This paper gives a proof of convergence for the approximate solution of an elliptic-hyperbolic system, describing the conservation of two immiscible incompressible phases flowing in a porous medium. The approximate solution is obtained by a mixed finite element method on a large class of meshes for the elliptic equation and a finite volume method for the hyperbolic equation. Since the considere...

A novel form of percolation is considered which is motivated by models of the displacement of one fluid by another from a porous medium. The physical idea is that if the displaced phase is incompressible, then regions of it which are surrounded by the displacing fluid become ‘trapped’ and cannot subsequently be invaded. We thus consider a new percolation process, ‘percolation with trapping’, in...

In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcy’s law. We show formation of singularities with infinite energy and for finite energy we obtain existence and uniqueness results of strong solutions for the sub-critical and critical cases. We prove global existence of weak solutions for different case...

In this paper melting of a carreau non-Newtonian PCM in the space between two concentric horizontal tubes, which is partially filled with porous material different shapes but same area, investigated numerically. A magnetic source located center geometry for process to occur presence ferro-hydrodynamic effects. Porous made Cu that covers cross-section inner tube. addition, and outer tubes satura...

In this paper we discuss an analytical study of hall current effects on unsteady magneto hydro dynamic flow of an incompressible electrically conducting couple stress fluid through a porous medium between parallel plates, taking into account pulsation of the pressure gradient effect and under the influence of a uniform inclined magnetic field of strength Ho inclined at an angle of inclination ...

This paper presents a theoretical study of blood flow through a tapered and overlapping stenosed artery under the action of an externally applied magnetic field. The fluid (blood) medium is assumed to be porous in nature. The variable viscosity of blood depending on hematocrit (percentage volume of erythrocytes) is taken into account in order to improve resemblance to the real situation. The go...

Nonlinear hydromagnetic two dimensional steady, laminar, boundary layer flow of a viscous, incompressible, electrically conducting and radiating liquid metal, with nonlinear radiation past a porous plate stretching with power-law velocity is analysed in the presence of a variable magnetic field. The liquid metal is assumed to be a gray, emitting, absorbing but non-scattering medium. Governing n...

The aim of this study is to present an exact analysis of combined effects of radiation and chemical reaction on the magnetohydrodynamic (MHD) free convection flow of an electrically conducting incompressible viscous fluid over an inclined plate embedded in a porous medium. The impulsively started plate with variable temperature and mass diffusion is considered. The dimensionless momentum equati...

In this study, a steady, incompressible, and laminar-free convective flow of a two-dimensional electrically conducting viscoelastic fluid over a moving stretching surface through a porous medium is considered. The boundary-layer equations are derived by considering Boussinesq and boundary-layer approximations. The nonlinear ordinary differential equations for the momentum and energy equations a...

We consider an immiscible incompressible two-phase flow in a porous medium composed of two different rocks so that the capillary pressure field is discontinuous at the interface between the rocks. This leads us to apply a concept of multi-valued phase pressures and a notion of weak solution for the flow which have been introduced in [Cancès & Pierre, SIAM J. Math. Anal, 44(2):966–992, 2012]. We...