In this study, the Generalized Integral Transformation Technique (GITT) is used to describe the effect of buoyancy force and magnetic field on the vortex breakdown process generated by the rotation of an electrically conductive fluid. A magnetic field is positioned vertically to stabilize the swirling flow caused by the rotation of the bottom disc of a cylindrical recipient. Three fluids were compared in this study where the range of Richardson number is 0 ≤Ri ≤2.0. When the temperature difference is greater than Ri = 0.1, many layers become visible. These stratified fluid layers act as thermal insulators. In the case of stratification, the increased magnetic field reduces the total number of layers formed in the fluid. The influence of gradient temperature on the distribution of the layers generated is discussed. The limitations between the multilayer structure and the monolayer structure for three fluids are calculated as a function of the flow parameters.