Unsteady Thin Film Third Grade Fluid on a Vertical Oscillating Belt using Adomian Decomposition Method

This work is an analytical study of unsteady thin film third grade fluid. The governing non linear partial differential equation has been solved analytically by Adomian Decomposition Method (ADM). The effect of model parameters on velocity profile have been plotted and discussed numerically as well as graphically. KEYWORDS: unsteady thin film fluid flow, lifting, drainage, Third grade, ADM. I INTRODUCTION Thin film fluid flows have large applications in engineering and industries. Like wire coating and fiber optics. The studies of Newtonian and non-Newtonian fluid films have been investigated by various researchers. The purpose of the present is to solve the non-linear differential equation of thin film flow on vertical moving and oscillating belt. In the best of author knowledge no attempt has been made to investigate thin film of third grade fluid on vertical moving and oscillating belt. Siddiqui et al. (1) investigated Sisko and Oldroyd 6- constant fluids on a vertical moving belt. They discussed the velocity field as well as volume flux and average velocity for different physical parameters. Mahmood et al. (2) discussed thin film of third grade fluid on an inclined plane the governing nonlinear equation for velocity are solved by perturbation technique and homotopy perturbation Method. Alam et al. (3- 4) investigated Johnson-Segalman thin film fluids on a vertical moving belt using Adomian Decomposition method (ADM). Shah et al. (5-6) discussed the exact solution of wire coating unsteady second grade fluid in a canonical die. They analyzed the motion of the fluid for small and large time levels. They have also discussed the effect of model parameters involved in the velocity profile. Aiyesimi et al. (7) investigated unsteady thin film flow of an electrically conducting third grade fluid down an inclined plane. They analyzed the effect of model parameters on velocity profile and temperature distributions. Ali et al. (8) investigated unsteady second grade fluid on oscillating vertical plate. They have been shown numerical results of skin friction and Nusselt number. Munson and Young (9) also investigated the thin-film flow of Newtonian fluids. Gul et al. (10) investigated the influence of a magnetic field on a vertical belt on the flow of an incompressible third grade electrically conducting fluid with slip boundary conditions. He studied the effect of various physical parameters. Ming Chu et al. (11) discussed lubricating thin film between two solid surfaces as three fixed layer. They discussed the non- Newtonian thin film elasto hydrodynamic lubrication (TFEHL) and the classical non- Newtonian elasto hydrodynamic lubrication (EHL).The effect of viscous dissipation and the temperature dependent thermal conductivity of thin film liquid of a non-Newtonian Ostwald-de Waele fluid over a porous stretching and horizontal surface is investigated by Chiu et al. (12). Asgar et al. (13) studied rotating fluid flow of third grade past a porous plate. They analyzed the effect of partial slip on the rotation of flow. Farooq et al. (14) discussed the exact solution of MHD flow over the porous sheet. The governing non linear partial differential equations are solved by using undetermined coefficient method and study the effect of different parameter on velocity profile and pressure. Ali et al. (15) studied the numerical solution of incompressible, viscous fluid flow and heat transfer over porous sheet. Sajid et al. (16) investigated thin film flow of fourth grade fluid on a vertical cylinder using Homotopy Analysis Method (HAM) to obtain the solution for the velocity profile and compare it with the exact solution. Ghanbarpour et al. (17) studied thin film flow of Sisko and Oldroyd 6 constant fluid on vertical moving belt and the governing nonlinear differential equations are solved by using (HAM). The related work can also be seen in (18-21). Husain and Ahmad et al (22-23) discussed different numerical techniques for the MHD flow on a stretching sheet in the presence of porosity. They show the effects of various parameters, Hartmann number, mass suction parameter, Prandtl number Pr and sink parameter on the velocity and temperature profiles. In 1992, Adomian (24-25) introduced the ADM for the approximate solutions for linear and non linear problems. Wazwaz (26-27) used ADM for the reliable treatment of Bratu-type and Emden-Fowler equations.