A new model for thin film flow down an incline

An accurate modeling of stationary waves on a thin film of viscous, incompressible, Newtonian fluid has been developed. A system of evolution equations for the film height h and flow rate
Q has been obtained using the depth averaged kinetic energy balance, namely the energy integral method with an ellipse type profile. The study is motivated by
the success of energy integral method with ellipse type profile in effectively and accurately predicting the squeeze film force in squeeze flow problems and in predicting the
inertial effects in the performance of squeeze film dampers. The linear stability of the basic flow is analyzed and the results are compared with the existing models.