Numerical Investigation of the Plane Problem of Convection of a Multicomponent Fluid in a Porous Medium

Scenarios of the development of continuous families of steady-state regimes branching off from mechanical equilibrium are investigated for the plane problem of filtrational convection of a multicomponent fluid saturating a porous block of rectangular cross-section. Convection of two- and three-component fluids is considered and unidirectional and differently directed vertical temperature and concentration gradients are analyzed. A new scenario of the formation of a continuous family of steady-state solutions realized in the case of oscillatory instability of mechanical equilibrium is studied.     

Casson Fluid Flow Due to Non-Coaxial Rotation of a Porous Disk and the Fluid at Infinity Through a Porous Medium

The flow of the Casson fluid due to non-coaxial rotation of a disk and the fluid at infinity is investigated. Partial differential equations are made dimensionless and coupled. The exact solution of the resultant nonlinear initial-boundary-value problem is solved by applying the Laplace transform. The shear stresses at the disk surface and the steady state stresses are computed. The effects of dimensionless parameters on the dimensionless primary and secondary velocities are analyzed.     

Numerical Investigation of the Second Transition in the Problem of Plane Convective Flow through a Porous Medium

The problem of convective flow through a porous medium in a plane rectangular vessel with a linear temperature profile steadily maintained on the boundary is considered. Single-parameter families of steady-state regimes resulting from the existence of cosymmetry of the corresponding differential equations are investigated using the Galerkin method. The onset and development of instability on these families and the characteristics of convective regimes as functions of the seepage Rayleigh number and the rectangle side ratio are studied. It is shown that the number of regimes which lose stability, the instability type, the number of convective rollers developed, and the heat transfer depend significantly on the vessel geometry. Several bifurcations of single-parameter families of steady-state regimes are identified and investigated.     

Poiseuille Flow of a Third Grade Fluid in a Porous Medium

Effects of porous medium have been investigated on the steady flow of a third grade fluid between two stationary porous plates. The continuity and momentum equations along with modified Darcy??s law are used for the development of mathematical problem. The governing nonlinear problem is solved by a homotopy analysis method. The dimensionless velocity and shear stresses at the plates are analyzed.     

Chaos in the Convective Flow of a Fluid Mixture in a Porous Medium

The results of the study of the global behaviour of the convective flow of a binary mixture in a porous medium are presented. Bifurcation diagram, fixed points, periodic, chaotic solutions, stable and unstable manifolds, and basins of attraction have been calculated. Different behaviours (chaos, undecidable behaviour, etc.) have been found.     

Unsteady Free Convection Boundary Layer Flows of a Bingham Fluid in Cylindrical Porous Cavities

Transport in Porous Media - We consider two unsteady free convection flows of a Bingham fluid when it saturates a porous medium contained within a vertical circular cylinder. The cylinder is...     

Brinkman Flow of a Viscous Fluid Through a Spherical Porous Medium Embedded in Another Porous Medium

An analytical investigation for a two-dimensional steady, viscous, and incompressible flow past a permeable sphere embedded in another porous medium is presented using the Brinkman model, assuming a uniform shear flow far away from the sphere. Semi-analytical solutions of the problem are derived and relevant quantities such as velocities and shearing stresses on the surface of the sphere are obtained. The streamlines inside and outside the sphere and the radial velocity are shown in several graphs for different values of the porous parameters \({\sigma _1 =(\mu /\tilde {\mu }) (a/\sqrt{K_1 })}\) and \({\sigma _2 =(\mu /\tilde {\mu }) (a/\sqrt{K_2 })}\) , where a is the radius of the sphere, μ is the dynamic viscosity of the fluid, \({\tilde {\mu }}\) is an effective or Brinkman viscosity, while K ₁ and K ₂ are the permeabilities of the two porous media. It is shown that the dimensionless shearing stress on the sphere is periodic in nature and its absolute value increases with an increase of both porous parameters σ ₁ and σ ₂.     

Diffuse-interface Modeling of Two-phase Flow for a One-component Fluid in a Porous Medium

The diffuse-interface (DI) model for the two-phase flow of a one-component fluid in a porous medium has been presented by Papatzacos [2002, Transport Porous Media 49, 139–174] and by Papatzacos and Skjæveland [2004, SPE J. (March 2004), 47–56]. Its main characteristics are: (i) a unified treatment of two phases as manifestations of one fluid with a van der Waals type equation of state, (ii) the inclusion of wetting, and (iii) the absence of relative permeabilities. The present paper completes the presentation by including the implementation of wetting in the general case of a mixed-wet rock. As a result of this implementation, some statements are made about capillary pressure, confirming similar statements by Hassanizadeh and Gray [1993, Water Resour. Res. 29, 3389–3405]. As an application of the model, we show that relative permeabilities depend on the spatial derivatives of the saturation.     

Unsteady Flow of an Oscillating Porous Disk and a Fluid at Infinity

An exact analytic solution of the unsteady Navier–Stokes equations is obtained for the flow caused by the non-coaxial rotations of a porous disk and a fluid at infinity. The porous disk is executing oscillations in its own plane with superimposed injection or suction. An increasing or decreasing velocity amplitude of the oscillating porous disk is also discussed. Further, it is shown that a combination of suction/injection and decreasing/increasing velocity amplitude is possible as well. In addition, the flow due to porous oscillating disk and a fluid at infinity rotating about an axis parallel to the z-axis is attempted as a second problem. Sommario. Si studia il flusso non stazionario prodotto dall'oscillazione di un disco poroso in un fluido e si fornisce una soluzione analitica delle equazioni di Navier–Stokes. Si discute l'effetto di una suzione/iniezione e di una variazione sull'ampiezza della velocità' di oscillazione. Infine si studia il flusso dovuto alle oscillazioni non coassiali di un disco poroso e di un fluido all'infinito.     

Flow of a Weakly Conducting Fluid in a Channel Filled with a Porous Medium

We investigate the fully developed flow in a fluid-saturated porous medium channel with an electrically conducting fluid under the action of a parallel Lorentz force. The Lorentz force varies exponentially in the vertical direction due to low fluid electrical conductivity and the special arrangement of the magnetic and electric fields at the lower plate. Exact analytical solutions are derived for fluid velocity and the results are presented in figures. All these flows are new and are presented for the first time in the literature.     

Similarities of Patterns in Fluid and Granulated Flow Inside a Horizontally Rotating Cylinder

The formation of flow patterns in liquid and granulated media is studied experimentally. Many phenomena such as segregation of particles different in dimensions, surface properties, and density are observed only in granulated media. However, there exist many effects typical of flows in both liquid and granulated media in a horizontal circular cylinder rotating about its axis. Eight classes of the following similar patterns in fluids and granulated mixtures were studied experimentally: vortex-like patterns, deformation of the trailing and leading edges of a layer, shark-teeth patterns, fish-like patterns, formation of rotating layers, ring-like patterns, and cellular patterns     

Numerical Investigation of Drug Delivery to Cancerous Solid Tumors by Magnetic Nanoparticles Using External Magnet

Chemotherapy as one of the most utilized cancerous tumor treatment methods introduces undesired side effects due to penetrating toxic drugs into the healthy organs. Delivery of anticancer therapeutic agents to solid tumors is also problematic. The purpose of current study is to investigate the penetration of magnetic drug carriers (MDCs) within the cancerous solid tumor tissue under the influence of external magnet. Capillary wall and tumor tissue is modeled as a saturated porous media. In order to solve the coupled governing equations, mass, momentum and concentration, an in-house finite volume-based code is developed and utilized. Results show the penetration of MDCs into the tumor in the absence of magnetic field is minimal and is limited to the surface of the tumor. On the other hand, under the influence of external magnet the penetration of MDCs within the tumor increases exponentially. They also penetrate deep into the tumor and cover the entire tumor which increase the effectivity and decrease the side effect of the treatment.     

Features of High-Viscosity Fluid Flow Through a Porous Medium Heated by Electromagnetic Radiation

Models describing the process of flow of a high- viscosity fluid through a porous medium heated by electromagnetic radiation are investigated analytically and numerically with allowance for the temperature dependence of the fluid viscosity and density. In addition to ordinary heating, the nonlinear electromagnetic heating regime associated with variation of the radiation absorption coefficient with temperature is considered.     

Modeling the Formation of Fluid Banks During Counter-Current Flow in Porous Media

Fluid banks sometimes form during gravity-driven counter-current flow in certain natural reservoir processes. Prediction of flow performance in such systems depends on our understanding of the bank-formation process. Traditional modeling methods using a single capillary pressure curve based on a final saturation distribution have successfully simulated counter-current flow without fluid banks. However, it has been difficult to simulate counter-current flow with fluid banks. In this paper, we describe the successful saturation-history-dependent modeling of counter-current flow experiments that result in fluid banks. The method used to simulate the experiments takes into account hysteresis in capillary pressure and relative permeabilities. Each spatial element in the model follows a distinct trajectory on the capillary pressure versus saturation map, which consists of the capillary hysteresis loop and the associated capillary pressure scanning curves. The new modeling method successfully captured the formation of the fluid banks observed in the experiments, including their development with time. Results show that bank formation is favored where the p_c-versus-saturation slope is low. Experiments documented in the literature that exhibited formation of fluid banks were also successfully simulated.     

Analytic Approximate Solution for a Flow of a Second-Grade Viscoelastic Fluid in a Converging Porous Channel

The problem of a two-dimensional steady flow of a second-grade fluid in a converging porous channel is considered. It is assumed that the fluid is injected into the channel through one wall and sucked from the channel through the other wall at the same velocity, which is inversely proportional to the distance along the wall from the channel origin. The equations governing the flow are reduced to ordinary differential equations. The boundary-value problem described by the latter equations is solved by the homotopy perturbation method. The effects of the Reynolds and crossflow Reynolds number on the flow characteristics are examined.     

Investigation of the Relative Motion of a Viscous Fluid and a Porous Medium Using the Brinkman Equations

Exact solutions are obtained for the following three problems in which the Brinkman filtration equations are used: laminar fluid flow between parallel plane walls, one of which is rigid while the other is a plane layer of saturated porous medium, motion of a plane porous layer between parallel layers of viscous fluid, and laminar fluid flow in a cylindrical channel bounded by an annular porous layer.     

Numerical Modeling of Two-Dimensional Flow of a Nonhomogeneous Fluid in a Confined Domain

The pattern of the two-dimensional vortex flow of a nonhomogeneous fluid in a confined domain is studied using two-dimensional numerical calculations. It is found that in the case of a nonhomogeneous initial density distribution the kinetic energy decay rates are proportional to the square root of viscosity at the active stage of flow restructuring. The correlation functions of the velocity and the density are derived for different moments of time in the inertial range. All these results indicate the choice of the two-dimensional turbulence development scenario in a nonhomogeneous fluid.     

Investigation of the Flow in an Annular Cavity in a Cylindrical Body in a Supersonic Stream

The results of an experimental investigation of the flow over an annular cavity in a cylindrical body are presented; the cavity-to-body diameter ratio was 0.7 and the incident flow Mach number was 2.84. Using the data on the pressure distribution and optical measurements of the flow pattern, the structure of the flow inside the cavity was studied on the relative cavity length range from 0.5 to 14 including the regimes with both open and closed separation zones.