The steady hydromagnetic flow in a porous medium of an incompressible viscous electrically conducting non-Newtonian fluid above an infinite rotating porous disk is studied with heat transfer. An external uniform magnetic field is applied perpendicular to the disk and a uniform injection or suction is applied through the surface of the disk. Numerical solutions of the nonlinear governing equatio...

We consider the fractional porous medium flow introduced by Caffarelli and Vazquez (2011) obtain local in time existence, uniqueness, blow-up criterion for smooth solutions. The proof is based on establishing a commutator estimate involving Laplacian operators.

Computational simulations of two-phase flow in porous media are used to investigate the feasibility of replacing a porous medium containing heterogeneities with an equivalent homogeneous medium. Simulations are performed for the case of infiltration of a dense nonaqueous phase liquid (DNAPL) in a water-saturated, heterogeneous porous medium. For two specific porous media, with periodic and rath...

We report an approach to fully visualize the flow of two immiscible fluids through a model three-dimensional (3-D) porous medium at pore-scale resolution. Using confocal microscopy, we directly image the drainage of the medium by the nonwetting oil and subsequent imbibition by the wetting fluid. During imbibition, the wetting fluid pinches off threads of oil in the narrow crevices of the medium...

A new formulation for shape and topology optimization in a Stokes flow is introduced. The investigated problem minimizes the total potential power of the flow. By combining a porous medium and a phase field approach we obtain a well-posed problem in a diffuse interface setting that can be reformulated into a problem without state equations. We can derive a sharp interface problem with zero perm...

A novel numerical method is presented for the simulation of flow in porous media, based on a mesoscopic-scale modelling using smoothed particle hydrodynamics. The method is demonstrated to provide encouraging results for both saturated and unsaturated porous media flow. The Darcy law is confirmed for low drift velocities in a saturated medium, while nonlinear behaviour is observed for higher va...

Magnetohydrodynamic(MHD) peristaltic flow of a Couple Stress Fluid through a permeable channel is examined in this investigation. The flow analysis is performed in the presence of an External Magnetic Field. Long wavelength and low Reynolds number approach is implemented. Mathematical expressions of axial velocity, pressure gradient and volume flow rate are obtained. Pressure rise, frictional f...

The Flow through saturated-unsaturated porous media is extremely important in various natural and industrial based applications. While the Darcy's law with various modifications are used to model the flow through a porous media, the flow through unsaturated porous media is largely based on conservation of mass and modified Darcy's law where non-linear relationship exists between the p...