UNSTEADY FLOW IN A POROUS MEDIUM BETWEEN PARALLEL PLATES IN THE PRESENCE OF UNIFORM SUCTION AND INJECTION WITH HEAT TRANSFER Hazem Ali Attia 1 , Waleed Abd El-Meged 1 , W. Abbas 2 , Mostafa A. M. Abdeen 3 1 Department of Engineering Mathematics and Physics, Faculty of Engineering, Fayoum University, El-Fayoum-63415, Egypt 2 Basic and Applied Science Dept., College of Engineering and Technology, Arab Academy for Science, Technology, and Maritime Transport, Cairo, Egypt. 3 Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza 12211, Egypt (mostafa_a_m_abdeen@hotmail.com) Abstract The unsteady flow in porous medium of a viscous incompressible fluid bounded by two parallel porous plates is studied with heat transfer. A uniform and constant pressure gradient is applied in the axial direction whereas a uniform suction and injection are applied in the direction normal to the plates. The two plates are kept at constant and different temperatures and the viscous dissipation is not ignored in the energy equation. The effect of the porosity of the medium and the uniform suction and injection velocity on both the velocity and temperature distributions are investigated. Keywords: Unsteady flow, viscous incompressible fluid, heat transfer, porous medium, numerical solution. Introduction The flow of a viscous electrically conducting fluid between two parallel plates has important applications as in magnetohydrodynamic (MHD) power generators, MHD pumps, accelerators, aerodynamics heating, electrostatic precipitation, polymer technology, petroleum industry, purification of molten metals from non-metallic inclusions and fluid droplets-sprays [1]. The flow between parallel plates of a Newtonian fluid with heat transfer has been examined by many researchers in the hydrodynamic case considering constant physical properties [2-6]. The extension of the problem to the MHD case has attracted the attention of many authors [7-12]. In this paper, the transient flow with heat transfer through a porous medium of an incompressible viscous fluid between two infinite horizontal porous plates is investigated. A constant pressure gradient is applied in the axial direction and a uniform suction and injection is imposed in the direction normal to the plates. The flow through a porous medium deals with the analysis in which the differential equation governing the fluid motion is based on the Darcy’s law which accounts for the drag exerted by the porous medium [13-15].The two plates are maintained at two different but constant temperatures. This configuration is a good approximation of some practical situations such as heat exchangers, flow meters, and pipes that connect system components. The cooling of these devices can be achieved by utilizing a porous surface through which a coolant, either a liquid or gas, is forced. Therefore, the results obtained here are important for the design of the wall and the cooling arrangements of these devices.The linear partial differential equations of motion are