Free-convection between vertical walls partially filled with porous medium

This paper presents an analytical study of laminar fully developed free-convection flow between two vertical walls partially filled with porous matrix and partially with a clear fluid having interface vertically. The momentum transfer in porous medium is described by the Brinkman-extended Darcy model and the two regions are coupled by equating the velocity and shear stress at the interface. The governing equations having non-linear nature have been solved by using perturbation method. It has been found that effect of Brinkman term is in entire porous domain for large values of Darcy number while its effect is confined nearer to interface and wall for small values of Darcy number. Received on 19 March 1997     

Steady flow and heat transfer of a magnetohydrodynamic Sisko fluid through porous medium in annular pipe

In this paper, the steady flow and heat transfer of a magnetohydrodynamic fluid is studied. The fluid is assumed to be electrically conducting in the presence of a uniform magnetic field and occupies the porous space in annular pipe. The governing nonlinear equations are modeled by introducing the modified Darcy's law obeying the Sisko model. The system is solved using the homotopy analysis method (HAM), which yields analytical solutions in the form of a rapidly convergent infinite series. Also, HAM is used to obtain analytical solutions of the problem for noninteger values of the power index. The resulting problem for velocity field is then numerically solved using an iterative method to show the accuracy of the analytic solutions. The obtained solutions for the velocity and temperature fields are graphically sketched and the salient features of these solutions are discussed for various values of the power index parameter. We also present a comparison between Sisko and Newtonian fluids. Copyright © 2011 John Wiley & Sons, Ltd.     

Creeping flow through a model fibrous porous medium

Pressure losses and velocity distributions were measured for creeping flow through three model fibrous porous media. The three models consisted of square arrays of circular rods with solid volume fractions of 2.5, 5 and 10%. Measurements of flow resistances are in good agreement with theoretical predictions after wall effects are accounted for using Brinkman’s equation. Two-dimensional velocity vector maps were obtained in each array using particle image velocimetry. The velocity distributions are necessary for identifying non-Newtonian effects in flows with viscoelastic fluids.     

Two-phase three-component flow through a porous medium with variable total flow

In analyzing the processes of the displacement of oil, in which intensive interphase mass transfer takes place, it is normally assumed that the partial volumes of the components as they mix are additive (Amagat's Law) [1, 2]. Then the equations of motion have an integral, which is the total volume flow rate through the porous medium, and the basic problems of frontal displacement, if there are not too many components in the system, permit an exact analytical study to be made [3–5]. If this assumption is rejected, the total flow becomes variable [3, 6, 7]. It appears that the consequences of this as applied to the processes of the displacement of oil by high pressure gases have not previously been considered. The results of such a study, developing the approach outlined in [4], are given below. The initial multicomponent system is simulated by a three-component one which contains oil (the component being displaced), gas (the neutral or main displacing component), and intermediate hydrocarbon fractions or solvent (the active component). It is shown that instead of the triangular phase diagram (TPD) normally used where the partial volumes of the components are additive, in this case it is convenient to use a special spatial phase diagram (SPD) of the apparent volume concentrations of the components to construct the solutions and to interpret them graphically. The method of constructing the SPD and its main properties are explained. A corresponding graphoanalytical technique is developed for constructing the solutions of the basic problems of frontal displacement which correspond to motions with variable total flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 113–120, May–June, 1985.     

Numerical simulation of non-Darcian flow through a porous medium

This work reports on fluid flow in a fluid-saturated porous medium, accounting for the boundary and inertial effects in the momentum equation. The flow is simulated by Brinkman-Forchheimer-extended Darcy formulation (DFB), using MAC (Marker And Cell) and Chorin pressure iteration method. The method is validated by comparison with analytic results. The effect of Reynolds number, Darcy number, porosity and viscosity ratio on velocity is investigated. As a result, it is found that Darcy number has a decisive influence on pressure as well as velocity, and the effect of viscosity ratio on velocity is very strong given the Darcy number. Additional key findings include unreasonable choice of effective viscosity can involve loss of important physical information.     

Equations of nonlinear anisotropic flow through a porous medium

A general law of nonlinear anisotropic flow through a porous medium is proposed. A corresponding equation for the pressure of the fluid is obtained in velocity hodograph variables. The conditions of ellipticity of this equation are expressed in terms of the dissipative function.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 158–160, September–October, 1980.I thank V. M. Entob for discussing the work.     

Some nonlinear problems of groundwater flow through a porous medium

Self-similar solutions of the equation of groundwater gravity flow through a porous medium are given. The water flows from a basin into an underground permeable reservoir bounded from below by an impervious bed. A periodic problem of flow through a porous medium in which the water level in the basin periodically oscillates is considered. It is shown that in this case the water table elevation effect, i.e., water pumping into the aquifer, develops at a sufficient distance from the littoral zone. The invariant-group solutions of the problem of flow through a porous medium are investigated with allowance for evaporation from the groundwater surface.     

Analytic solution for flow of Sisko fluid through a porous medium

This paper presents the analytic solution for flow of a magnetohydrodynamic (MHD) Sisko fluid through a porous medium. The non-linear flow problem in a porous medium is formulated by introducing the modified Darcy’s law for Sisko fluid to discuss the flow in a porous medium. The analytic solutions are obtained using homotopy analysis method (HAM). The obtained analytic solutions are explicitly expressed by the recurrence relations and can give results for all the appropriate values of material parameters of the examined fluid. Moreover, the well-known solutions for a Newtonian fluid in non-porous and porous medium are the limiting cases of our solutions.     

Three dimensional unsteady convection and mass transfer flow through porous medium

The problem of three dimensional unsteady convection flow through a porous medium, with effect of mass transfer bounded by an infinite vertical porous plate is discussed, when the suction at the plate is transverse sinusoidal and the plate temperature oscillates in time about a constant mean. Assuming the free stream velocity to be uniform, approximate solutions are obtained for the flow field, the temperature field, the skin-friction and the rate of heat transfer. The dependence of solution on Pr (Prandtl number), Gr (Grashof number based on temperature), Gc (modified Grashof number based on concentration difference), Sc (Schimdt number), the frequency and the permeability parameter is also investigated.     

Unsteady dissipative structures in non-Newtonian fluid flow through a porous medium

The nonuniform space-time pressure and velocity distributions in an initially nonempty stratum with constant initial pressure created by pumping a non-Newtonian fluid through the boundary of the stratum are investigated. The injected fluid and the fluid present in the stratum before injection have identical physical properties. The conditions of formation of traveling fronts and localized structures are analyzed as functions of the nonlinearity of the rheological law of the fluid and the injection regime.Baku. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 106–112, November–December, 1994.     

MHD stagnation flow of a micropolar fluid through a porous medium

The unsteady MHD boundary layer flow of a micropolar fluid near the forward stagnation point of a two dimensional plane surface is investigated by using similarity transformations. The transformed nonlinear differential equations are solved by an analytic method, namely homotopy analysis method (HAM). The solution is valid for all values of time. The effect of MHD and porous medium, non dimensional velocity and the microrotation are presented graphically and discussed. The coefficient of skin friction is also presented graphically.     

Magnetohydrodynamics convective flow in a vertical slot through a porous medium

An analysis is presented with magnetohydrodynamics natural convective flow of a viscous Newtonian fluid saturated porous medium in a vertical slot. The flow in the porous media has been modeled using the Brinkman model. The fully-developed two-dimensional flow from capped to open ends is considered for which a continuum of solutions is obtained. The influence of pertinent parameters on the flow is delineated and appropriate conclusions are drawn. The asymptotic behaviour and the volume flux are analyzed and incorporated graphically for the three-parameter family of solution.     

Mathematical model of nonisothermal multiphase binary mixture flow through a porous medium

A model of nonisothermal binary mixture flow through a porous medium, applicable over a wide range of thermobaric conditions, including temperatures higher than the critical mixture temperature, is proposed. A nonclassical approach used for modeling the mixture properties makes it possible to uniformly describe its single-, two- and three-phase thermodynamic equilibria and the corresponding flows under sub- and supercritical thermodynamic conditions. The wide application of thermodynamic methods to determining the real mixture properties leads to a nonstandard mathematical model in which the conservation laws are closed with a conditional extremum problem, not finite or differential equations. A dispersion analysis of the model equations is performed and the characteristic velocities in zones of different mixture phase states are determined.