The flow of a Carreau fluid down an incline with a free surface

This paper deals with the effect of a Carreau fluid flow down an inclined plane with a free surface. The fluid film is thin, so that lubrication approximation may be applied. In general, the flow equations resulting from the variable viscosity model must be solved numerically. However, when the viscosity variation is small, then an asymptotic approximation is possible. The full solutions for the velocity and temperature profiles are derived using the fourth order Runge-Kutta numerical method. The flow controlling parameters such as the non-dimensional viscosity variation parameter, the Biot and the Brinkman numbers, are found to have a profound effect on the resulting flow profiles.