Flow over a Finite Forchheimer Porous Layer with Variable Permeability (original) (raw)

MHD Darcy-Forchheimer Slip Flow in a Porous Medium with Variable Thermo-Physical Properties

MHD Darcy-Forchheimer Slip Flow in a Porous Medium with Variable Thermo-Physical Properties was studied. The governing partial differential equations are converted into nonlinear ordinary differential equations using a similarity transformation and solved numerically. The variable and thermal conductivity were studied. Different physical parameters' effects on temperature, velocity and concentration distribution are studied. The effects of Darcy-Forchheimer parameter, suction/blowing parameter, velocity slip and thermal slip parameter on the velocity, temperature and mass transfer rates nature are examined with the aid of graphs. Schmidt number and Soret number effect are also presented. The results shows that when the porosity parameter is increased, the velocity of the fluid decrease, while temperature profile and skin friction decreases. Also increasing the velocity slip parameter result in increase in velocity and Nusselt number whereas the concentration decreases in same case. Also the temperature at a point decreases with increase in thermal slip parameter while the skin friction decrease in both cases.

Analysis of generalized Forchheimer flows of compressible fluids in porous media

2009

This work is focused on the analysis of non-linear flows of slightly compressible fluids in porous media not adequately described by Darcy's law. We study a class of generalized nonlinear momentum equations which covers all three well-known Forchheimer equations, the so-called two-term, power, and three-term laws. The non-linear Forchheimer equation is inverted to a non-linear Darcy equation with implicit permeability tensor depending on the pressure gradient. This results in a degenerate parabolic equation for the pressure. Two classes of boundary conditions are considered, given pressure and given total flux. In both cases they are allowed to be unbounded in time. The uniqueness, Lyapunov and asymptotic stabilities, and other long-time dynamical features of the corresponding initial boundary value problems are analyzed. The results obtained in this paper have clear hydrodynamic interpretations and can be used for quantitative evaluation of engineering parameters. Some numerical simulations are also included.

Flow over a Darcy Porous Layer of Variable Permeability

Journal of Applied Mathematics and Physics, 2016

In this work we consider coupled-parallel flow through a finite channel bounded below by a porous layer that is either finite or infinite in depth. The porous layer is one in which Darcy's equation is valid under the assumption of variable permeability. A suitable permeability stratification function is derived in this work and the resulting variable velocity profile is analyzed. It will be shown that when an infinite porous layer is implemented, Darcy's equation must be used with a constant permeability.

A Revisit To Forchheimer Equation Applied In Porous Media Flow

A brief reference to various non-linear forms of relation between hydraulic gradient and velocity of flow through porous media is presented, followed by the justification of the use of Forchheimer equation. In order to study the nature of coefficients of this equation, an experimental programme was carried out under steady state conditions, using a specially designed permeameter. Eight sizes of coarse material and three sizes of glass spheres are used as media with water as the fluid medium. Equations for linear and non-linear parameters of Forchheimer equation are proposed in terms of easily measurable media properties. These equations are presented in the form of graphs as quick reckoners.

Fluid mechanics of the interface region between two porous layers

Applied Mathematics and Computation, 2002

Flow through and over a fluid-saturated porous layer is investigated. The flow through a porous channel (which is assumed to be governed by Forchheimer equation) is terminated by a porous layer possessing a different structure (the flow through which is governed by the Brinkman equation). At the interface between the physical regions, matching conditions on the velocity and shear stress are imposed. The flow through this configuration admits solutions which are linear combinations of polynomial and exponential functions. The effect of the Reynolds number and the Darcy numbers on the interface velocity is presented in this work. Ó

Pressure-driven flow in a channel with porous walls

Journal of Fluid Mechanics, 2011

The finite-Reynolds-number three-dimensional flow in a channel bounded by one and two parallel porous walls is studied numerically. The porous medium is modelled by spheres in a simple cubic arrangement. Detailed results on the flow structure and the hydrodynamic forces and couple acting on the sphere layer bounding the porous medium are reported and their dependence on the Reynolds number illustrated. It is shown that, at finite Reynolds numbers, a lift force acts on the spheres, which may be expected to contribute to the mobilization of bottom sediments. The results for the slip velocity at the surface of the porous layers are compared with the phenomenological Beavers-Joseph model. It is found that the values of the slip coefficient for pressure-driven and shear-driven flow are somewhat different, and also depend on the Reynolds number. A modification of the relation is suggested to deal with these features. The Appendix provides an alternative derivation of this modified relation.

Brinkman–Forchheimer-Darcy flow past an impermeable cylinder embedded in a porous medium

INCAS Buletin, 2015

For the flow past an impervious cylinder embedded in a fluid saturated porous medium only the linear (Darcy and Darcy-Brinkman) models were used. In this work, the flow past an impermeable cylinder embedded in a fluid saturated porous medium was studied numerically considering a nonlinear model valid (the Brinkman-Forchheimer-Darcy or Brinkman-Hazen-Dupuit-Darcy model). The flow is viscous, laminar, steady and incompressible. The porous medium is isotropic, rigid and homogeneous. The stream function-vorticity equations were solved numerically in cylindrical coordinates system. The influence of the cylinder Reynolds number, Darcy number and Forchheimer term on the velocities field and surface pressure was investigated for two boundary conditions on the surface of the cylinder: slip and no-slip.