American Journal of Modeling and Optimization, 2013, Vol. 1, No. 3, 47-55 Available online at http://pubs.sciepub.com/ajmo/1/3/5 © Science and Education Publishing DOI:10.12691/ajmo-1-3-5 Finite Difference Technique for Unsteady MHD Periodic Flow of Viscous Fluid through a Planer Channel Pawan Preet Kaur 1 , SP Agrawal 2 , Anil Kumar 3,* 1 Deparment of Applied Mathematics, Lyallpur Khalsa College Engineering Jalandhar Punjab 2 Department of Civil Engineering, World Institute of Technology Sohna, Gurgaon, India 3 Department of Applied Mathematics, World Institute of Technology Sohna, Gurgaon, India *Corresponding author: dranilkumar06@yahoo.co.in Received October 24, 2013; Revised November 13, 2013; Accepted November 15, 2013 Abstract In the present paper we investigate an unsteady periodic flow of a viscous incompressible fluid through a porous planer channel in the presence of transverse magnetic field. The governing equations have been solved by finite difference method. The analytical expressions for the velocity profiles of the fluid have been obtained and numerical computations involved in the solution have been shown by tables. The effects of various parameters on the flow field have been discussed with the help of graphs and tables. Keywords: magnetohydrodynamics, planer channel, periodic flow, viscous fluid, Hartmann number, Finite difference technique Cite This Article: Pawan Preet Kaur, SP Agrawal, and Anil Kumar, “Finite Difference Technique for Unsteady MHD Periodic Flow of Viscous Fluid through a Planer Channel.” American Journal of Modeling and Optimization 1, no. 3 (2013): 47-55. doi: 10.12691/ajmo-1-3-5. 1. Introduction The fluid flow through porous medium has been of great interest for a long time. In the history of fluid flow through channels, Navier investigated a boundary condition of fluid slip at solid surface such that u u h y   ∂ =   ∂   , where h is the slip coefficient and u the velocity along x axis. In a case γ =0 indicates that there is no slip at the boundary. Sparrow and Cess (1961) investigated the effect of a magnetic field on a free convective heat transfer. Raptis et al. (1982) have been discussed hydro magnetic free convection flow through a porous medium between two parallel plates. Pal et al. (1984) investigated a longitudinal dispersion of tracer particles in a channel bounded by porous media using slip condition. Singh and Kumar (1993) investigated a free convective fluctuating flow through a porous medium with variable permeability. Aldoss et al. (1995) depicted a mixed convection flow from a vertical plate embedded in porous medium in the presence of magnetic field. Makinde (1995) investigated a laminar flow in a channel of varying width with permeable boundaries. Soltani and Yilmazar (1998) studied a slip velocity and slip layer thickness in flow of concentrated suspensions. Jha (1998) discussed an effect of applied magnetic field on transient free convective flow in a vertical channel. Helmy (1998) investigated MHD unsteady free convective flow past a vertical porous plate.Hossain et al. (1998) investigated heat transfer response of MHD free convective flow along a vertical plate to surface temperature oscillation. Kim (2000) discussed an unsteady MHD convective heat transfer past a semi-infinite vertical porous moving plate with variable suction. Yu and Ameel (2002) investigated a slip low heat transfer in rectangular micro channels. Derek et al. (2002) established an apparent fluid slip at hydrophibic microchannel walls. Sharma et al. (2002) investigated the flow between annular spaces surrounded by coaxial cylindrical porous medium. Steinruck (2003) investigated about the physical relevance of similarity solution of the boundary layer flow equation describing mixed convection flow along a vertical plate. Khaled and Vafai (2004) discussed the effect of slip condition on Stokes and Coutte flows due to an oscillating wall. Makinde and Mhone (2005) investigated a heat transfer to MHD Oscillatory flow in a channel filled with porous medium. Makinde and Osalusi (2006) discussed a MHD steady flow in a channel with slip at permeable boundaries. Kumar et al. (2007) investigated a viscous flow coaxial cylinder in the presence of magnetic field. Mahmood and Ali (2007) established the effect of slip condition on unsteady MHD oscillatory flow of a viscous fluid in a planer channel. Mishra et al. (2008) investigated a flow and heat transfer of a MHD viscoelastic fluid in a channel with stretching walls. Kumar et al. (2010) investigated Finite difference technique for reliable MHD steady flow through channels permeable boundaries. Kumar et al. (2013) investigated a Finite difference technique for reliable MHD steady flow through channels permeable boundaries. Kumar et al. (2013) made a Perturbation Technique of MHD Free Convection Flow through Infinite Vertical Porous Plate with Constant Heat