J. Appl. Environ. Biol. Sci., 5(3)22-30, 2015 © 2015, TextRoad Publication ISSN: 2090-4274 Journal of Applied Environmental and Biological Sciences www.textroad.com *Corresponding Author: Taza Gul, Department of mathematics, Abdul Wali K.U Mardan, KPK Pakistan Influence of Slip Condition on MHD Thin Film Flow of a Third Grade Fluid over a Vertical Belt with Temperature Dependent Viscosity Taza Gul 1 , Mubashir 2 , Muhammad Altaf Khan 1 , S.Islam 1 , R.A. Shah 3 , I. Khan 4 , M.Idrees 5 , S. Shafie 6 1 Department of mathematics, Abdul Wali K.U Mardan, KPK Pakistan 2 Department of mathematics, ISPaR/Bacha Khan University Charsaddah, KPK Pakistan 3 Department of mathematics, U.E.T Peshawar, KPK Pakistan 4 Faculty of Basic Sciences, College of Engineering Majmaah University, Majmaah, Saudi Arabia. 5 Department of mathematics, Islamia College University, Peshawar, KPK Pakistan 6 Department of mathematical Sciences, Faculty of science, University Teknology Malaysia, Johar Malaysia. Received: December 9, 2014 Accepted: February 16, 2015 ABSTRACT This paper investigates the influence of slip condition on unsteady magnetohydrodynamics (MHD) thin film flow of an incompressible third grade fluid with temperature dependent viscosity. Both cases of lift and drainage problems are considered. The problem is modeled in terms of non-linear partial differential equations with some physical initial and boundary conditions. Exact analytic solutions are obtained via two efficient techniques namely the Adomian decomposition method (ADM) and Optimal Homotopy Asymptotic Method (OHAM). Both of these solutions are presented graphically and compared. This comparison is also shown in tabular form. An excellent agreement is observed. The influence of various physical parameters on velocity and temperature profiles has also been studied graphically. KEYWORDS: Thin Film, MHD, Variable Viscosity, Slip Conditions, Lifting, Drainage, Heat transfer, Third Grade Fluid, ADM & OHAM. I. INTRODUCTION Recently the study of thin film flow of non-Newtonian fluids has received considerable attention of researchers in many fields of science and technology especially with the development of polymer industry, petroleum industries and other types of pulp industries. Siddiqui et al. [1, 2] studied the problem of thin film flow of Oldroyd 8-constant fluid on a vertically moving belt. Alam et al. [3] discussed the steady thin film flow of pseudo-plastic fluid on a vertical cylinder. The velocity profile have solved analytically by using OHAM. Miladinova et al. [4] examined the thin layer problems of power law model. Nemati et al. [5] modeled the problem of thin film flow of Sisko fluid and Oldroyd 6-constant fluid on moving vertical belt. Ali and Awais [6] studied the solution of unsteady second grade fluid through a porous medium using Laplace the transform method. Hayat and Sajid [7] developed HPM and HAM solutions for thin film flow of fourth grade fluid. The analysis of fluid flow and heat transfer on a thin liquid film has extensive consideration in several fields of engineering and chemical industries such as wire coating and fiber coating analysis, metal and polymer industry, food stuff processing, continuous casting, drawing of plastic sheets and exchangers. Noor et al. [8] studied the problem of heat transfer due to MHD thin liquid film. Abel et al. [9] investigated the numerical solution of heat transfer and MHD flow to laminar film liquid on horizontal surface using shooting method. Zheng et al. [10] studied Soret and Dufour effects on heat and mass transfer of MHD fluid over moving and oscillating surfaces. Due to the fact that these days non-Newtonian fluids have become quite prevalent in industry and engineering, several constitutive models are used to describe their diverse physical structures. Generally there are three non-Newtonian fluids models namely (i) the differential type, (ii) the rate type, and (iii) the integral type. But the most famous amongst them are the first two models. In this work, we will study the first model, the differential type and consider its subclass known as third grade fluid. This fluid model is described in terms of non-linear differential equations with some physical conditions. Amongst the several investigations on third grade fluid, Aiyesimi et al. [11, 12] examined the ohmic heat and MHD steady flow of third grade fluid down an inclined plane. They analyzed the effect of physical parameters like magnetic parameter and Brinkman number on the velocity and temperature profiles. Asghar et al. [13] studied the effect of variable suction on the flow of a third order fluid. Similarly, the steady flows of incompressible third grade fluid have been studied by Mohyuddin et al. [14]. Besides, Sajid et al. [15] investigated numerical solutions for third order fluid over a porous plate with slip boundary conditions. Currently the study of the non-Newtonian flows with slip boundary has become vigorous due to the wide uses of such fluids in food engineering, petroleum production, power engineering, and in polymer melt. Gul et al. [16, 17] investigated the lifting and drainage problems for MHD thin-film flow of a third grade fluid under the state of constant and variable viscosity. Hashmi et al. [18] studied the partial slip condition of a third grade fluid through an inclined plane. Nadeemand Awais [19] examined the unsteady thin film flow with variable viscosity. Sahoo and Poncet [20] analyzed the flow and heat transfer of a third grade fluid past an exponentially stretching sheet 22