J. Appl. Environ. Biol. Sci., 5(4)72-79, 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 WaliKhanUniversityMardan, KP Pakistan Unsteady Third Order Fluid Flow with Heat Transfer Between Two Vertical Oscillating Plates Taza Gul 1 , Inayatur Rehman 2 , S. Islam, Muhammad Altaf Khan 1 ,Wajid Ullah 2 , Zahir Shah 1 , 1 Department of mathematics, Abdul WaliKhanUniversityMardan, KP Pakistan 2 Department of mathematics, ISPaR/Bacha Khan University Charsadda, Pakistan. Received: December 31, 2014 Accepted: March 6, 2015 ABSTRACT In this research article we study an unsteady flow of a third grade fluid with heat. The flow phenomenon of Non- Newtonian fluid between two oscillating vertical plates.The problem is modeled in terms of non-linear partial differential equation. The model differential equations are solved analytically by using Adomain Decomposition Method (ADM). This method is frequently used for solving non-linear differential equations arise in various applied sciences and is found quite useful.The physical influence of various parameters on velocity is studied graphically and discussed. KEYWORDS: Unsteady, Temperature Field, Non-Newtonian, Adomain Decomposition Method (ADM). INTRODUCTION Non-Newtonian fluids has got attractive importance in research field, especially in mathematics, industry and engineering problems. Examples of non-Newtonian fluids include plastic manufacturing, food processing, movement of biological fluids, wire and fiber coating, paper production, gaseous diffusion, transpiration cooling, heat pipes etc. Several complex fluids such as polymer melts, paint, shampoo, mud, ketchup, blood, certain oils and greases, and many emulsions are involved in the class of nonNewtonian fluids. These fluids are described by a non- linear relationship between stress and the rate of deformation tensors and therefore several models have been proposed. Over the past few decades, there has been growing recognition of the fact that many fluids of industrial significance do not obey the Newtonian postulate of linear relationship between the shear stress and shear rate. Therefore, these fluids are known as non-Newtonian fluids. Common examples of such fluids are slurries, pastes, gels, molten plastics and lubricants containing polymer additives.Akyildiz et al [1] discussed a note on the flow of a non-Newtonian fluid film.Sankar et al [2] observed a non-Newtonian fluid flow model for blood flow through a catheterized artery Steady flow.Erdogan et al [3] study an unsteady flows of a non-Newtonian fluids. Moulic et al [4,5] dicussed Non-Newtonian Natural Convection flow.The unsteady flow of Non-Newtonian fluid was discussed in [6,7]. Qayyum Shah et al in [8] have investigated gravity driven flow of an unsteady second order fluid between two parallel and vertical oscillating plates.Taza Gul et al [9] observed a heat transfer analysis of thin film flow of an unsteady second grade fluid past a vertical oscillating belt. Sidra Abid et al [10] discussed an unsteady second grade fluid between two vertical plates with oscillating boundary conditions. A thin film flow of unsteady third grade fluid between two vertical plates when one of the plates oscillating and the other is stationary was discussed in [11,12]. Taza Gul et al [13] have observed a temperature dependent viscosity ofthin film flow of third grade fluid on a vertical belt. Ali et al [14] has investigated a Laplace transform method for unsteady thin film flow of a second grade fluid through a porous medium.Unsteady Couette Flow between Two Infinite Parallel Porous Plates in an Inclined Magnetic Field with Heat Transfer was discussed in [15, 16].Hameed et al [17]an unsteady flow of a non- Newtonian fluid on a porous plate. For the solution of nonlinear differential equation,Mabood et al [18] used Optimal Homotopy Asymptotic Method for the solution of differential equation various method are used. Aamer Khan et al [19] have observed OHAM Solution for the non-linear differential equation. Wazwaz et al [20] discussed a new modification of the Adomian Decomposition Method for linear and nonlinear operators.. Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations was used in [21, 23]. In the present article we will use Adomian decomposition method (ADM) for the solution of nonlinear differential equations of gravity driven flow of an unsteady third order fluid between two parallel and vertical oscillating plates. 72