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

Abstract

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.