Nonlinear equation governing flow in a saturated porous medium

Abstract

It is argued that the appropriate generalization of Darcy' s law when inertia effects are included takes the form Vp = -(Mk) V -(pc/kl/2)lv[v, div V = 0, where k is the permeability of the medium and the 'form drag constant' c is a coefficient which is independent of the pressure p, the seepage velocity V, and the density p and viscosity g of the fluid but which is dependent on the geometry of the medium. We formulate a nonlinear extension of Brinkman's self-consistent theory for the flow of a viscous fluid through a swarm of spherical particles. We equate the drag per unit volume given by the right hand side of the first of the above equations to the total drag ND on the N particles contained within that unit volume, in an infinite region 11, where D is the drag on a single particle placed in a velocity field v subject to p(v. V)v + grad p = •2¾ _ /.dk v -(cp/kl/2)lvlv, div v = 0, vlon is a prescribed constant, where g is the viscosity. Without solving these equations, we obtain an estimate for c from the known experimental drag law for a solid sphere placed in a uniform stream.

Retracted: Unsteady flow and heat transfer on a rotating disk in a porous medium

“…The unsteadiness is caused by the time-dependent angular velocity of the disk ( = A/t, A>0, t>0). The flow in the porous medium deals with the analysis in which the differential equation governing the macroscopic fluid motion is based on the Darcy's law which accounts for the drag exerted by the porous medium [8][9][10]. The flow is assumed axi-symmetric.…”

On the Hydrodynamics and Heat Convection of an Impinging External Flow Upon a Cylinder with Transpiration and Embedded in a Porous Medium

“…A two-dimensional Darcy-Brinkman model of transport of momentum along with the oneequation model of transport of thermal energy in cylindrical coordinate is employed in this study (Nield and Bejan 2006;Joseph et al 1982;Wu et al 2005). The following summarises the governing equations and the corresponding boundary conditions in the cylindrical coordinate system shown in Fig.…”

Effect of Porosity on the Transient MHD Generalized Couette Flow With Heat Transfer in the Presence of Heat Source and Uniform Suction and Injection

“…This is the total magnetic field acting on the fluid since the induced magnetic field is neglected. The fluid flows between the two plates in a porous medium where the Darcy model is assumed [12][13][14]. From the geometry of the problem, it is evident that all quantities are independent of x and z-coordinates apart from the pressure gradient dP/dx.…”

“…The fluid is acted upon by a constant pressure gradient, a uniform suction and injection and a uniform magnetic field perpendicular to the plates. The flow through a porous medium deals with the analysis in which the differential equation governing the fluid motion is based on the Darcy's law which accounts for the drag exerted by the porous medium [12][13][14]. The two plates are maintained at two different but constant temperatures.…”