Horizontal Porous Layer Research Articles

Weak Nonlinear Oscillatory Double Diffusive Convection in a Viscoelastic Fluid-Saturated Porous Layer Under Gravity Modulation

A thermal instability caused by buoyancy force is investigated in an initially quiescent indefinitely extended horizontal porous layer saturated with non - Newtonian fluid. The characteristics of fluid motion are explained by using Modified Darcy’s law. Here, we considered the time periodic gravity field, and its effect on the system has been investigated. For the oscillatory mode of convection, a weakly non-linear stability analysis has been performed to evaluate Heat and Mass transfers in terms of the Nusselt number and Sherwood Number. To compute the results, the complex non-autonomous Ginzburg – Landau equation is used. It has been studied how viscoelastic fluid relaxation and retardation times impacts on heat and mass transmission. Further, the research confirms that heat and mass transfer can be successfully regulates by a technique that is external to the system. Finally, it has been discovered that excessive stability delays the onset of convection, hence increasing in the heat and mass transmission.

EFFECT OF VISCOUS DISSIPATION AND INTERNAL HEAT SOURCE ON MONO-DIFFUSIVE THERMOCONVECTIVE STABILITY IN A HORIZONTAL POROUS MEDIUM LAYER

A mathematical model is developed for studying the onset of mono-diffusive convective fluid flow in a horizontal porous layer with temperature gradient, internal heat generation, and viscous dissipation effects. Darcy's model is used for the porous medium, which is considered to be isotropic and homogenous. A linear instability analysis is conducted, and transverse or longitudinal roll disturbances are examined. The dimensionless emerging eigenvalue problem is solved numerically with the Runge-Kutta and shooting methods for both cases of disturbances, i.e,. longitudinal and transverse rolls. Critical wave number and critical vertical thermal Rayleigh number <i>R<sub>z</sub></i> are identified. For higher values of Gebhart number, Ge, a significant destabilizing effect of Hadley-Prats flow is computed. Internal heat generation also strongly modifies the critical vertical Rayleigh number. Extensive interpretation of the solutions related to the onset of convection is provided. The study is relevant to geophysical flows and materials processing systems.

INSTABILITY INVESTIGATION OF THERMO-BIOCONVECTION OF OXYTACTIC MICROORGANISM IN JEFFREY NANOLIQUID WITH EFFECTS OF INTERNAL HEAT SOURCE

The intent of this article is to investigate the influence of internal heat source on the stability of a suspension containing oxytactic microorganisms in a shallow horizontal porous fluid layer saturated by Jeffrey nanoliquid. The Jeffrey-Buongiorno model governs the nanofluid bioconvection flow. Normal mode analysis is utilized, and the principle of exchange of stability is invoked due to the absence of opposing agencies. The stability criteria is defined in terms of critical thermal Rayleigh number as a function of various flow governing parameters by using the weighted residual Galerkin method. It is perceived that the increment of uniform heat supply and the presence of oxytactic microorganism cells as well as the nanoparticles enhances heat transfer and constitutes an unstable system that hastens bioconvection. The nanoparticle Lewis number is found to have a dual impact on the system stability that relies on the nanoparticle Rayleigh number and exhibits destabilizing nature for top-heavy nanoparticle concentration. It is also observed that the Jeffrey parameter produces nonoscillatory instability in the system.

A weakly nonlinear analysis of the effect of vertical throughflow on Darcy–Bénard convection

The aim of this paper is to analyze the effect of a downward vertical net mass flow on the type of instability that occurs in a horizontal fluid-saturated porous layer that is heated from below. The strength of the downflow is modelled by Pe, the Péclet number. First, we prove the validity of the principle of exchange of stabilities; consequently, we perform a linear instability analysis of the basic steady flow to determine the critical Darcy–Rayleigh number for the onset of steady convective instability as a function of Pe. Then, a weakly nonlinear stability analysis is performed to determine the smallest value of the Péclet number for which the onset of convection corresponds to a subcritical instability.

PERMEABILITY MEASUREMENTS IN EXPERIMENTS ON CONVECTIVE HEAT TRANSFER IN A COMPLEX FIBROUS POROUS MEDIUM STRUCTURED BY A 3D PHOTOPOLYMER FRAMEWORK

The paper is devoted to the experimental study concerning the properties of a complex fibrous porous medium. The medium consists of cylindrical fibers structured by a 3D photopolymer framework. Three porous samples with the porosities of 0.77, 0.82, and 0.88 are manufactured. An alternative method has been developed for determining the permeability of samples. It is based on the measurements of convective heat transfer in a horizontal porous layer saturated with fluid under the gravitational field. The values of permeability are found for the investigated samples by the two formulas which are derived through the Darcy and Darcy-Brinkman models and include our experimental data. Agreement between the permeability values obtained by the two different models is achieved. It is shown that the permeability of the complex fibrous porous medium grows with decreasing the solid volume fraction of functional fibers and tends to the value of the permeability of the 3D photopolymer framework. The permeability of the 3D photopolymer framework is evaluated independently of the method presented in the paper.

Forchheimer–Bénard Instability of the Non-Newtonian Fluid

The present paper examines the effect of vertical throughflow on the onset of convective instability in a horizontal porous layer filled with a non-Newtonian power-law fluid (PL). The permeable boundary layers are exposed to two different uniform constant temperature conditions, The Oberbeck-Boussinesq hypothesis is considered with the Darcy-Forchheimer model. A fourth-order eigenvalue problem is stemmed from the performance of the linear stability analysis, and the critical values are obtained using the shooting method combined with the Runge-Kutta method. The non-Newtonian Darcy-Rayleigh number (R), the Péclet number (Pe), the Forchheimer number (G), and the power-law index (n) are the parameters whose value play a crucial role in the onset of instability. The finding shows more stabilizing effects arise in pseudoplastic fluid than dilatant one at Peclet number Pe << 1 where the inverse behaviour takes place at large Peclet number even with the existence of the drag number or without it.

Effect of triangular porous layer on the transfer of heat and species in a channel‐open cavity

AbstractThis paper addresses the heat and species transfer in a composite cavity linked with a horizontal channel. The cavity comprises a triangular porous layer and one of its vertical sides is exposed to a high temperature and concentration. The mathematical conservation equations are solved numerically using the Galerkin finite element method. The ranges of Reynolds and Richardson numbers are taken to ascertain laminar flow, Re = 50–250 and Ri = 0.1–100. The size of the porous layer is quantified by the thickness of the porous layer Hp = 0.25–1. The problem is studied for two cases of heat and species sources; the opposing case, when the active side is on the right, and assisting case, when the active side is on the left. Results reveal that for specified conditions, the triangular porous layer increases Nusselt and Sherwood numbers by 30% and 32%, respectively, more than the horizontal porous layer. The opposing case gives maximum convective heat transfer, where for Ri = 0.01, the Nusselt number is higher by 61% and 134% for Re = 50 and 250, respectively, while for Ri = 100, the percentages increase are 67% and 43%.

Density inversion phenomenon in porous penetrative convection

Penetrative convection occurs in many natural phenomena where an unstable stratified fluid moves into a stable one. This topic is of interest in many research fields like, for example, in geophysics and astrophysics. In the present paper, on taking into account for quadratic density law, the onset of penetrative convection in a horizontal porous layer is investigated. For the problem at stake, since the principle of exchange of stabilities has been proved, the convection can occur only through a secondary stationary motion. The critical Rayleigh numbers for the onset of stationary convection have been found via the linear instability analysis of the conduction solution. Moreover, the nonlinear stability of the motionless state has been investigated via the energy method. Numerical simulations have been performed through Chebyshev-τ spectral method in order to analyse the behaviour of stability and instability thresholds with respect to the upper plane temperature.

Buoyancy segregation suppresses viscous fingering in horizontal displacements in a porous layer

We consider the axisymmetric displacement of an ambient fluid by a second input fluid of lower density and lower viscosity in a horizontal porous layer. If the two fluids have been segregated vertically by buoyancy, then the flow becomes self-similar with the input fluid preferentially flowing near the upper boundary. We show that this axisymmetric self-similar flow is stable to angular-dependent perturbations for any viscosity ratio. The Saffman–Taylor instability is suppressed due to the buoyancy segregation of the fluids. The radial extent of the segregated flow is inversely proportional to the viscosity ratio. This horizontal extension of the intrusion eliminates the discontinuity in the pressure gradient between the fluids associated with the viscosity contrast. Hence at late times, viscous fingering is shut down even for arbitrarily small density differences. The stability is confirmed through numerical integration of a coupled problem for the interface shape and the pressure gradient, and through complementary asymptotic analysis, which predicts the decay rate for each mode. The results are extended to anisotropic and vertically heterogeneous layers. The interface may have relatively steep shock-like regions, but the flow is always stable when the fluids have been segregated by buoyancy, as in a uniform layer.

Effect Of MFD Viscosity On Ferroconvection In A Fluid Saturated Porous Medium With Variable Gravity

<p>Convective instability of a horizontal ferromagnetic fluid saturated porous layer with magnetic field dependent (MFD) viscosity subjected to gravity field varying with distance in the layer is investigated. The fluid motion is described by the Brinkman model. The method of small perturbation is applied and the resulting eigenvalue problem is solved using the higher order Galerkin technique. The stationary instability is shown to be the preferred mode of instability and the resulting eigenvalue problem is solved by taking into account the realistic rigidrigid- isothermal boundary conditions. The study reveals that the effect of MFD viscosity is to delay the onset of ferroconvection and the stabilizing effect of MFD viscosity is reduced when the magnetic Rayleigh number is sufficiently large. In the presence of variable gravity, the effect of magnetic and non-magnetic parameters on ferroconvective instability is also discussed.</p>

Effect of Time-Dependent Sinusoidal Boundary Temperatures on the Onset Of Ferroconvection in a Porous Medium

<p>The effect of temperature modulation on the onset of Darcy ferroconvection in a horizontal porous layer heated from below is investigated. The analysis is based on the assumption that the amplitude of the temperature modulation is small enough compared with the imposed steady temperature difference. The effect of the oscillating temperature field is treated by a perturbation expansion in powers of the amplitude of the applied field. The effect of magnetic parameters, Vadasz number and temperature modulation in the cases of symmetric, asymmetric and bottom wall modulation, were discussed. The study divulges that subcritical motion exists for symmetric temperature modulation for low frequency. In the case of asymmetric and bottom wall modulation only supercritical motion exists.</p>

Soret and Dufour effects on thresholds of stability in a horizontal Brinkman porous layer submitted to vertical temperature and species gradients using linear and non-linear analysis

The present study deals with Soret and Dufour effects on the onset of double-diffusive natural convection in a horizontal Brinkman porous layer with a free-stress upper boundary. The thresholds of stationary, oscillatory, and subcritical bifurcations are derived on the basis of linear and non-linear analysis, as functions of the governing parameters. The effect of Dufour ([Formula: see text]) and Soret [Formula: see text] parameters on the thresholds of instabilities is illustrated and discussed. There are critical combinations [Formula: see text] for which the thresholds of supercritical bifurcations are independent of the buoyancy ratio. Particularly, for [Formula: see text] and [Formula: see text], the stationary convection starts at the threshold of the pure thermal convection whatever the value of the buoyancy ratio.

Effects of thermodiffusion on Darcy–Brinkman convection in a rotating binary nanofluid saturating a porous layer

In this study, the onset of convection in a rotating horizontal porous layer saturated by a binary nanofluid was theoretically investigated under the influence of thermodiffusion and nanoparticles. To study the onset of convection, the Darcy–Brinkman model was employed for the porous medium, and the thermal Rayleigh number was derived analytically using linear stability analysis. Water–ammonia-based silver, copper, and alumina, three binary nanofluids, were considered, and the effect of nanoparticles on the stability of the system was analysed using addition factor analysis. The Brinkman model for viscosity and Bruggeman model under the mean field approach for thermal conductivity were used to study the impact of nanoparticles. Heat transport was examined by calculating the heat transfer coefficient. The effects of nondimensional parameters involved in binary nanofluids on the onset of convective instabilities are depicted pictorially. The dependence of the size of the convection cells on nondimensional parameters is also discussed. The Darcy–Taylor number decreases the size of convection cells, whereas the Darcy number increases the size of convection cells. The size of the convection cells is independent of the porosity of the medium, Lewis number, volume fraction of nanoparticles, Soret effect of nanoparticles, and the solute in binary nanofluids. Furthermore, the Darcy–Taylor number and porosity have stabilising effects, whereas the Darcy number, volume fraction of nanoparticles, and Lewis number have destabilising effects on the system. Soret effects of nanoparticles and solutes exhibit dual consequences on stability. They stabilise the binary nanofluid layer if δ4 < –1 and destabilise when δ4 > –1. Their effect is immaterial if δ4 = –1.

Time-evolving to space-evolving Rayleigh–Bénard instability of a horizontal porous medium flow

The Rayleigh–Bénard instability of the stationary throughflow in a horizontal porous layer, also known as Prats' problem, is analyzed here in a fresh new perspective. In fact, the classical analysis of linear instability, carried out by employing time-evolving and space-periodic Fourier modes, is reconsidered here by focusing on the effects of time-periodic and space-evolving modes. The basic stationary flow is assumed to be perturbed by a localized source of perturbation that is steady-periodic in time. Then, the spatial development of such perturbations is monitored in order to detect their possible amplification or decay in their direction of propagation. Accordingly, the spatial stability/instability threshold is determined. The study is carried out by employing a Fourier transform formalism, where the transformed variable is time.

Rayleigh-Benard Convection in Nanofluids Layer saturated in a Rotating Anisotropic Porous Medium with Feedback Control and Internal Heat Source

Control strategy on Rayleigh-Benard convection in rotating nanofluids saturated in anisotropic porous layer heated from below is studied in the presence of uniformly internal heat source for rigid-rigid, free-free, and lower-rigid and upper-free boundaries. Feedback control strategy with an array of sensors situated at the top plate and actuators located at the bottom plate of the nanofluids layer are considered in this study. Linear stability analysis based on normal mode technique has been performed, the eigenvalue problem is obtained numerically by implementing the Galerkin method and computed by using Maple software. Model employed for the nanofluids includes the mechanisms of Brownian motion and thermophoresis. The problem of the onset of convective rolls instabilities in a horizontal porous layer with isothermal boundaries at unequal temperatures known as Horton-Roger-Lapwood model based on the Darcy model for the fluids flow is used. The influences of internal heat source’s strength, modified diffusivity ratio, nanoparticles concentration Darcy-Rayleigh number and nanofluids Lewis number are found to advance the onset of convection, meanwhile the mechanical anisotropy parameter, thermal anisotropy parameter, porosity, rotation, and controller effects are to slow down the process of convective instability. No visible observation on the modified particle density increment and rigid-rigid boundaries are the most stable system compared to free-free and rigid-free boundaries.

Double rotations of cylinders on thermosolutal convection of a wavy porous medium inside a cavity mobilized by a nanofluid and impacted by a magnetic field

PurposeThe purpose of this paper is to work out the magnetic forces on heat/mass transmission in a cavity filled with a nanofluid and wavy porous medium by applying the incompressible smoothed particle hydrodynamics (ISPH) method.Design/methodology/approachThe cavity is filled by a nanofluid and an undulating layer of a porous medium. The inserted two circular cylinders are rotated around the cavity’s center by a uniform circular velocity. The outer circular cylinder has four gates, and it carries two different boundary conditions. The inner circular cylinder is carrying Th and Ch. The Lagrangian description of the dimensionless regulating equations is solved numerically by the ISPH method.FindingsThe major outcomes of the completed numerical simulations illustrated the significance of the wavy porous layer in declining the nanofluid movements, temperature and concentration in a cavity. The nanofluid movements are declining by an increase in nanoparticle parameter and Hartmann number. The variations on the boundary conditions of an outer circular cylinder are changing the lineaments of heat/mass transfer in a cavity.Originality/valueThe originality of this study is investigating the dual rotations of the cylinders on magnetohydrodynamics thermosolutal convection of a nanofluid in a cavity saturated by two wavy horizontal porous layers.

A note on “Double-diffusive Soret convection phenomenon in porous media: effect of Vadasz inertia term”

In this short paper, some analytical results found in “Double-diffusive Soret convection phenomenon in porous media: effect of Vadasz inertia term” by F. Capone, R. De Luca, M. Vitiello, Ricerche Mat. 68, 581–595 (2019), are recalled in order to better explore the dynamic of thermosolutal convection in a horizontal porous layer with the influence of Vadasz and Soret terms.

Solute transport in a horizontal porous layer at a high solute concentration

Solute transport in a porous media has not been studied systematically up to present, and there is an uncertainty about the proper governing law for describing the transport process in such media. In this study, we analyze the data of solute transport experiments in a horizontal sand column packed with uniform glass beads. Sodium chloride (NaCl) is chosen to be the tracer. A number of tracer tests are conducted to examine the transport process under different NaCl concentrations. The obtained velocity-time profiles and BTCs indicate different stages of filtering. Based on the results a possible scenario of solute transport under fixed flow rate is proposed.

Instability of Vertical Throughflows in Bidisperse Porous Media

In this paper, the instability of a vertical fluid motion, or throughflow, is investigated in a horizontal bidisperse porous layer that is uniformly heated from below. By means of the order-1 Galerkin approximation method, the critical Darcy–Rayleigh number for the onset of steady instability is determined in closed form. The coincidence between the linear instability threshold and the global nonlinear stability threshold, in the energy norm, is shown.

Buoyancy-driven instabilities of partially miscible fluids in inclined porous media

This study presents a buoyancy-driven stability analysis in a three-dimensional inclined porous medium with a capillary transition zone that is formed between a non-wetting and an underlying wetting phase. In this two-phase, two-component, partially miscible system, a solute from a non-wetting phase diffuses into a porous layer saturated with a wetting-phase fluid, creating a dense diffusive boundary layer beneath an established capillary transition zone. Transient concentration and gravity-driven velocity fields are derived for the wetting phase while the saturation field remains fixed. Linear stability analysis with the quasi-steady-state approximation is employed to determine the onset of solutal convective instability for buoyancy-dominant, in-transition and capillary-dominant systems. The analysis of the problem leads to a differential eigenvalue problem composed of a system of three complex-valued equations that are numerically solved to determine the critical times, critical wavenumbers and neutral stability curves as a function of inclination angle for different Bond numbers. The layer inclination is shown to play an essential role in the stability of the problem, where the gravity-driven flow removes solute concentrations in the diffusive boundary layer. The results indicate that the horizontal porous layer exhibits the fastest onset of instability, and longitudinal rolls are always more unstable than oblique and transverse rolls. The inclination angle has a more substantial impact on stabilizing the diffusive boundary layer in the buoyancy-dominant than in the capillary-dominant systems. Furthermore, for both buoyancy-dominant and capillary-dominant systems, the critical times and wavenumbers vary exponentially with inclination angle ≤ 60° and follow the Stirling model.