Stability of conducting liquid flowing down an inclined plane at moderate Reynolds number in the presence of constant electromagnetic field

The stability of a conducting viscous film flowing down an inclined plane at moderate Reynolds number in the presence of electromagnetic field is investigated under induction-free approximation. Using momentum integral method a non-linear evolution equation for the development of the free surface is derived. The linear stability analysis of the evolution equation shows that the magnetic field stabilizes the flow whereas the electric field stabilizes or destabilizes the flow depending on its orientation with the flow. The weakly non-linear study reveals that both the supercritical stability and subcritical instability are possible for this type of thin film flow. The influence of magnetic field on the different zones is very significant, while the impact of electric field is very feeble in comparison.