Nonlinear stability analysis of film flow down a heated or cooled inclined plane with viscosity variation (Q1115268)

Nonlinear kinematic equations for film thickness which takes into account the effect of viscosity variation governed by the Arrhenius-type relation are used to investigate the nonlinear stability of film flows. The results show that cooling (heating) from the wall will stabilize (destabilize) the film flows both linearly and nonlinearly. The supercritical stability and subcritical instability both prove possible here with higher heating tending to reduce the threshold amplitude in the subcritical unstable region and increase the amplitude of supercritical waves. Stability is also influenced by the Prandtl number in the way that stability increases (decreases) as the Prandtl number increases when cooling (heating).