Stability analysis on the flow of thin second-grade fluid over a heated inclined plate with variable fluid properties

Abstract

This work investigates the thin film instability of a non-Newtonian second-grade fluid flowing down a heated inclined plane subject to linear variation of physical properties such as density, viscosity, thermal diffusivity, and surface tension concerning temperature. A nonlinear evolution equation for the description of the free surface is derived using long-wave approximation. The critical conditions for the onset of instability, such as critical Reynolds number, critical wave number, and the linear phase speed of wave propagation, are obtained by linear stability analysis through the normal mode approach. Further, the investigation on the weakly nonlinear stability characteristic of the fluid using a multi-scale approach reveals that both supercritical stability and subcritical instability exist. The influence of the non-Newtonian parameter and the variable fluid properties on subcritical, supercritical, unconditional, and explosive zones are discussed. It also discusses the amplitude of disturbances in subcritical and supercritical regions. The results show the destabilizing nature of the second-grade parameter.