J. Appl. Environ. Biol. Sci., 5(10)36-49, 2015 © 2015, TextRoad Publication ISSN: 2090-4274 Journal of Applied Environmental and Biological Sciences www.textroad.com *Corresponding Author: Wajid Ullah, Department of Mathematics, ISPaR Peshawar/Bacha Khan University KPK, Pakistan. OHAM Solution of MHD Third Grade Thin film Flow on a Vertical Lubricating Belt with Porosity Wajid Ullah 1 , Taza Gul 2 , Muhammad Altaf Khan 2 , S. Islam 2 , M. Jebran 1 , H. Rasheed 1 1 Department of Mathematics, ISPaR Peshawar/Bacha Khan University KPK, Pakistan. 2 Department of Mathematics, Abdul Wali khan university Mardan, Pakistan. Received: April 18, 2015 Accepted: September 3, 2015 ABSTRACT The study of heat transfer analysis of a thin film flows past on a vertical lubricating and porous belt have been considered in the presence of a uniform magnetic field. The governing nonlinear differential equations of third order fluid have been solved analytically by using Optimal Homotopy Asymptotic Method (OHAM). The comparison of the present work and published work is also shown graphically and numerically. The combined effects of heat and magnetic field have been observed in the thin film fluid motion where the effects of various physical parameters on the temperature and velocity fields have been studied physically. KEY WORDS: Lifting and drainage, Third grade fluid, MHD, OHAM, Porosity, Heat, Slip boundary conditions. 1. INTRODUCTION Heat transfer in thin films is widely used everywhere in civil and mechanical engineering, geophysical and biological sciences, elsewhere. The importance of its numerous applications is Seen in everyday life as well, such as reactor fluidization, wire coating, different food materials like sauce, ketchup and honey. The thin film flow of third grade fluid on a lubricating vertical belt investigated by Taza Gul et al. in [1]. The influence of various physical parameters has been shown in their work in the presence of MHD. The problem of heat dependents viscosity in thin film was examined by Nadeemand Awais[2]. Taza Gul et al [3]investigated thin film flow on vertical belt with variable viscosity. They used OHAM and ADM methods for both velocity and temperature fields. The comparisons of these methods have been studied also.Lavrik et al. [4] considered the problem of chemical and biological detection system for fluid. Khaled and vafai [5] also discussed heat transfer inside thin film flow with variable pressure. Munson and Young [6] discussed thin flow of Newtonian fluid. Taza Gul et al. [7, 8] investigated the flow of non-Newtonian single and double layer thin film fluids with no slip boundary conditions on a vertical belt.In their research the characteristic of volume flux, Skin friction and average velocities have been discussed. The combined effects of MHD and heat transfer have great importance in chemical processing. Related and attractive workmay be found in [9, 10]. Third grade fluid is awell-known model innon-Newtonian fluids which have their constitutive equations based on physically powerful theoretical foundations,because in this model the relation between stress and strain is notlinear. To solve real world problems, different approximate techniques have been used in mathematics, fluid mechanics, and engineering sciences. Some of the common methods are VIM [11,12], DTM [13, 14], HPM [15], HAM, and OHAM [16–19]. These methods deal with the nonlinear problems efficiently. During the last few years, lots of studies have been done through porous medium [20, 21]. Due to its large applications in various fields of science and technology, such as in oil recovery and heat storage etc. In the present work we study thin film flow of third grade fluid on a vertical lubricating and porous belt in the presence of MHD. The related problem was investigated by Tahir et al [22] replaced the open half space by porous half space. The flow modeling is based on modified Darcy’s Law for third grade fluid. k U p µφ − = ∇ 2. Basic Equations The governing equations are 0 . = ∇ U (1) 36