stability of an electrically conducting fluid flow between coaxial cylinders under magnetic field

This research aims to investigate the vortex breakdown zone, the stability margin, and the fluid layers of the rotating flow between two vertical coaxial cylinders under the effect of thermal gradient and an axial magnetic field. the governing navier-stokes, temperature, and potential equations are solved using the finitevolume method. three combinations of aspect ratios (γ) and reynolds numbers (re) are compared. the pumping action sets up a secondary circulation along the meridional plane of the annular gap. for certain combinations, the vortex breakdown bubble occurred near the inner wall. bifurcation in form of multiple fluid layers becomes apparent when the temperature difference exceeds a critical value. these fluid layers play the role of thermal insulation and limit the heat transfer between the hot top and cold bottom of the coaxial cylinders. both the vortex breakdown and fluid layers could be suppressed by the magnetic field; the increasing of hartmann number (ha) would reduce the number of fluid layers. diagrams represent the effect of increasing richardson number (ri) on fluid layers are established. then stability diagrams corresponding to the transition from the multiple fluid layers zone to the one fluid layer zone for increasing prandtl number (pr) are obtained.