IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728,p-ISSN: 2319-765X, Volume 7, Issue 2 (Jul. - Aug. 2013), PP 05-14 www.iosrjournals.org www.iosrjournals.org 5 | Page Thermal Effects in Stokes’ Second Problem for Unsteady Second Grade Fluid Flow through a Porous Medium under the Effect Of A Magnetic Field K. Srinivasa Rao 1 , B. Rama Bhupal Reddy 2 , P. Koteswara Rao 3 1 Research Scholar, Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar, Guntur – 522510, A.P., India. 2 Associate Professor, Dept. of Mathematics, K.S.R.M. College of Engineering, Kadapa, A.P., India. 3 Professor, Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar, Guntur – 522510, A.P., India. Abstract: In this paper, we investigated the effects of magnetic field and thermal in Stokes’ second problem for unsteady second grade fluid flow through a porous medium. The expressions for the velocity field and the temperature field are obtained analytically. The effects of various pertinent parameters on the velocity field and temperature field are studied through graphs in detail. Keywords: Thermal Effects, Fluid Flow, Porous Medium, Magnetic field. I. Introduction The study of non-Newtonian fluid flows past an oscillatory plate has attracted much attention in recent years because of their practical applications. With the growing importance of non-Newtonian fluids in modern technology and industries, investigations of such fluids are desirable. A number of industrially important fluids including molten plastics, polymers, pulps, foods and fossil fuels, which may saturate in underground beds are exhibits non-Newtonian behavior. Due to complexity of fluids, several non-Newtonian fluid models have been proposed. In the category of such fluids, second grade fluid is the simplest subclass for which one can hope to gain an analytic solution. Exact analytic solutions for the flows of non-Newtonian fluids are most welcome provided they correspond to physically realistic situations, as they serve a dual purpose. First, they provide a solution to flow that has technical relevance. Second, such solutions can be used as checks against complicated numerical codes that have been developed for much more complex flows. Various studies on the flows of non- Newtonian fluids have been made under different physical aspects. However some recent contributions in the field may be mentioned (Fetecau and Fetecau [11]; Hayat et al. [14]; Chen et al.[6]; Fetecau and Fetecau[12]; Tan and Masuoka [25]). The flow of a viscous fluid caused by the sinusoidal oscillation of a flat plate is termed as Stokes’ second problem by Schliching [23]. Initially, both the plate and fluid are assumed to be at rest. At time t = 0+, the plate suddenly starts oscillating with the velocity 0 it Ue  . The study of the flow of a viscous fluid over an oscillating plate is not only of fundamental theoretical interest but it also occurs in many applied problems such as acoustic streaming around an oscillating body, an unsteady boundary layer with fluctuations (Tokuda) [26]. Penton [17] have presented a closed-form to the transient component of the solution for the flow of a viscous fluid due to an oscillating plate. Puri and Kythe [18] have discussed an unsteady flow problem which deals with non-classical heat conduction effects and the structure of waves in Stokes’ second problem. Much work has been published on the flow of fluid over an oscillating plate for different constitutive models (Erdogan [9]; Zeng and Weinbaum [28]; Puri and Kythe [19]; Asghar et al. [3]; Ai and Vafai [1]; Ibrahem et al. [15]). The use of electrically conducting fluids under the influence of magnetic fields in various industries has led to a renewed interest in investigating hydromagnetic flow and heat transfer in different geometrices. For example, Sparrow and Cess [24] have studied the effect of a magnetic field on the free convection heat transfer from surface. Buoyancy driven convection in rectangular enclosure with a transverse magnetic field was studied by Garandet et al. [13]. Chamkha [4] have investigated free convection effects on three-dimensional flow over a vertical stretching surface in the presence of a magnetic field. Erdogan [10] have analyzed the unsteady flow of viscous fluid due to an oscillating plane wall by using Laplace transform technique. Vajravelu and Rivera [27] discussed the hydromagnetic flow at an oscillating plate. Recently, Reddappa et al. [21] have investigated the Submitted Date 22 June 2013 Accepted Date: 27 June 2013