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

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Hamid Reza Seyf ◽  
Seyed Moein Rassoulinejad-Mousavi
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Numerical Study ◽  
Nonlinear Ordinary Differential Equation ◽  
Flow In Porous Media ◽  
Analytical Models ◽  
Vapor Flow ◽  
Brinkman Equations ◽  
Various Boundary Conditions

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.

Conservation of Mass

1997 ◽  
Author(s):  
David Jon Furbish
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Unsaturated Flow ◽  
Flow In Porous Media ◽  
Degree Of Saturation ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Conservation Of Mass ◽  
Special Case

The concept of conservation of mass holds a fundamental role in most problems in fluid physics. For a given problem this concept is cast in the form of an equation of continuity. Such an equation describes a condition—conservation of mass—that must be satisfied in any formal analysis of a problem. Thus an equation of continuity often is one of several complementary equations that are solved simultaneously to arrive at a solution to a flow problem, for example, the flow velocity as a function of coordinate position in a flow field. (Typically these complementary equations, as we will see in later chapters, involve conservation of momentum or energy, or both.) Although we did not explicitly use this idea in analyzing the one-dimensional flow problems at the end of Chapter 3, it turns out that continuity was implicitly satisfied in setting up each problem. We will return to these problems to illustrate this point. We will develop equations of continuity for three general cases: purely fluid flow, saturated single-phase flow in porous media, and unsaturated flow in porous media. The most general of the three equations is that for unsaturated flow, where pores are partially filled with the fluid phase of interest, such that the degree of saturation with respect to that phase is less than one. We will then show that this equation reduces, in the special case in which the degree of saturation equals one, to a simpler form appropriate for saturated single-phase flow. Then, this equation for saturated flow could be reduced further, in the special case in which the porosity equals one, to a form appropriate for purely fluid flow. For pedagogical reasons, however, we shall reverse this order and consider purely fluid flow first. In addition we will consider conservation of a solid or gas dissolved in a liquid, and take this opportunity to introduce Fick’s law for molecular diffusion. For simplicity we will consider only species that do not react chemically with the liquid, nor with the solid phases of a porous medium. Most of the derivations below are based on the idea of a small control volume of specified dimensions embedded within a fluid or porous medium.

Two-phase gravity currents in porous media

2011 ◽  
Vol 678 ◽  
pp. 248-270 ◽  
Author(s):  
MADELEINE J. GOLDING ◽  
JEROME A. NEUFELD ◽  
MARC A. HESSE ◽  
HERBERT E. HUPPERT
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Current Model ◽  
Gravity Current ◽  
Capillary Forces ◽  
Gravity Currents ◽  
Flow In Porous Media ◽  
Two Phase ◽  
Residual Trapping

We develop a model describing the buoyancy-driven propagation of two-phase gravity currents, motivated by problems in groundwater hydrology and geological storage of carbon dioxide (CO2). In these settings, fluid invades a porous medium saturated with an immiscible second fluid of different density and viscosity. The action of capillary forces in the porous medium results in spatial variations of the saturation of the two fluids. Here, we consider the propagation of fluid in a semi-infinite porous medium across a horizontal, impermeable boundary. In such systems, once the aspect ratio is large, fluid flow is mainly horizontal and the local saturation is determined by the vertical balance between capillary and gravitational forces. Gradients in the hydrostatic pressure along the current drive fluid flow in proportion to the saturation-dependent relative permeabilities, thus determining the shape and dynamics of two-phase currents. The resulting two-phase gravity current model is attractive because the formalism captures the essential macroscopic physics of multiphase flow in porous media. Residual trapping of CO2 by capillary forces is one of the key mechanisms that can permanently immobilize CO2 in the societally important example of geological CO2 sequestration. The magnitude of residual trapping is set by the areal extent and saturation distribution within the current, both of which are predicted by the two-phase gravity current model. Hence the magnitude of residual trapping during the post-injection buoyant rise of CO2 can be estimated quantitatively. We show that residual trapping increases in the presence of a capillary fringe, despite the decrease in average saturation.

scholarly journals Numerical Study of the Effect of Magnetic Field on Nanofluid Heat Transfer in Metal Foam Environment

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Hamid Shafiee ◽  
Elaheh NikzadehAbbasi ◽  
Majid Soltani
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Volume Fraction ◽  
Numerical Study ◽  
Computational Simulation ◽  
Thermodynamic Efficiency ◽  
Two Phase

The magnetic field can act as a suitable control parameter for heat transfer and fluid flow. It can also be used to maximize thermodynamic efficiency in a variety of fields. Nanofluids and porous media are common methods to increase heat transfer. In addition to improving heat transfer, porous media can increase pressure drop. This research is a computational simulation of the impacts of a magnetic field induced into a cylinder in a porous medium for a volume fraction of 0.2 water/Al2O3 nanofluid with a diameter of 10 μm inside the cylinder. For a wide variety of controlling parameters, simulations have been made. The fluid flow in the porous medium is explained using the Darcy-Brinkman-Forchheimer equation, and the nanofluid flow is represented utilizing a two-phase mixed approach as a two-phase flow. In addition, simulations were run in a slow flow state using the finite volume method. The mean Nusselt number and performance evaluation criteria (PEC) were studied for different Darcy and Hartmann numbers. The results show that the amount of heat transfer coefficient increases with increasing the number of Hartmann and Darcy. In addition, the composition of the nanofluid in the base fluid enhanced the PEC in all instances. Furthermore, the PEC has gained its highest value at the conditions relating to the permeable porous medium.

SECOND-GRADE MAGNETOHYDRODYNAMIC FLUID FLOW IN POROUS MEDIA

2010 ◽  
Vol 13 (11) ◽  
pp. 1033-1037
Author(s):  
Muhammad R. Mohyuddin ◽  
S. Islam ◽  
A. Hussain ◽  
A. M. Siddiqui
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Flow In Porous Media ◽  
Second Grade ◽  
Magnetohydrodynamic Fluid

scholarly journals Statistical Inference Over Persistent Homology Predicts Fluid Flow in Porous Media

2019 ◽  
Vol 55 (11) ◽  
pp. 9592-9603
Author(s):  
Chul Moon ◽  
Scott A. Mitchell ◽  
Jason E. Heath ◽  
Matthew Andrew
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Statistical Inference ◽  
Persistent Homology ◽  
Flow In Porous Media
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