Several benchmark problems recommended by the fusion community have been analysed using the ANSYS FLUENT magnetohydrodynamic (MHD) code and the results have been compared with available literature data. The selected problems are: (i) 2D fully developed laminar steady MHD flow inside the electrically insulating square duct, (ii) 3D laminar steady developing MHD flow in a non-uniform magnetic field and (iii) natural convection transient MHD flow. Fairly good agreement has been found between the simulation and reported results. The FLUENT has been found to be capable of predicting 3D MHD effects, which arise in the presence of the transverse fringing magnetic field. The natural convection phenomena under the uniform constant magnetic field have also been successfully captured by the code.