Instability of the Non-Isothermal Inclined Film Flow of a Power-Law Fluid With Temperature Dependent Consistency

In this thesis we undertake a theoretical study of the flow stability of a liquid film with power-law rheology down a heated incline. We develop and implement a mathematical model for the flow that captures the variation with temperature of the rheological aspect of the fluid. We carry out a linear stability analysis and obtain Orr-Sommerfeld type equations for the evolution of infintesimal perturbations imposed on the equilibrium flow. We obtain asymptotic solutions based on the assumption of perturbations of long wavelength and small variation in viscosity with respect to temperature. We investigate the critical conditions for the onset of instability and determine the effect of a non-Newtonian reheology and the dependence of the fluid properties on temperature