Laminar falling liquid film with variable viscosity along an inclined heated plate

This paper examines the steady-state solutions of a laminar falling variable viscosity liquid film along an inclined heated plate. The upper surface of the liquid film is considered free with uniform temperature. Analytical solutions are constructed for the governing nonlinear boundary-value problem using perturbation technique together with a special type of Hermite–Padé approximants and important properties of the velocity and temperature fields including bifurcations and thermal criticality are discussed.