Spectral approximation for a nonlinear partial differential equation arising in thin film flow of a non-Newtonian fluid

Start-up thin film flow of fluids of grade three over a vertical longitudinally oscillating solid wall in a porous medium is investigated. The governing non-linear partial differential equation representing the momentum balance is solved by the Fourier–Galerkin approximation. The effect of the porosity, material constants as well as oscillations on the drainage rate and flow enhancement is explored and clarified.