Stability analysis of thin liquid film flow of second grade fluid over a stretching sheet

This work analyzes the linear stability of a thin second-grade liquid film flowing over a stretching sheet. The one-dimensional thin liquid film model of second-grade fluid based on long-wave theory is considered for this analysis. Taking into account the sinusoidal perturbation process, we carried out the linear stability analysis and obtained the linear growth rate, which defines the stability and instability of the fluid flow. Simulation results show the stabilizing effect on the flow for higher values of the second-grade non-Newtonian parameter, Froude number and the surface tension parameter. Furthermore, it is essential to note that the impact of the Froude number on the stability at high values of the second-grade parameter is very relevant. At the same time, at small parameter values of second grade, it has a feeble effect.