Retraction Note to: Effect of electromagnetic field on the stability of viscoelastic fluid film flowing down an inclined plane

Abstract

The stability of thin electrically conducting viscoelastic fluid film flowing down on a non-conducting inclined plane in the presence of electromagnetic field is investigated under induction-free approximation. Surface evolution equation is derived by long-wave expansion method. The stabilizing role of Hartman number M (magnetic field) and the destabilizing role of the viscoelastic property \({\varGamma}\) and the electric parameter E on such fluid film are established through the linear stability analysis of the surface evolution equation. Investigation shows that at small values of Hartman number (M), the influence of electric parameter (E) on the viscoelastic parameter \({(\varGamma)}\) is insignificant, while for large values of M, E introduces more destabilizing effect at low values of \({\varGamma}\) than that at high values of \({\varGamma }\). An interesting result also perceived from our analysis is that the stabilizing effect of Hartman number (M) is decreasing with the increase of the values of \({\varGamma}\) and E, even it gives destabilizing effect after a certain high value of the electric field depending on the high value of \({\varGamma}\). The weakly nonlinear study reveals that the increase of \({\varGamma}\) decreases the explosive and subcritical unstable zones but increases the supercritical stable zone keeping the unconditional zone almost constant.