The problem of unsteady unidirectional hydromagnetic flow due to stress applied
at the free surface is studied here. The applied magnetic field is normal to the horizontal
boundary. The dynamics of fluid and electric currents are investigated as functions of magnetic
Prandtl number Pm , which measures the ratio of viscous diffusion to magnetic
diffusion. In contrast to hydrodynamic Rayleigh problem, the transient dynamics consists of
two diffusively growing layers as in the conventional MHD Rayleigh problem (see Dix [5]).
The viscous Hartmann layer becomes steady soon, while the magnetic diffusion layer diffuses
to infinity with Alfven speed. The electric currents generated in the Hartmann layer find a
return path in the magnetic diffusion layer. It may also be seen that the free surface Hartmann
layer is weak compared to rigid surface Hartmann layer.