Film flow with temperature dependent fluid properties over heated inclined surfaces

The gravity driven film flow down a heated inclined ramp and how it is affected by temperature dependent fluid properties is examined. The five temperature dependent fluid properties examined were: surface tension, mass density, dynamic viscosity, thermal conductivity and specific heat capacity. The investigation utilized a theoretical model based on the conservation of mass, momentum and energy, including the physically appropriate Newton's Law of Cooling to incorporate temperature changes on the surface of the film. A two-scale model of his system was also considered and a Benney equation was derived. A depth-integrated model was also considered and modified Integral Boundary layer (IBL) equations were generated. A linear stability analysis was carried out in all cases. Numberical simulations were carried out on the nonlinear modified IBL equations and their agreement to the linear approximations was good. The nonlinear analysis was also used to determine the evolution of the unstable flow.