Effect of a non-uniform external magnetic field on the 3D stagnation-point flow

This paper is concerned with the study of the influence of a non-uniform external magnetic field on the steady three dimensional stagnation-point flow of a Newtonian fluid when the total magnetic field is parallel to the velocity at infinity. The fluid occupies the half-space over a solid obstacle which is a rigid uncharged dielectric at rest. We solve the problem both in the fluid and in the solid. We prove that the fluid flow is possible only in the axisymmetric case and it is described by an ordinary differential boundary value problem. The numerical integration shows that the viscosity appears only in a boundary layer whose thickness depends on the Reynolds and the Alfvén numbers.