An exact solution for the 3D MHD stagnation-point flow of a micropolar fluid

• We obtain an exact solution for the steady MHD 3D stagnation-point flow of a homogeneous, incompressible micropolar fluid.
• The region where the fluid motion occurs is bordered by the boundary of a rigid uncharged dielectric at rest.
• The total magnetic field is parallel to the velocity at infinity only if the flow is axisymmetric.
• The thickness of the boundary layer depends in a relevant way on RmRm and βmβm.
• The micropolar nature of the fluid reduces all the descriptive quantities of the flow in comparison to the Newtonian case.

The influence of a non-uniform external magnetic field on the steady three dimensional stagnation-point flow of a micropolar fluid over a rigid uncharged dielectric at rest is studied. The total magnetic field is parallel to the velocity at infinity. It is proved that this flow is possible only in the axisymmetric case. The governing nonlinear partial differential equations are reduced to a system of ordinary differential equations by a similarity transformation, before being solved numerically. The effects of the governing parameters on the fluid flow and on the magnetic field are illustrated graphically and discussed.