Effect of electromagnetic field on the wave dynamics of conducting viscoelastic fluid flow

This study focuses on the linear and nonlinear stability analysis of an electrically conducting viscoelastic fluid flowing over an inclined plane under the influence of an electromagnetic field. The constitutive equation for the non-Newtonian flow field follows the rheological properties of Walters' B″ model. The nonlinear evolution equation for the free surface is derived using the classical momentum integral approach. The linear stability analysis discloses that both viscoelasticity and the presence of an electric field destabilize the liquid film, while the magnetic field enhances its stability. The weakly nonlinear analysis reveals the existence of different flow zones in the vicinity of instability onset, which are significantly influenced when the viscoelasticity and the intensity of the electromagnetic field vary. The stronger magnetic field dissipates the weakly nonlinear wave amplitude, which is increased by the higher viscoelasticity and electric field. Furthermore, the numerical solution of the surface evolution equation ensures the occurrence of different types of permanent finite-amplitude waves in the supercritical stable zone. The long-time waveforms manifest themselves as either a permanent form of time-independent waves or as time-dependent modes with slight amplitude oscillations. Both viscoelasticity and electromagnetic field substantially influence the shape and amplitude of the wave. Overall, viscoelasticity and the electric field tend to destabilize and induce oscillatory long-time wave behavior, whereas the magnetic field counteracts these effects and aids stabilization.