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A theoretical investigation has been made for a radiating and chemically reacting viscous-fluid of a conducting gas over a vertical porous surface immerse in a saturated porous medium for the impact of magnetic drag-force, buoyancy forces and thermal-diffusion (Soret) order under oscillatory suction and heat absorption. The analytical solutions have been derived for the physical variables related to the governing equations under the appropriate boundary conditions. It is found that the velocity profiles increase with the increasing values of Soret number (S0) and higher Soret number (S0 = 5) shows the large temperature difference. It is noticed that increasing radiation parameter (R) elevated the velocity profiles near the plate. In the effects of Soret number (S0) the velocity profiles are an increasing function for both the cases of M = 0 and M = 10. The validity and accuracy of the flow model is presented and found suitable to proceed the work. In this study, the findings would be useful in many practical areas such as diffusion operations, which involved molecular diffusion of species with molar concentration.

This study deals with review of different improvements done in the formulation of the governing equations to simulate accurate solute transport in saturated porous media over the years. The traditional advection-dispersion equation (ADE) model is the simplest lumped model founded on the assumptions of Fick’s law of diffusion. But it typically underestimates the breakthrough concentration in leading and/or tailing region due to non-fickian transport. It is modified into mobile-immobile model (MIM) considering the medium having micropores with stagnant water pockets but allowing solute exchange by diffusion between mobile and immobile zone which is quantified by mass transfer coefficient. Multi-process non-equilibrium (MPNE) model further simulates for a system with both physical and chemical non-equilibrium by assuming instantaneous and rate-limited sorption in advective and non-advective domains. Using the concept of dual permeability, slow fast transport (SFT) model divides the liquid phase in the domain into three zones i.e. fast, slow and immobile. Here chemical interaction between the fluid and soil matrix takes place only in slow and immobile zones. Non-fickian solute transport does not follow Brownian motion rules so a random variable is required to explain it. Hence continuous time random walk (CTRW) model is used where solute transport is characterized by joint probability variable. Special case of CTRW with solute having considerable probability of moving long distances and follow power law gives Fractional advection-dispersion equation (FADE) model. These models varying from relatively simple to more complex formulations and assumptions are discussed here highlighting the merits and demerits of each.

The paper presents the mathematical formulation which describes the dispersion of solute in a laminar flow in a sparsely packed porous medium. The effect of interphase mass transfer on dispersion in a unidirectional flow through a horizontally extent of infinite porous channel is examined using the generalized dispersion model of Sankarasubramanian and Gill. The model brings into focus three important coefficients namely the exchange coefficient, the convection coefficient and the dispersion coefficient. The time-dependent dispersion coefficient and mean concentration distribution are computed and results are represented graphically. The problem finds many applications in waste water management, in chromatography and in biomechanical problems.

We present a planar one-dimensional theoretical model and numerical solutions for the process of the formation of methane gas hydrate by injecting gas into a porous reservoir partially saturated with water. The case where the intensity of formation of the gas hydrate is limited by the diffusion of gas through a hydrate layer formed between water and gas in the pore channel core is considered. Within this process, the kinetics of hydrate formation is determined by empirical parameter D, having the dimension of a diffusion coefficient (m2/s). The effect of the value of this parameter on the characteristics of the hydrate formation process is studied depending on the parameters that determine the initial state of the porous reservoir and its porosity and permeability characteristics. The equilibrium mechanism of hydrate formation is considered, which is a limit adopted by the diffusion pattern that corresponds to the case of D → ∞.

We investigate transient heat and solute transfers in liquid-saturated porous media. The macroscopic equivalent models are obtained by a homogenization process from the pore-scale description. The large value of the Lewis number in liquid mixtures introduces a possible separation of scales between the heat and solute diffusion wavelengths \(L^{\mathrm{heat}}\) and \(L^{\mathrm{solute}}\) at a given excitation time. Thus, two separations of scales could be present between the pore scale of characteristic length l and \(L^{\mathrm{heat}}\) and \(L^{\mathrm{solute}}\). Depending on the ratio of these two separations of scales results in different equivalent macroscopic models or in non-homogenizable situations. Among numerous possibilities, we present two different homogenizable problems and a non-homogenizable situation. As the characteristic excitation time is decreased, the solute pseudo-wavelength and the heat pseudo-wavelength increase; a unique separation of scales between both solute and heat transfers and the pore scale appears, and we recover the classical macroscopic thermodiffusion model.

The present paper addresses the problem of MHD forced convective flow in a fluid saturated porous medium with Brinkman-Forchheimer model, which is an important physical phenomena in engineering applications. The paper extends the previous models to account for effects of variable fluid properties on the forced convective flow through a porous medium in the presence of radiative heat loss using bivariate spectral relaxation method (BSRM). The dynamic viscosity and thermal conductivity of the newtonian fluid are assumed to vary linearly respectively, with temperature whereas the contribution of thermal radiative heat loss is based on Rosseland diffussion approximation. The flow model is described and expressed in form of a highly coupled nonlinear system of partial differential equations. The method of solution BSRM as proposed by Motsa [25] seeks to decouple the original system of PDEs to form a sequence of equations that can be solved in a computationally efficient manner. BSRM is an approach that applies spectral collocation independently in all underlying independent variable is executed to obtain approximate solutions of the problem. The proposed algorithm is supposed to be a very accurate, convergent and very effective in generating numerical results. The results obtained show a significant effects of the flow control parameters on the fluid velocity and temperature respectively. Consequently, the wall shear stress and local heat transfer rate of the present paper are compared with the available results in literatures. Remarkable impacts and a good agreement are found.

We developed an inverse technique based on the Boltzmann-Matano method from which apparent coefficients of diffusion of decaying radionuclides in saturated porous media can be calculated. The technique uses the assumption that the concentration profiles (or breakthrough curves) have S shapes and can be well approximated by the error function with three adjustable parameters (the position, height, and slope). The resulting dependence of the apparent diffusion coefficient on concentration was given as a rather simple formula involving inverse error function. Here we wish to apply this straightforward technique to obtain concentration dependences of the apparent diffusion coefficients of 22Na+ and 134Cs+ for which the corresponding breakthrough curves were measured for two types of dense opalinus clay rocks. We compare our more general results with those from the original study in which the apparent diffusion coefficient was assumed to be constant and indicate that the latter approach need not be appropriate.

The main purpose of this article is to present a high-accurate reference solution for double-diffusive convection in a confined saturated porous medium. The solution is developed using the Fourier-Galerkin spectral method for the coupled flow, heat, and mass transfer equations. The accuracy of the obtained solution is investigated in terms of the truncation orders of the Fourier series and by comparison against a newly developed finite-element model. Results of simulations highlight the accuracy of the proposed reference solution and show its worthiness for benchmarking numerical models dealing with Darcy-Brinkman double-diffusive convection.

We propose and analyze a model of coupled heat transport and water flow in variably saturated porous media under conditions of freezing and thawing. Solution of the model provides temperature, liquid water content and ice content in porous media as a function of space and time. We employ the Rothe method to construct systems of approximate solutions for which the existence and regularity are proved. Numerical scheme is based on specific semi-implicit discretization in time, which preserve the pseudo-monotone structure of the discrete problem. Numerical results are compared with experimental data reported in the literature. The model satisfactorily predicts characteristic phenomena in porous media under frost actions such as water movement toward freezing fronts and the presence of liquid water in frozen regions.

We consider a saturated porous medium of Darcy type with an exothermic reaction occurring on the domain boundary. In this model the reaction is the main driving force behind convection and we establish continuous dependence of the solution on the reaction terms.

The development of velocity, temperature and concentration fields of an incompressible viscous electrically conducting fluid, caused by impulsive stretching of the surface in two lateral directions and by suddenly increasing the surface temperature from that of the surrounding fluid in a saturated porous medium is studied. The partial differential equations governing the unsteady laminar boundary layer flow are solved analytically. For some particular cases, closed form solutions are obtained, and for large values of the independent variable asymptotic solutions are found. The surface shear stress in x and y directions and the surface heat transfer and surface mass transfer increase with the magnetic parameter and with permeability parameter and the stretching ratio, and there is a smooth transition from the short-time solution to the long-time solution.

This paper analyzes the laminar, incompressible mixed convective transport inside vertical channel in an electrically conducting fluid saturated porous medium. In addition, this model incorporates the combined effects of Soret, Hall current and Joule heating. The nonlinear governing equations and their related boundary conditions are initially cast into a dimensionless form using suitable similarity transformations and hence solved using Adomian Decomposition Method (ADM). In order to explore the influence of various parameters on fluid flow properties, quantitative analysis is exhibited graphically and shown in tabular form.

In this paper, the physical models of the porous solar wall heating system with localized underfloor air distribution (UFAD) are established. Based on Brinkman-Forchheimer Extended Darcy and energy two-equation models for saturated porous medium, the influences of the structure of underfloor space on the heat transfer and flow characteristics of the system are simulated, analyzed and compared.The results show that the underfloor space with rational partition is good for improving the heat transfer and flow characteristics of system, and maintaining the cable system in the underfloor space.

This paper deals with the analysis of an unsteady mixed convection flow of a fluid saturated porous medium adjacent to heated/cooled semi-infinite stretching vertical sheet in the presence of heat source. The unsteadiness in the flow is caused by continuous stretching of the sheet and continuous increase in the surface temperature. We present the analytical and numerical solutions of the problem. The effects of emerging parameters on field quantities are examined and discussed.

A general approach is proposed for defining the macroscopic free energy density function (and its complement, the free enthalpy) of a saturated porous medium submitted to finite deformations under non-isothermal conditions, in the case of compressible fluid and solid constituents. Reference is made to an elementary volume treated as an ‘open system’, moving with the solid skeleton. The proposed free energy depends on the generalised strains (namely an appropriate measure of the strain of the solid skeleton and the variation in fluid mass content) and the absolute temperatures of the solid and fluid phases (which are assumed to differ from each other for the sake of generality). This macroscopic energy proves to be a potential for the generalised stresses (namely the associated measure of the total stress and the free enthalpy of the pore fluid per unit mass) and the entropies of the solid and fluid phases. In contrast with mixture theories, the resulting free energy is not the simple sum of the free energies of the single constituents. Two simplified cases are examined in detail, i.e. the semilinear theory (originally proposed for isothermal conditions and extended here to non-isothermal problems) and the linear theory. The proposed approach paves the way to the consistent non-isothermal-hyperelastic-plastic modelling of saturated porous media with a compressible fluid and solid constituents.

This article examines the thermal effects in an unsteady flow of a pressure driven, reactive, variable viscosity, third-grade fluid through a porous saturated medium with asymmetrical convective boundary conditions. We assume that exothermic chemical reactions take place within the flow system and that the asymmetric convective heat exchange with the ambient at the surfaces follow Newton’s law of cooling. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using a semi-implicit finite difference scheme. Graphical results are presented and discussed qualitatively and quantitatively with respect to various parameters embedded in the problem.

In recent years the industrial applications of porous materials has shown a growing relevance. Most of the technological thermal processes in porous media involve time-dependent thermal conditions. Therefore, the temperature at each point of the material also changes in time. In order to correctly carry out the technological process, it becomes necessary to know the temperature distribution inside the material. This is a problem of heat conduction in a fluid saturated porous media subject to a lack of local thermal equilibrium (LTNE). The purpose of this paper is to elucidate the several causes of LTNE, even in steady or quasi steady heat transfer processes in saturated porous media, and to evaluate the influence of structural characteristic of porous media and the presence of surfactant in the saturating liquid phase.

Heat and mass transfer with condensation in porous media was numerically studied coupling with distributions of temperature, vapor concentration, pressure and water saturation. The transport processes in porous media displayed two distinct stages, or early and late stages. Different characteristics during these stages were described with the consideration of physical nature. A systematical investigation was conducted to explore the influence of different parameters on the processes, including the temperature, the particle diameter, the porosity, and the thermal conductivity of the particle. A modeling experiment was conducted to partially validate the calculation.

Bacterial transport models were evaluated in this study to determine the suitable model at describing bacterial transport in saturated column experiments. Four models used in the evaluation were: advective-dispersive equation (ADE) + equilibrium sorption/retardation (ER) + kinetic reversible sorption (KR) (Model I), ADE + two-site sorption (Model 2), ADE + ER + kinetic irreversible sorption (KI) (Model 3), ADE + KR + KI (Model 4). Firstly, analyses were performed with the first experimental data, showing that Model 4 is appropriate for describing bacterial transport. Even if Model 1 and 2 fit well to the observed data, they have a defect of not including the irreversible sorption, which is directly related to mass loss of bacteria. Model 3 can not properly describe the tailing observed in the data. However, further analysis with the second data indicates that Model 4 can not describe retardation of bacteria, even if the sorption-related parameters are varied. Therefore, Model 4 is modified by incorporating retardation factor into the model, resulting in the improved fitting to the data. It indicates that the transport model, into which retardation, kinetic reversible sorption, and kinetic irreversible sorption are incorporated, is suitable at describing bacterial transport in saturated column experiments. It is expected that the selected transport model could be applied to properly analyze the bacterial transport in saturated porous media.

Normalized, coupled governing equations for one-dimensional thermal consolidation problems are established. The non-dimensional coefficients of thermal consolidation and thermal diffusivity are defined accordingly. An analytical solution is deduced by using the Laplace transform and the Gauss–Legendre method of Laplace transform inversion. The responses of saturated porous media subjected to cyclic thermal loading are studied. The evolution of temperature, pore pressure and displacement from instantaneous state to quasi-steady state, with elapsed time, are analysed. The characteristics of cyclic fluctuation and the attenuation of the field variables with increased depth are also analysed. The influences of the permeability of media on thermal responses are discussed.

The forced convection thermal boundary layer in a porous medium as an analytically tractable special case of a mixed convection problem is considered. It is shown that some general features of the mixed convection solutions reported recently by other authors [B. Brighi, J.-D. Hoernel, On the concave and convex solutions of mixed convection boundary layer approximation in a porous medium, Appl. Math. Lett. (published online, 2005); M. Guedda, Multiple solutions of mixed convection boundary layer approximations in a porous medium, Appl. Math. Lett. (published online, 2005)] can already be recovered from this exactly solvable case.

The effect of heterogeneity on the onset of convection induced by a vertical density gradient in a saturated porous medium is discussed. The distinction between moderate and high heterogeneity of permeability is emphasized. Topics discussed include the limitations of the use of the log–normal distribution for permeability, the different effects of vertical and horizontal heterogeneity, and the use of an electrical resistor analogy applied to an illustrative quartered-square example. In a postscript, a new approximate criterion for instability applicable to the case of strong heterogeneity is proposed.

The problem of fully developed forced convection in a parallel-plates channel filled with a saturated porous medium (involving a Brinkman model for the momentum equation), with the effect of viscous dissipation (involving a Brinkman number), is discussed. Some general matters relating to the possibility of fully developed convection are also discussed.

This paper continues the theoretical exploration of the heat and mass transfer in a biporous medium with the coupled phase transformations. A more complicated system is considered, such as porous medium-ice-aqueous solution. General statements been formulated for a simple medium [4] , remain in force for the given system: the heat and mass fluxes each depend linearly on all thermodynamical forces, the transport coefficients satisfy the Onsager reciprocal relations; the coupled phase transformations intensify significantly the cross effects. The presence of contaminants in water imparts the osmotic properties to the biporous medium and decreases the rate of the heat and mass transfer in the system. The dissolved matter takes effect beginning with the concentration of ∼0.001 mol l −1 . At the high concentration of the aqueous solution (>0.1 mol l −1 ) the cross effects become negligible small and the medium loses its unique capacities.

A mathematical model to describe bacterial transport in saturated porous media is presented. Reversible/irreversible attachment and growth/decay terms were incorporated into the transport model. Additionally, the changes of porosity and permeability due to bacterial deposition and/or growth were accounted for in the model. The predictive model was used to fit the column experimental data from the literature, and the fitting result showed a good match with the data. Based on the parameter values determined from the literature experimental data, numerical experiments were performed to examine bacterial sorption and/or growth during bacterial transport through saturated porous media. In addition, sensitivity analysis was performed to investigate the impact of key model parameters for bacterial transport on the permeability and porosity of porous media. The model results show that the permeability and porosity of porous media could be altered due to bacterial deposition and growth on the solid matrix. However, variation of permeability due to bacterial growth was trivial compared with natural permeability variation. Copyright © 2005 John Wiley & Sons, Ltd.

La localisation de la deformation dans les sols et les roches fait l'objet d'etudes experimentales depuis une vingtaine d'annees. Parmi ces etudes, un petit nombre ont aborde la localisation en situation non-drainee. Il a ete montre que les bandes de cisaillement peuvent apparaitre dans les echantillons contractants comme dans les dilatants, avec des effets specifiques par rapport au cas draine, dus au couplage fluide-squelette. On discute ici la pertinence du critere de bifurcation resultant de l'analyse de bande de cisaillement, dans le cas ou le couplage hydromecanique est pris en compte.

The lattice gas automata method is applied to study the electrical transport properties of porous media saturated with oil-water. We introduce the reflective coefficient to the border between phases to demonstrate how free the lattice gas particles can go through them, so the difference of electrical transport properties can be changed by adjusting the reflective coefficient. The simulation results show that there is a power law dependent of F and porosity (φ), also of I and water saturation (Sw) in term of F = αφ−m and I = bSw−n with the definition of F = Ro/Rw, I = Rt/Ro where Ro is the resistivity of porous media fully saturated with water, Rw is the resistivity of water, and Rt is the resistivity of oil-water saturated porous media. The parameters a and m are strongly dependent on the micro-scale structure of porosity, and the parameters b and n are affected by the distribution of fluids and the porosity.

A detailed numerical study of heat transfer to a fluid passing through a saturated porous medium is the subject of this study. The Green's function solution method is selected in order to accomplish this task. The interesting features of this methodology are the focus of this article. As a test case, primary consideration is given to the computation of heat transfer to a fluid flowing through a circular passage with impermeable walls filled with porous materials. The analysis includes the heating/cooling effects due to a temperature change at the wall of the passage. In addition, the contributions of frictional heating are examined.

Steady state solutions are obtained for non-Darcy free convection flow along a horizontal cylinder in a non-Newtonian fluid saturated porous medium. The boundary-layer equations governing the flow are solved numerically by using an implicit finite-difference method developed by Keller. Numerical results are obtained for the velocity and heat transfer at the wall for various values of the parameters namely, the Ergun number, Rayleigh number, power-law index and transpiration parameter.

Until now, the theory, methodology of investigations, and interpretation of thermometry data have been most completely developed for single-phase (oil, water, or gas) flows in formations. However, multiphase (oil+gas, oil+water, and oil+water+gas) flows in formations are more common in practice. This is primarily typical for fields featuring a high value of gas factor and saturation pressure, as well as for cases of formation tests at low values of bottom-hole pressure. Analysis of actual thermograms under these conditions has shown that the earlier-developed techniques for the cases of single-phase flows in the formation and the well cannot be applied here. This paper presents research data on the influence of the adiabatic and Joule–Thomson effects and the heat of fluid degassing on temperature field in porous medium.

The temperature fields arising in the filtration of a gassed liquid in saturated porous media have been theoretically investigated with simultaneous consideration for the gas‐phase imperfection, phase transitions, and heat exchange between an oil pool and the surrounding rocks.

A problem of the Stefan type which describes heat and mass transfer in a porous body with the double phase transition liquid–ice–vapor has been formulated and solved.

Durability of concrete structures is often dependant on ion diffusion transport and more particularly on chloride diffusion. The mechanisms of diffusion involved during the transport of chloride ions into saturated concrete are classically described by the Fick's laws which supposed that ions are non electrical particles. Nevertheless, some experimental results remain yet unexplained. Starting from this state of the art, a new approach called the multi-species approach has been developed. This approach makes it possible to account for the interactions between the different species present in the solution. The aim of this paper is first, to clarify the scientific basis of ionic diffusion into saturated porous media and second to describe and understand some experimental data, the significance of which had not been fully understood.

In this work we develop the volume averaged form of the frequency-dependent governing equations for electrohydrodynamics in a saturated porous medium. The concept of local electrical equilibrium is identified, and when this condition is valid we obtain a one-equation model describing the coupled transport of momentum and electric charge. When local electrical equilibrium is not valid, separate forms of Maxwell's equations must be developed for both the fluid and solid phases.

An analysis is presented to investigate the effect of radiation on mixed convection from a vertical flat plate in a saturated porous medium. Both a hot surface facing upward and a cold surface facing downward are considered in the analysis. The conservation equations that govern the problem are reduced to a system of nonlinear ordinary differential equations. The important parameters of this problem are the radiation parameter R, the buoyancy parameter B, and the freestream to wall temperature ratio T∞/Tw for the case of a hot surface or the wall to freestream to wall temperature Tw/T∞ for the case of a cold surface.

A study on similarity solutions for a mathematical model for thawing in a saturated porous medium is considered when change of phase induces a density jump and the influence of pressure on the melting temperature is considered. The mathematical analysis is made for different cases, depending on the sign of the three physical parameters.