Buoyancy effects on the 3D MHD stagnation-point flow of a Newtonian fluid

This work examines the steady three-dimensional stagnation-point flow of an electrically conducting Newtonian fluid in the presence of a uniform external magnetic field H0 under the Oberbeck–Boussinesq approximation. We neglect the induced magnetic field and examine the three possible directions of H0 which coincide with the directions of the axes. In all cases it is shown that the governing nonlinear partial differential equations admit similarity solutions. We find that the flow has to satisfy an ordinary differential problem whose solution depends on the Hartmann number M, the buoyancy parameter λ and the Prandtl number Pr. The skin-friction components along the axes are computed and the stagnation-point is classified. The numerical integration shows the existence of dual solutions and the occurrence of the reverse flow for some values of the parameters.