Stationary magnetic flow of a second grade fluid past a rotating plane: exact solutions

Exact solutions are given for the steady flow of a second grade fluid occupying the halfspace S past the plane z=0 uniformly rotating about a fixed normal axis (z-axis). No conditions on the sign of the material parameters characterizing the second grade fluid are imposed. The solutions are obtained in a velocity field of the form considered by Berker. Then a uniform magnetic field H_0 orthogonal to the (electrically non conducting) rotating plane is impressed. The induced magnetic field is supposed depending only on z. The results are compared with those corresponding to the Newtonian case and some numerical simulations are given.