Finite amplitude long wave instability of a film of conducting fluid flowing down an inclined plane in presence of electromagnetic field

Stability characteristics of a thin conducting liquid film flowing down, on a non-conducting plane in the presence of the electromagnetic field is investigated under the assumption of a small magnetic Reynolds number. A surface evolution equation is derived by using the long-wave approximation method. A linear and non-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. It is found that both the subcritical instability and supercritical stability are possible in a finite amplitude regime. Two critical Hartmann numbers Mc and Mc>(Mc) are observed for subcritical and supercritical zones respectively. The existence of a subcritical unstable zone may be ruled out when Mc>Mc which is independent of other parameters whereas supercritical and explosive zones are possible till Mc