The study of the thin-film flows have developed rapidly in the recent years for various applications, for example, lava flow, in coating process and in electronic devices. This thesis aims to study the travelling-wave similarity solution for unsteady threedimensional flows of thin films of Newtonian and non-Newtonian power-law fluids on an inclined plane. Specifically, flow around slender dry patch and flow of slender rivulet are considered. The flow is driven by gravity or shear stress at the free surface in the case of weak and strong surface-tension effects. The lubrication approximation is applied to the Navier-Stokes equations and continuity equation subject to the boundary conditions of no slip and no penetration, the balances of normal and tangential stress together with the kinematic condition to yield a governing partial differential equation
