Hermite-Padé approximation approach to steady flow of a liquid film with adiabatic free surface along an inclined heat plate

The thermal stability of boundary layer flows of a temperature-dependent viscosity liquid film with adiabatic free surface along an inclined heated plate is studied using a special type of Hermite-Padé approximation approach. This semi-numerical scheme offers some advantages over solutions obtained by using traditional methods such as finite differences, spectral method, shooting method, etc. It reveals the analytical structure of the solution function and the important properties of overall flow structure including velocity field, temperature field, thermal criticality and bifurcations are discussed.