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Research Papers: Fundamental Issues and Canonical Flows

An Analytical Study for Fluid Flow in Porous Media Imbedded Inside a Channel With Moving or Stationary Walls Subjected to Injection/Suction

[+] Author and Article Information
Hamid Reza Seyf

Department of Mechanical Engineering, Karaj branch,  Islamic Azad University, Karaj, IranHamid_seyf2001@yahoo.com

Seyed Moein Rassoulinejad-Mousavi

Department of Mechanical Engineering, Karaj branch,  Islamic Azad University, Karaj, Iran

J. Fluids Eng 133(9), 091203 (Sep 08, 2011) (9 pages) doi:10.1115/1.4004822 History: Received April 19, 2010; Revised February 21, 2011; Published September 08, 2011; Online September 08, 2011

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 ordinary 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 (α,β) and wall axial velocity coefficients (λ and γ) 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.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of a channel filled with porous medium with various boundary conditions

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Figure 2

Comparison between present velocity profiles and those of Tamoyol [29] for ub=1,ɛ=0.7,K=0.001m2 and H→∞

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Figure 3

(a), (b) Comparison of velocity profiles for clear fluid between present work and those of Zhu and Vafai [30]

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Figure 4

Comparison between analytical and numerical solutions in different test cases for ɛ=0.7

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Figure 5

Comparison between analytical and numerical solutions for velocity and pressure distribution in different test cases

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Figure 6

Effect of β on velocity profile in the channel with stationary walls

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Figure 7

(a), (b) Effect of Re on (a) velocity profile and (b) pressure distribution in the channel with stationary walls

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Figure 8

(a), (b) Effect of Da on (a) velocity profile and (b) pressure distribution in the channel with stationary walls

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Figure 9

Effect of Re on velocity profile in the channel when one of the upper or bottom walls is moving

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Figure 10

Effect of Da on velocity profile in the channel with moving walls

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