 tesla, vortices of cavity flow disappear. higher values of magnetic field create larger vortices.