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.

► We consider the nonlinear differential equation arising from flow of a non-Newtonian fluid.
► We used the Fourier-Galerkin method to solve the nonlinear differential equation.
► The effect of the porous medium parameter on the drainage rate is explored.