Anisotropic Porous Layer Research Articles

Combined Effect of Thermal Modulation and AC Electric Field on the Onset of Electrothermoconvection in Anisotropic Porous Layer

Combined Effect of Thermal Modulation and AC Electric Field on the Onset of Electrothermoconvection in Anisotropic Porous Layer

On Double-Diffusive Convection in a Binary Viscoelastic Fluid Saturated Anisotropic Porous Layer

On Double-Diffusive Convection in a Binary Viscoelastic Fluid Saturated Anisotropic Porous Layer

Stability of a liquid film flowing down an inclined anisotropic and inhomogeneous porous layer: an analytical description

We study the effect of anisotropy and inhomogeneity in the permeability of the porous layer on the stability of surface waves of an inclined fluid–porous double-layer system. The fluid is assumed to be Newtonian and the porous layer to be Darcian. The porous layer is saturated with the same fluid and the two layers are coupled at the interface via the Beavers–Joseph condition. Linear stability analysis is performed based on a long-wave approximation. The resulting eigenvalue problem is exactly solved up to third order in the wavenumber. The anisotropic behaviour of permeability, cross-stream component of permeability, surface tension and porosity are found to have only higher-order effects on the stability characteristics of the system. On the other hand, the inhomogeneous feature in the streamwise component of permeability play a dominant role in determining the stability of the gravity-driven surface waves; as do other system parameters such as the thickness of the fluid layer relative to that of the porous layer and the Beavers–Joseph coefficient.

A multiple-relaxation-time lattice Boltzmann model for the flow and heat transfer in a hydrodynamically and thermally anisotropic porous medium

A multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for simulating flow and heat transfer in the hydrodynamically and thermally anisotropic porous medium at the representative-elementary-volume (REV) scale. By selecting the appropriate equilibrium distributions, relaxation matrix and discrete force/heat source terms, the present MRT LB model can recover the correct Darcy–Brinkman–Forchheimer and energy equations with anisotropic permeability and thermal conductivity through the Chapman–Enskog procedure. Several natural convection problems in anisotropic porous medium are simulated to validate the present LB model. The corresponding numerical results are in good agreement with data in the available literature. Especially, natural convection in a cavity with two anisotropic porous layers is investigated. The numerical results indicates that, the use of anisotropic porous layer with some optimal parameters can produce higher rate of heat transfer compared with the isotropic porous layer.

Generation of SH-type waves in a poroelastic layer sandwiched between prestressed orthotropic and nonhomogeneous mantles

ABSTRACTThe present work is concerned with a detailed illustration on the study of horizontally polarized shear waves (SH-type) propagation in a prestressed fluid saturated anisotropic porous layer sandwiched by prestressed orthotropic medium and nonhomogeneous mantles. The frequency equation for the assumed model is derived and their medium characteristics, such as porosity, prestress, anisotropy, and nonhomogeneity, are discussed. Numerical treatment is given to analyze these effects on phase velocities of SH-type waves and is plotted in various graphs. The parametric study divulges that the magnitude of wave velocities increases with the increase of nonhomogeneity parameter and prestress parameter.

Cross-Diffusion Effects on the Onset of Double Diffusive Convection in a Couple Stress Fluid Saturated Rotating Anisotropic Porous Layer

Cross-Diffusion Effects on the Onset of Double Diffusive Convection in a Couple Stress Fluid Saturated Rotating Anisotropic Porous Layer

Effect of irregularity on torsional surface waves in an initially stressed anisotropic porous layer sandwiched between homogeneous and non-homogeneous half-space

The present paper is concerned with the propagation of torsional surface waves in an initially stressed anisotropic porous layer sandwiched between homogeneous and non-homogeneous half-space. We assume the quadratic inhomogeneity in rigidity and density in the lower half-space and irregularity is taken in the form of rectangle at the interface separating the layer from the lower half-space. The dispersion equation for torsional waves has been obtained in a closed form. Velocity equation is also obtained in the absence of irregularity. The study reveals that the presence of irregularity, initial stress, porosity, inhomogeneity and anisotropy factor in the dispersion equation approves the significant effect of these parameters in the propagation of torsional waves in porous medium. It has also been observed that for a uniform media, the velocity equation reduces to the classical result of Love wave.

Impacts on the Propagation of SH-Waves in a Heterogeneous Viscoelastic Layer Sandwiched between an Anisotropic Porous Layer and an Initially Stressed Isotropic Half Space

AbstractThe present study deals with the affected behaviour of SH-wave propagation through a viscoelastic layer sandwiched between an anisotropic porous layer of finite thickness and an isotropic half space. The sandwiched viscoelastic layer is considered as heterogeneous medium of finite thickness and isotropic half-space is considered as initially stressed medium. The method of separation of variables has been applied to obtain the dispersion equation of SH-wave in their respective media. The obtained complex dispersion relation has been separated into real and imaginary parts. Moreover, the dispersion relation has been satisfied with the classical condition of Love waves. The effects of heterogeneity, attenuation constant, dissipation factor of viscoelasticity, initial stress (compressive), thickness ratio of two layers and porosity on the propagation of SH-waves have been shown by number of graphs. Graphs have been plotted for the dimensionless phase and damping velocity on the propagation of SH-waves with respect to the dimensionless real wave number. The results may be useful to explore the nature and peculiarity of SH-wave propagation in the viscoelastic structure.

On the onset of stationary convection in double-diffusive binary viscoelastic fluid saturated anisotropic porous layer

Linear stability of double diffusive convection in a binary viscoelastic fluid saturated anisotropic porous layer has been studied analytically. A sufficient condition for the occurrence of stationary convection has been derived in terms of the parameters of the system alone. It is further proved the above result is uniformly valid for any combination of the bounding surfaces.

On dispersion of Love type surface wave in anisotropic porous layer with periodic non uniform boundary surface

The paper present a theoretical investigation of the propagation of Love waves past an anisotropic fluid saturated porous layer with irregular periodic boundaries and sandwiched between two elastic isotropic half spaces. The porous layer is assumed to be initially stressed. Fourier series expansion has been implemented to describe the irregular boundaries of the layer. Using appropriate boundary conditions a closed form dispersion and absorption relation for Love wave in the porous layer have been derived. The dispersion equation has been investigated extensively through numerical calculation for particular irregular interface to explore the effect of non dimensional average thickness and the periodic roughness of the boundaries on the phase velocity of Love wave. Also the effect of initial stress as well as the porosity on wave velocity is studied. A comparative study has been carried out through various graphs to study the consequence of different parameters on the phase velocity between porous and corresponding non porous layer. A close compliance is also established in some special cases to the existing solutions available from analytical methods.

Influence of fluid flow and heat transfer on crack propagation in SOFC multi-layered like material with anisotropic porous layers

An advanced numerical model based on the eXtended Finite Element Method (XFEM) is developed and used to investigate the effect of heat transfer and fluid flow on crack propagation in multi-layered SOFC with anisotropic porous layers. Effect of the anisotropy on the onset and the propagation path of cracks are investigated. Heat transport in the porous media is described by heat convection in the fluid phase, and heat conduction in both the fluid and solid phases. A time splitting technique is used to allow different numerical treatment for the heat transfer processes within the porous layer. A combination of Discontinuous Galerkin (DG) and Multi-Point Flux Approximation (MPFA) methods are used to solve the advection–diffusion heat transfer in the flow channel and the fluid phase in the porous material. XFEM is used to solve the heat diffusion within the porous layers and the thermomechanical problem. The fluid flow, governed by Navier–Stokes and Darcy's law, is discretised with the nonconforming Crouzeix–Raviart (CR) finite element method. The multi-physics model is implemented and validated by comparing the computed Stress Intensity Factors (SIF) to ones from the literature. The methodology seems to be robust, accurate and the computational cost is reduced thanks to the XFEM.

Stability of Poiseuille flow in a fluid overlying an anisotropic and inhomogeneous porous layer.

We present the linear stability analysis of horizontal Poiseuille flow in a fluid overlying a porous medium with anisotropic and inhomogeneous permeability. The generalized Darcy model is used to describe the flow in the porous medium with the Beavers-Joseph condition at the interface of the two layers and the eigenvalue problem is solved numerically. The effect of major system parameters on the stability characteristics is addressed in detail. It is shown that the anisotropic and inhomogeneous modulation of the permeability of the underlying porous layer provides an effective means for passive control of the flow stability.

Propagation of Torsional Surface Wave in an Anisotropic Porous Medium over a Dry Sandy Half-Space

AbstractThe present paper deals with the propagation of torsional surface waves in an anisotropic porous layer over an inhomogeneous dry sandy half-space. The shear modulus of elasticity and density has been considered as variable in a porous layer, and the modulus of rigidity remains variable in a sandy half-space. The Whittaker function and its derivative give the result of the phase velocity equation using suitable boundary conditions. The effect of a dimensionless wave number on a dispersion curve has been found numerically, and a graphical representation of porosity and sandiness has been given. The derived dispersion equation found that the velocity of a torsional wave is influenced because of the presence of porosity, inhomogeneity, and sandy half-space. The study may be useful to understand the nature of seismic-wave propagation during earthquakes.

Magnetic field and throughflow effects on double-diffusive convection in internally heated anisotropic porous media

A model for double-diffusive convection in an anisotropic porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source and subjected to a vertical magnetic field and variable gravity effect. The validity of both the linear instability and global nonlinear stability thresholds are tested using three dimensional simulation. Our results show that the linear theory produce a good prediction on the onset of instability in the steady state throughflow. It is known that as Rc increases the onset of convection is more likely to be via oscillatory convection as opposed to steady convection, and the three dimensional simulation results show that as Rc increases, the actual threshold moving toward the nonlinear stability threshold and the behaviour of the perturbation of the solutions becomes more oscillated.

Local thermal non-equilibrium effects on thermal convection in a rotating anisotropic porous layer

Effects of local thermal non-equilibrium (LTNE) on thermal convection in a rotating fluid-saturated anisotropic porous layer are investigated. The analysis has been carried out by constructing a simplified model consisting of six coupled nonlinear ordinary differential equations. The study reveals the equivalence of linear and nonlinear stability boundaries indicating the linearized instability theory captures completely the physics of the onset of convection. Results show that the presence of rotation is to introduce oscillatory convection once the Taylor number exceeds a threshold value. The preferred mode of instability is found to be influenced significantly by the mechanical anisotropy parameter as well and it is demonstrated that it has both stabilizing and destabilizing effects on the steady onset in the presence of rotation. Besides, asymptotic analyses for small and large values of the interphase heat transfer coefficient are presented. Heat transport is calculated in terms of Nusselt number. Also, the coupled nonlinear ordinary differential equations are solved numerically using Runge–Kutta method and the transient behavior of Nusselt number is demonstrated for various values of physical parameters.

Onset of Convection in an Anisotropic Porous Layer with Vertical Principal Axes

A Horton–Rogers–Lapwood problem for onset of thermal convection in a horizontal porous layer with anisotropic permeability and diffusivity is solved analytically. There is full 3D anisotropy, with the restriction that one of each set of principal axes points in the vertical direction. The porous layer has infinite horizontal extent. The upper and lower boundaries are taken to be impermeable and kept at constant temperatures. The critical Rayleigh number for the onset is calculated as a function of the five parameters governing the anisotropy: two permeability ratios, two diffusivity ratios and the angle (in the horizontal plane) between the principal axes of permeability and diffusivity.

Penetrative Brinkman convection in an anisotropic porous layer saturated by a nanofluid

The onset of penetrative Brinkman convection in a nanofluid saturated anisotropic porous layer is investigated via uniform internal heating for rigid-rigid, free-free, and lower-rigid and upper-free boundaries. The flux of volume fraction of nanoparticles is taken to be zero on the isothermal boundaries and the eigenvalue problem is solved using the Galerkin method. The numerical computations carried out indicated the validity of principle of exchange of stability for all types of velocity boundary conditions. The effect of heat source strength, mechanical anisotropy parameter, modified diffusivity ratio, nanoparticle concentration Darcy-Rayleigh number and Lewis number is to hasten, while the Darcy number and thermal anisotropy parameter are to delay the onset of convection. In contrast to the regular fluid saturating a Darcy porous medium, the onset of convection for nanofluids is found to be influenced even when the ratio of mechanical anisotropy parameter to thermal anisotropy parameter is unity.

A pore-scale model for the cathode electrode of a proton exchange membrane fuel cell by lattice Boltzmann method

A pore-scale model based on the lattice Boltzmann method (LBM) is proposed for the cathode electrode of a PEM fuel cell with heterogeneous and anisotropic porous gas diffusion layer (GDL) and interdigitated flow field. An active approach is implemented to model multi-component transport in GDL, which leads to enhanced accuracy, especially at higher activation over-potentials. The core of the paper is the implementation of an electrochemical reaction with an active approach in a multi-component lattice Boltzmann model for the first time. After model validation, the capability of the presented model is demonstrated through a parametric study. Effects of activation over-potential, pressure differential between inlet and outlet gas channels, land width to channel width ratio, and channel width are investigated. The results show the significant influence of GDL microstructure on the oxygen distribution and current density profile.

Instabilities in a fluid overlying an inclined anisotropic and inhomogeneous porous layer

AbstractIn this paper, linear stability analysis on a Newtonian fluid film flowing under the effect of gravity over an inclined porous medium saturated with the same fluid in isothermal condition is carried out. The focus is placed on the effect of the anisotropic and inhomogeneous variations in the permeability of the porous medium on the shear mode and surface mode instabilities. The fluid–porous system is modelled by a coupled two-dimensional Navier–Stokes/Darcy problem. The perturbation equations are solved numerically using the Chebyshev collocation method. Detailed stability characteristics as a function of the depth ratio (the ratio of the depth of the fluid layer to that of the porous layer), the anisotropic parameter (the ratio of the permeability in the direction of the basic flow to that in the direction transverse to the basic flow) and the inhomogeneity functions are presented.

Effect of Internal Heating on Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Medium

The effect of internal heat source on double diffusive convection in a couple stress fluid saturated horizontal anisotropic porous layer was studied analytically by performing linear and nonlinear stability analyses. For linear stability analysis, normal mode technique was used, whereas for nonlinear stability analysis a minimal representation of Fourier series upto two terms was used. Effects of anisotropic parameter, couple stress parameter, solute Rayleigh number, Vadasz number, Lewis number, internal heat source parameter on stationary, oscillatory and finite amplitude convection were obtained and shown graphically. Also the graphs for heat and mass transport, streamlines, isotherms, isohalines for steady and unsteady cases were drawn. It was found that internal heat source parameter had destabilizing effect on all modes of convection. Heat transport increased and mass transport decreased with the increase in internal heat source parameter.