A modified Shkadov's model for thin film flow of a power law fluid over an inclined surface

A new evolution equation coherent up to order one in the long wave parameter is derived to describe the non-linear behavior of a thin film flow down an inclined plane of a power law fluid for small to moderate Reynolds numbers. The method we have used combines the lubrication theory and the weighted residual approach, with a suitable weighting function. That approach was first developed by Ruyer-Quil and Manneville (2000) for Newtonian fluids. The model has the advantages of both the Shkadov type approach far