Abstract
The nonlinear stability of a conducting viscous film flowing through porous medium down an inclined plane in the presence of electromagnetic field is investigated under an induction-free approximation. Using the momentum integral method a nonlinear evolution equation for the development of the free surface is derived. A normal mode approach and the method of multiple scales are used to obtain the linear and nonlinear solutions. The linear stability analysis of the evolution equation shows that the electric field destabilizes the film flow while magnetic field stabilizes it at not too large an electric field, and these effects are stronger in the presence of porous medium than in its absence, whereas the porosity of porous medium and the medium permeability destabilize the film flow. The weakly nonlinear study reveals that both the subcritical instability and supercritical stable are possible for this type of thin film flow. The influence of magnetic field on the flow is strong, and its effect in the absence of porous medium is stronger than in the presence of porous medium, while the influence of electric field parameter on the flow is feeble in both cases of absence or presence of porous medium. The behaviors of threshold amplitude and nonlinear wave speed in both subcritical unstable and supercritical stable regions under the effects of all physical parameters have been discussed in detail.