1. Hamid Reza Seyf e-mail: Hamid_seyf2001@yahoo.comHamid_seyf2001@yahoo.com Seyed Moein Rassoulinejad-Mousavi Department of Mechanical Engineering, Karaj branch, Islamic Azad University, Karaj, Iran An Analytical Study for Fluid Flow in Porous Media Imbedded Inside a Channel With Moving or Stationary Walls Subjected to Injection/Suction This paper reports a new analytical solution for 2D Darcy-Brinkman equations in porous channels filled with porous media subjected to various boundary conditions at walls. The governing equations of fluid flow through porous medium are reduced to a nonlinear or- dinary differential equation (ODE) based on physics of fluid flow. The obtained ODE is solved analytically using homotopy perturbation method (HPM). The analytical models for velocity profile and pressure distribution along the length of channel are validated with data available in the open literature and an independent numerical study using finite volume method (FVM). It was shown that there is an excellent agreement between the presented models and the results of the CFD and previous works. Finally, the effects of Reynolds (Re) and Darcy (Da), numbers suction or injection parameters (a; b) and wall axial velocity coefficients (k and c) on velocity profiles and pressure drop in different cases are investigated. The models are applicable to analyze flow in channels filled with and without porous media for both moving and stationary walls and can be used to predict flow in micro and macro channels and over stretching sheets in porous medium as well as study of vapor flow in evaporator section of flat plate heat pipes. [DOI: 10.1115/1.4004822] 1Introduction The fluid flow and heat transfer in porous saturated channels with various cross sections have important applications in many fields of engineering such as filtration and purification processes, underground water resources, geological studies and petroleum industries. Therefore, in recent and past years, a considerable in- terest has been drawn to study thermal as well as flow characteris- tics inside channels filled with porous medium [1–12]. The research on fluid flow and heat transfer in porous or non- porous rectangular ducts subjected to injection or suction remain a central topic in heat transfer and fluid mechanics despite the con- siderable attention that it has received in the past. The vast major- ity of these investigations were directed toward laminar flow in parallel and circular channels subjected to uniform injection or suction at walls. For instance, Jankowski et al. [13] analytically and numerically studied the laminar flow in a porous channel with large suction along the permeable walls and a weakly oscillatory pressure. Attia [14] numerically solved the unsteady form of Nav- ier Stokes and energy equations of a viscous and incompressible liquid flow between two parallel plates subject to uniform injec- tion and suction at walls. They assumed that the thermal conduc- tivity and viscosity of fluid vary with temperature and the fluid is subject to constant pressure gradient. Attia [15] by use of finite difference method studied the unsteady Couette flow and heat transfer of an incompressible, electrically conducting and viscous fluid inside a porous channel with Hall current and ion-slip. Also, the effects of various parameters such as ion-slip, injection and suction, Hall current and magnetic field on velocity and tempera- ture fields were investigated. Sharma and Saini [16] analytically studied the effect of injection and suction on fluid flow and heat Contributed by the Fluids Engineering Division of ASME for publication in the J OURNAL OF F LUIDS E NGINEERING. Manuscript received April 19, 2010; final manuscript received February 19, 2011; published online September 8, 2011. Assoc. Editor: Neelesh A. Patabkar. transfer between two parallel plates with transpiration cooling using regular perturbation method; they found an approximate so- lution for sinusoidal injection at stationary plate and periodic suc- tion at moving plate. Recently, Layeghi and Seyf [17] analytically and numerically studied the fluid flow in an annular microchannel subjected to uniform injection. They used a similarity solution to transform the Navier Stokes equations to a nonlinear ODE and solved the ODE analytically using series solution method. Their model validated by numerical solution of full Navier Stokes equa- tion and they found complete agreement between analytical and CFD results. The governing equations of fluid flow inside channels filled with porous medium are a set of nonlinear PDEs and finding exact solution for them is very complex. But, in many practical instan- ces such as optimization analyses, parametric study and basic design, it is often required to obtain the reasonable estimate and trends of pressure drop and velocity profiles. Therefore an analyti- cal or approximate model that estimate the velocity profiles and pressure drop inside the channel will be of great value. Homotopy perturbation method (HPM) is one of the novel methods for solv- ing nonlinear differential equations which is used by various researchers in the recent years. In particular, Biazar et al. [18] used HPM to solve general form of porous medium equation. Dehghan and Shakeri [19] solved partial differential equation aris- ing in modeling of flow in porous media using homotopy pertur- bation method. Tasawar et al. [20] utilized HPM to solve thin-film flow of magnetohydrodynamic third grade fluid in a porous me- dium and compared the results with homotopy analysis method. Rafei et al. [21] implemented HPM to obtain the solutions of sys- tems of nonlinear ordinary and partial differential equations for laminar mixed convection in a vertical pipe, for a plane Couette flow with variable viscosity, and coupled Burger’s equations. Jafari et al. [22] applied HPM to solve nonlinear gas dynamics equation. Esmaeilpour and Ganji [23] studied generalized Couette Journal of Fluids Engineering Copyright V C 2011 by ASME SEPTEMBER 2011, Vol. 133 / 091203-1 DownloadedDownloaded 08 Sep 2011 to 213.233.160.15. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm