In this paper we are interested with a strongly coupled system of partial differential equations that modelizes free convection in a two-dimensional bounded domain filled with a fluid saturated porous medium. This model is inspired by the one of free convection near a semi-infinite impermeable vertical flat plate embedded in a fluid saturated porous medium. We establish the existence and unique...

Flow through a saturated, granular, porous medium can lead to internal erosion, preferential flow enhancement, and the formation of channels within the bulk of the medium. We examine this phenomenon using a combination of experimental observations, continuum theory and numerical simulations in a minimal setting. Our experiments are carried out by forcing water through a Hele-Shaw cell packed wi...

unsteady hydromagnetic generalised couette flow of a viscous, incompressible and electrically conducting fluid between two horizontal parallel porous plates darcian channel in the presence of a uniform transverse magnetic field taking hall current and ion-slip into account in a rotating system is investigated. an exact solution of the governing equations is obtained by laplace transform techniq...

Linear stability analysis of double diffusive convection in a horizontal porous layer saturated with fluid is examined by considering the effects of viscous dissipation, concentration based internal heat source and vertical throughflow. The basic steady state solution for Governing equations is derived. Linear stability analysis has been implemented numerically by using shooting and Runge-kutta...

The plane strain deformation of an isotropic, homogeneous, poroelastic medium caused by an inclined line-load is studied using the Biot linearized theory for fluid saturated porous materials. The analytical expressions for the displacements and stresses in the medium are obtained by applying suitable boundary conditions. The solutions are obtained analytically for the limiting case of undrained...

The various industrial, biological and engineering applications of flow of squeezing flow of fluid between parallel plates have been the impetus for the continued interest and generation renewed interests on the subject. As a part of the renewed interests, this paper presents the study of axisymmetric magnetohydrodynamic squeezing flow of nanofluid in porous media under the influence of slip bo...

The purpose of the present paper is to study an unsteady laminar flow of an incompressible conducting viscous dusty fluid between two infinitely non-conducting parallel plates, where above plate is bounded by porous medium. The flow is influenced by pulsatile pressure gradient, uniform magnetic field which is applied perpendicular to the plates and due to oscillations of the plates under the ef...

The present paper investigates penetrative convection in a bi-disperse porous medium. In particular, is modeled via quadratic dependence on the temperature for fluid density. For problem under examination, can occur only through secondary stationary motion since validity of principle exchange stabilities proved. Via linear instability analysis conduction solution, critical Rayleigh number onset...

a numerical investigation of forced convection in a channel with hot solid block inside a square porous block mounted on a bottom wall was carried out. the lattice boltzmann method was applied for numerical simulations. the fluid flow in the porous media was simulated by brinkman-forchheimer model. the effects of parameters such as porosity and thermal conductivity ratio over flow pattern and t...

We study the asymptotic behavior, with respect to high Péclet numbers, of the solutions of the nonlinear elliptic-parabolic system governing the displacement of one incompressible fluid by another, completely miscible with the first, in a porous medium. Using compensated compactness techniques, we obtain the existence of a global weak solution to the nonlinear degenerate elliptic-parabolic syst...