Convection Flow In Porous Medium Research Articles

Unsteady three-dimensional MHD flow and heat transfer in porous medium suspended with both microorganisms and nanoparticles due to rotating disks

In the present study, the silent characteristics of magnetized mixed convection flow in porous medium suspended with both microorganisms and nanoparticles induced by two expanded or contracted disks are investigated. The Buongiorno’s model, in which the Brownian diffusion and thermophoresis are taken as dominant factors, is introduced to describe behaviors of the nanofluid. Multiple slip boundary conditions are also included into this problem. The nonlinear system is converted into five fully coupled nonlinear ordinary differential equations via suitable scaling transformations. The homotopy-based algorithm BVPh2.0 is employed to give their solutions. Physical interpretation is made through analyzing the graphs of different constraints for profiles of velocity, temperature, nanoparticle volume concentration and density of motile organism. Furthermore, we extend this model to seek the physical behaviors of heat transfer and the wall motile microorganism fluxes. Significant findings are presented, including that the wall expansion ratio and the magnetic parameter impose contrary effects on microorganism profiles, the Prandtl number and the radiation parameter play opposite roles on heat transfer rate, and the Brownian motion and the thermophoresis exhibit totally different influence on microorganism flux rate. It is expected that this study is helpful to understand heat transfer mechanism in multiple physical fields.

A Method for Numerical Simulation of Haline Convective Flows in Porous Media as Applied to Geology

A numerical code for simulating haline convective flows in porous media based on the finite difference method on a staggered nonuniform grid is developed. The mathematical model includes the equations of continuity, Darcy, and transport of contaminants with variable properties of the solid and fluid phases. The convective term in the convection–diffusion equation is approximated using the QUICK scheme. The code is tested using the problem of the concentration step motion as an example. A numerical solution of the onset and development of haline convection in a semi-infinite porous (homogeneous or inhomogeneous) domain with a contaminant source on the upper boundary is obtained.

Viscous and Ohmic dissipation on non-Darcy MHD nanofluid mixed convection flow in porous medium with suction/injection effects

The paper presents the influence of nanofluid flow on MHD mixed convection, incompressible and electrically conducting fluid along a vertical flat plate with viscous and ohmic dissipation effects. The plate is permeable and embedded in a fluid saturated on non-Darcy (Forchheimer flow model) porous medium with suction and injection. Dissipation parameters are described in the energy equation. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformation. The non linear ordinary differential equations are linearized by using Quasi-linearization technique and then solved numerically by using implicit finite difference scheme. To compute the numerical values C programming code is used. The numerical results are analyzed for the effects of various physical parameters such as magnetic parameter Ha, Reynolds number Red, Eckert number, Ec thermophoresis parameter Nt, Brownian motion parameter Nb, suction and injection parameter fw and Lewis number Le. The results obtained are discussed with the help of graphical illustrations.

Numerical study of laminar mixed convection flow in a lid-driven square cavity filled with porous media

PurposeThe purpose of this study is to produce a numerical model capable of predicting the mixed convection flows in a rectangular cavity filled with a porous medium and to analyze the effects of several parameters on convective flow in porous media in a differentially heated enclosure.Design/methodology/approachThe authors used the finite volume method.FindingsThe authors predicted and analyzed the effects of Richardson number, Darcy number, porosity values and Prandtl number in heat transfer and fluid flow. On other hand, the porosity and Richardson number values lead to reducing the heat transfer rate of mixed convection flow in a porous medium.Originality/valueA comparison between Darcy–Brinkman–Forchheimer model and Darcy–Brinkman model is discussed and analyzed. The authors finally conclude that the Darcy–Brinkman model overestimates the heat transfer rate.

Mixing across fluid interfaces compressed by convective flow in porous media

We study mixing in the presence of convective flow in a porous medium. Convection is characterized by the formation of vortices and stagnation points, where the fluid interface is stretched and compressed enhancing mixing. We analyse the behaviour of the mixing dynamics in different scenarios using an interface deformation model. We show that the scalar dissipation rate, which is related to the dissolution fluxes, is controlled by interfacial processes, specifically the equilibrium between interface compression and diffusion, which depends on the flow field configuration. We consider different scenarios of increasing complexity. First, we analyse a double-gyre synthetic velocity field. Second, a Rayleigh–Bénard instability (the Horton–Rogers–Lapwood problem), in which stagnation points are located at a fixed interface. This system experiences a transition from a diffusion controlled mixing to a chaotic convection as the Rayleigh number increases. Finally, a Rayleigh–Taylor instability with a moving interface, in which mixing undergoes three different regimes: diffusive, convection dominated and convection shutdown. The interface compression model correctly predicts the behaviour of the systems. It shows how the dependency of the compression rate on diffusion explains the change in the scaling behaviour of the scalar dissipation rate. The model indicates that the interaction between stagnation points and the correlation structure of the velocity field is also responsible for the transition between regimes. We also show the difference in behaviour between the dissolution fluxes and the mixing state of the systems. We observe that while the dissolution flux decreases with the Rayleigh number, the system becomes more homogeneous. That is, mixing is enhanced by reducing diffusion. This observation is explained by the effect of the instability patterns.

A Generalized Lattice Boltzmann Model for Simulating Axisymmetric Convective Flow in Porous Media

Axisymmetric convective flow in porous media is frequently encountered in nature and industry applications. In recent years, Lattice Boltzmann method has been developed as a powerful tool for such kind of flow and heat transfer. Despite its success in many problems regarding to porous flow, the existing LB model for the axisymmetric thermal flow in porous media at the representative volume scale suffers from a serious drawback. That is, it can not handle the cases where the heat capacitance of porous media varies spatially obviously. In this paper, a generalized LB model for axisymmetric temperature field is proposed to remedy this shortcoming. Chapman-Enskog analysis demonstrates that the energy equation in the cylindrical coordinates system can be recovered by the proposed model. Natural convection in a vertical annulus filled with saturated porous media, natural convection in a vertical annulus without porous media, have been carried out, and the results predicted by the present LB model agree well with the existing numerical data. More, natural convection in a vertical annulus with spatially varying heat capacitance shows that the present model can address the problem where the heat capacitance varies spatially obviously successfully.

Dispersion-driven instability of mixed convective flow in porous media

This paper investigates the impact of hydrodynamic dispersion on the stability of free convection in a saturated horizontal porous layer subject to a transient vertical concentration gradient and a steady horizontal background flow. A linear stability analysis (LSA) was conducted using the quasi-steady-state approximation to obtain neutral stability curves, critical times, and the corresponding wavenumbers as a function of dispersivity ratio (α) and longitudinal dispersion strength (β). The LSA results showed that the dispersive boundary layer becomes less unstable as longitudinal and transverse dispersivity increase. In addition, for the isotropic dispersive system with α = 1, the critical time and its corresponding wavenumber follow τc = 167.6/(1 − β) and κc = 0.0696 (1 − β), respectively. The nonlinear dynamics of the system were studied by examining the interaction of convective fingers, dissolution flux, and the time-dependent Sherwood number. Finally, the results were applied to 24 deep saline aquifers in the Alberta Basin.

Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag

Recent interest in the effects of viscous dissipation on convective flows in porous media has centred almost exclusively on forced convection flows. In this paper, we investigate the manner in which it affects the onset and early stages of convection in Darcy–Bénard convection. A weakly nonlinear theory is described briefly, and it is shown that hexagonal cells are preferred over rolls when the Rayleigh number is sufficiently close to 4 π 2 . At higher Rayleigh numbers, two-dimensional rolls are preferred. When weak form drag is included, then subcritical convection eventually disappears as the Forchheimer parameter increases, yielding a highly novel situation wherein hexagonal convection arises supercritically. The range of stability of hexagons is found to increase.

Double MRT lattice Boltzmann model for axisymmetric convective flow in porous media

A double multiple-relaxation-time lattice Boltzmann (MRT LB) model for the axisymmetric thermal flow in porous media at the representative element volume, which uses the Darcy-Brinkmann-Forchheimer equation to describe the flow in porous region, is presented. The present model utilizes non-orthogonal transformation matrixes instead of the classical orthogonal ones. Validations are carried out in term of two numerical tests, including natural convection in a vertical annulus without and with a porous medium, respectively, and the results show good agreement with the previous studies.

Comparison between continuum and porous continuum models in studying natural convection in porous cavity with random distribution of solid obstacles

Purpose – The purpose of this paper is to improve the volume-averaged models for free convection flow in porous media. Design/methodology/approach – A pore scale simulation is conducted against which an independent volume-averaged solver is fine-tuned. Findings – Micro and macro scale results can merge if proper choice of local thermal non-equilibrium and thermal dispersion models are selected. This depends on the range of Ra values investigated. Originality/value – This is the first time a work like this is published in the literature.

Influence of Chemical Reaction, Heat Source, Soret and Dufour Effects on Separation of a Binary Fluid Mixture in MHD Natural Convection Flow in Porous Media

Separation of a heat absorbing or generating binary fluid mixture of incompressible viscous fluids in MHD natural convection flow about a vertical surface embedded in a saturated porous medium subjected to a chemical reaction is numerically analyzed, by taking into account the Soret and Dufour effects. The temperature and concentration profiles are drawn and the effects of magnetic, Lewish, Dufour, Soret, heat source, sustention parameter, order of the chemical reaction and chemical reaction parameter are exhibited graphically. The Nusselt and local Sherwood numbers are tabulated for various values of the above mentioned parameters. It is observed from the table that the Nusselt and local Sherwood numbers are effected significantly due to the presence of the chemical reaction and the magnetic field.

Effects of viscous dissipation on the convective instability of viscoelastic mixed convection flows in porous media

The thermal instability induced by small-amplitude perturbations superposed to the basic horizontal through flow in a plane porous layer (Prats problem) is here revisited. The fluid saturating the porous medium is assumed to be viscoelastic, and described through the Oldroyd-B model. The effect of viscous dissipation is taken into account. The main features of the linear instability are first described for the special case of negligible viscous dissipation, namely in the limit of a vanishing Gebhart number. Transverse rolls emerge as the selected normal modes at onset of convection. This same feature also arises when viscous dissipation is taken into account. In the general case, neutral stability curves as well as critical values of the Darcy–Rayleigh number, wave number and frequency are obtained by the numerical solution of an eigenvalue problem. It is shown that an adequate description of the combined effects of viscoelasticity and viscous dissipation can be obtained with the large Péclet number approximation. Such an approximation allows a simplified numerical solution and an optimised scaling of the parameters governing the transition to convective instability.

熱伝導性を有する多孔質体中の自然対流現象に対する多相場モデルの適用性

熱伝導性を有する多孔質体中の自然対流現象に対する多相場モデルの適用性

Geothermal data analysis and optimization

The possibility of convective upwelling in the sedimentary Perth Basin, based on available data and simple models, was examined and its relative contribution to heat transport in a geothermal context assessed. The presence of such upwelling could greatly increase the viability of geothermal power extraction from the Basin. The onset of convection is determined by the Rayleigh number, which provides a measure for the balance between buoyancy driven upwelling and viscous resistance to flow. Being sedimentary, the porous aquifer system is layered and fractured so that the effects of anisotropy, especially that in permeability, need to be accounted for when determining the critical Rayleigh number. Variations in viscosity and the coefficient of thermal expansion also occur within the convection zone. Estimates were made for the relative size of the convective contribution to heat transport. The possibility of the surface detection of cellular convection and the effects of horizontal inflow into the convection zone were examined. References D. N. Smith, ``Cockburn No. 1 Well, Western Australia, Well Completion Report'', Western Australian Petroleum, Pty. Limited , October 1967. O. Kvernvold and P. A. Tyvand, ``Nonlinear thermal convection in anisotropic porous media'', J. Fluid Mech. , 90, pp.609--624, 1979. E. R. Lapwood, ``Convection of a fluid in a porous medium'', Proc. Camb. Phil. Soc. , 44, pp.508--521, 1948. R. McKibbin, ``Convection in an aquifer above a layer of heated impermeable bedrock'', NZ J. Sci., 26, pp.49--64, 1983. R. McKibbin, ``Thermal convection in layered and anisotropic porous media: a review'', In: Wooding, R. A. and I. White, (eds) ``Convective Flows in Porous Media'', Dept. Sci. Indust. Res., Wellington, New Zealand, pp.113--127, 1985. R. McKibbin, N. Hale, R. W. Style, and N. Walters, ``Convection and heat transport in layered sloping warm-water aquifers'', Journal of Porous Media, In press. D. A. Nield and A. Bejan, Convection in porous media , 3rd Edition, Springer, 2006. R. C. Ransom, Practical formation evaluation , Wiley, 1995. K. Regenauer-Lieb, H. T. Chua, X. Wang, F. G. Horowitz and J. Wellman, ``Direct heat geothermal applications in the Perth Basin of Western Australia'', Proc. 34th Annual Stanford Workshop on Geothermal Engineering , Chapter 14, Stanford University, California, 2009.

Influence of boundary conditions on free convection flow in porous medium with newtonian heating from a vertical surface

The system of energy and momentum conservation equations, describing a free convection flow formed near a vertical surface in a semi-infinite porous medium under third-kind boundary conditions, is considered using boundary layer approximations. Asymptotic expansions in powers of a Darcy parameter (Da) are constructed. The dependence of flow characteristics on the governing dimensionless parameters Da and is analyzed. Analytical solutions available for the entire flow domain are derived.

Numerical study of natural convection in porous media (metals) using Lattice Boltzmann Method (LBM)

A thermal lattice BGK model with doubled populations is proposed to simulate the two-dimensional natural convection flow in porous media (porous metals). The accuracy of this method is validated by the benchmark solutions. The detailed flow and heat transfer at the pore level are revealed. The effects of pore density (cell size) and porosity on the natural convection are examined. Also the effect of porous media configuration (shape) on natural convection is investigated. The results showed that the overall heat transfer will be enhanced by lowering the porosity and cell size. The square porous medium can have a higher heat transfer performance than spheres due to the strong flow mixing and more surface area.

The method of fundamental solutions for oscillatory and porous buoyant flows

Accurate solutions of oscillatory Stokes flows in convection and convective flows in porous media are studied using the method of fundamental solutions (MFS). In the solution procedure, the flows are represented by a series of fundamental solutions where the intensities of these sources are determined by the collocation on the boundary data. The fundamental solutions are derived by transforming the governing equation into the product of harmonic and Helmholtz-type operators, which can be classified into three types depending on the oscillatory frequencies of temperature field. All the velocities, the pressure, and the stresses corresponding to the fundamental solutions are expressed explicitly in tensor forms for all the three cases. Three numerical examples were carried out to validate the proposed fundamental solutions and numerical schemes. Then, the method was also applied to study exterior flows around a sphere. In these studies, we derived the MFS formulas of drag forces. Numerical results were compared accurately with the analytical solutions, indicating the ability of the MFS for obtaining accurate solutions for problems with smooth boundary data. This study can also be treated as a preliminary research for nonlinear convective thermal flows if the particular solutions of the operators can be supplied, which are currently under investigations.

Comment on “Radiative Effect on Natural Convection Flows in Porous Media”, A. A. Mohammadein, M. A. Mansour, Sahar M. Abd El Gaied and Rama Subba Reddy Gorla [Transport in Porous Media 32:263–283, 1998

In the above paper the authors treat the natural convection boundary layer flow in a Darcy-Brinkman-Forchheimer porous medium. In the energy equation the radiation effect has been taken into account. A two-parameter perturbation method is used for the solution of the equations. The first order results are presented in tables and figures. This is an interesting work but there are some weak points which are presented below:

Nonlinear global modes in inhomogeneous mixed convection flows in porous media

The aim of this work is to investigate the fully nonlinear dynamics of mixed convection in porous media heated non-uniformly from below and through which an axial flow is maintained. Depending on the choice of the imposed inhomogeneous temperature profile, two cases prove to be of interest: the base flow displays an absolute instability region either detached from the inlet or attached to it. Results from a combined direct numerical simulations and linear stability approach have revealed that in the first case, the nonlinear solution is a steep nonlinear global mode, with a sharp stationary front located at a marginally absolutely unstable station. In the second configuration, the scaling laws for the establishment of a nonlinear global mode quenched by the inlet are found to agree perfectly with the theory. It is also found that in both configurations, the global frequency of synchronized oscillations corresponds to the local absolute frequency determined by linear criterion, even far from the threshold of global instability.

Response to the comments of Asterios Pantokratoras on “Perturbation analysis of radiative effect on free convection flows in porous medium in the presence of pressure work and viscous dissipation”

Response to the comments of Asterios Pantokratoras on “Perturbation analysis of radiative effect on free convection flows in porous medium in the presence of pressure work and viscous dissipation”