italian journal of pure and applied mathematics – n. 31-2013 (161-168) 161 VARIATION OF PARAMETERS METHOD FOR THIN FILM FLOW OF A THIRD GRADE FLUID DOWN AN INCLINED PLANE Z.A. Zaidi COMSATS Institute of Information Technology University Road, Abbottabad Pakistan Department of Mathematics Faculty of Sciences HITEC University Taxila Cantt Pakistan S.U. Jan COMSATS Institute of Information Technology University Road, Abbottabad Pakistan Naveed Ahmed Umar Khan Department of Mathematics Faculty of Sciences HITEC University Taxila Cantt Pakistan Syed Tauseef Mohyud-Din 1 e-mail: syedtauseefs@hotmail.com Abstract. Thin film Flow of a third grade fluid down an inclined plane is considered. Non-linear differential equation which governs the flow model is obtained by using laws of conservation along with suitable similarity transforms. Variation of Parameters Method (VPM) is then employed to solve aforementioned differential equation. Analytical solu- tion is backed by RK-4 numerical solution and both show excellent agreement. Effects of flow parameters β and m on velocity field are demonstrated graphically with com- prehensive discussions. Keywords: non-Newtonian fluid, thin film flow, nonlinear equation, inclined plane, Variation of Parameters Method (VPM). 1 Corresponding author