Fluid Saturated Porous Layer Research Articles

Effects of Uniform and Non-Uniform Temperature Gradients on Marangoni Convection in a Composite Layer with Variable Heat Sources

An investigation is carried out to determine the effect of uniform and non-uniform temperature profiles on single component Darcy-Benard Marangoni (DBM) convection in a composite layer system consisting of an incompressible fluid saturated porous layer on top of which is a layer of the same fluid with variable heat sources in both layers. The upper surface of the fluid layer is free with surface tension effects depending on temperature and the lower surface of the porous layer is rigid. The eigen value, thermal Marangoni number (TMN) is solved exactly for linear, parabolic and inverted parabolic temperature profiles for the adiabatic thermal boundary conditions at the horizontal boundaries of the composite layer. The influence of various dimensionless parameters on the eigen value against depth ratio is discussed in detail.

Hydrodynamic instability of flow through a rotating channel filled with isotropic porous media

Various geophysical and engineering applications have underlying physics, comprising system rotation's effects on the dynamics and transport phenomena in porous media flows. Comprehensive knowledge of the instability in a rotating fluid-saturated porous layer is beneficial for controlling the transport phenomena and the mixing process. The present study focuses on the temporal evolution of small disturbances in a pressure-induced fluid flow through a spanwise rotating channel filled with an isotropic porous material. A Darcy–Brinkman model, including the Coriolis force term in the momentum equation, is employed to describe the developed flow. A normal mode analysis is performed, and the coupled Orr–Sommerfeld–Squire eigenvalue problem is formulated to capture the linear instability of the perturbed flow. The Chebyshev collocation technique is used to solve the fourth-order eigenvalue problem to capture the transient behavior of the finite-amplitude disturbances. The temporal growth rate and marginal stability curves related to the Coriolis force-based instabilities are investigated. The rotating porous media flow is unstable at a much lower Reynolds number than the non-rotating configuration. The analysis confirms co-existing unstable modes and mode coalescence for a specific range of parameters, which can enhance the mixing and transport inside the porous layer. The neutral stability curves show the appearance of two different unstable zones corresponding to the long and moderate waves. Moreover, the higher permeability and porosity of the porous medium have a destabilizing influence.

Onset of triply diffusive convection in a power-law fluid saturated porous layer

Onset of triply diffusive convection in a power-law fluid saturated porous layer

Effects of Throughflow and Gravity Modulation on Thermal Convection in a Couple Stress Fluid Saturated Porous Layer

In this paper, we have investigated the effects of throughflow and gravity modulation on a couple stress fluid saturated porous layer using non-autonomous Ginzburg-Landau model. A small variation of disturbances has been considered to examine the nonlinear thermal instability in a couple stress fluid saturated porous media. At third order, the finite amplitude of convection has been calculated which determines heat transfer. The effect of throughflow i.e., inflow and outflow have dual nature of heat transfer. The couple-stress parameter has stabilizing nature on thermal instability. The couple-stress parameter has stabilizing nature on thermal instability. Further it is found that upward directed flow enhances and downward directed flow diminishes heat transfer.

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 maximum density and internal heating on the stability of rotating fluid saturated porous layer using LTNE model

The impact of heat generated inside the porous layer containing a fluid and density maximum when the porous structure is studied analytically subjected to rotation for the case of unlike temperatures of both solid and fluid phases. Two equations each representing solid and fluid phases are used as energy equations. The linear stability theory is used and is based on normal mode technique. Galerkin method is used to find the Eigen values of the problem. The rotation of the porous layer provides extra strength to the system, protecting the structure from instability, however internal heat generation does not support the system in retaining its strength, causing the system to destabilize. Both the conductivity ratio and the density function have a negative impact on system stability. Consequently, the rotation parameter Ta stabilizes the system, whereas internal heat generation, conductivity ratio, and density function destabilizes the onset of convection.

Weakly Nonlinear Stability of Thermosolutal Convection in an Oldroyd-B Fluid-Saturated Anisotropic Porous Layer Using a Local Thermal Nonequilibrium Model

Abstract The two-temperature model of local thermal nonequilibrium (LTNE) is utilized to investigate a weakly nonlinear stability of thermosolutal convection in an Oldroyd-B fluid-saturated anisotropic porous layer. The anisotropies in permeability, thermal conductivities of the porous medium, and solutal diffusivity are accounted for by second-order tensors with their principal directions coinciding with the horizontal and vertical coordinate axes. A modified Darcy–Oldroyd model is employed to describe the flow in a porous medium bounded by impermeable plane walls with uniform and unequal temperatures as well as solute concentrations. The cubic-Landau equations are derived in the neighborhood of stationary and oscillatory onset using a modified perturbation approach and the stability of bifurcating equilibrium solutions is discussed. The advantage is taken to present some additional results on the linear instability aspects as well. It is manifested that the solutal anisotropy parameter also plays a decisive role on the instability characteristics of the system. It is found that the stationary bifurcating solution transforms from supercritical to subcritical while the oscillatory bifurcating solution transforms from supercritical to subcritical and revert to supercritical. The Nusselt and Sherwood numbers are used to examine the influence of LTNE and viscoelastic parameters on heat and mass transfer, respectively. The results of Maxwell fluid are outlined as a particular case from this study.

Nonlinear stability analysis of double diffusive convection in a fluid saturated porous layer with variable gravity and throughflow

This paper develops a detailed study of linear and nonlinear stability analyses, for the double diffusive convection problem in a porous medium, when heating is done from below and, salting is done from below as well as from above. The linear analysis is performed using normal mode technique and nonlinear analysis is developed using energy technique. The Chebyshev pseudo-spectral technique is performed to analyze the effect of variable gravity field and throughflow on the behavior of system stability. The results obtained from linear and nonlinear analysis are compared and found that the results are in better agreement for the heated from below and salted from above system however, the comparatively less agreement is obtained for the system when both heating and salting are done from below. The direction of throughflow and gravity field have considerable effect on the stability of system. The behavior of gravity field is invariant for both the type of system heating and salting from below as well as heating from below and salting from above. The solute Rayleigh number stabilizes the system for heating from below and salting from below, however, destabilizes the system for heating from below and salting from above. In the absence of gravity field, a comparatively good agreement between thresholds is seen for Q = 0, however, the agreement is shifted towards positive value of Q or negative value of Q when gravity is found to be present in the system. Thus, effect of gravity field is dominant on the influences of throughflow on the stability of system.

Double diffusive convective motion in a reactive porous medium layer saturated by a non-Newtonian Kuvshiniski fluid

The impact of chemical reactions on the double-diffusive convective motion in a non-Newtonian viscoelastic fluid (Kuvshiniski type) saturated porous layer is examined applying both linear and nonlinear stability techniques. The Darcy model that includes the Kuvshiniski type viscoelastic effect of viscoelastic fluid and the Boussinesq estimation is employed as the momentum equation. The conditions for the occurrence of the stationary and oscillatory style of convective motions are determined by applying linear stability theory in terms of a critical thermal Rayleigh–Darcy number. Using the weakly nonlinear stability analysis, the convective heat and mass transfers are calculated. It is observed that the occurrence of oscillatory convection is possible only if the value of the solute Rayleigh–Darcy number is negative and also depends on other involved physical parameters. With rising values of the Kuvshiniski parameter and the heat capacity ratio, the range of the solute Rayleigh–Darcy number in which oscillatory convection is privileged diminishes, whereas it grows with the chemical reacting parameter and the Lewis number. The critical thermal Rayleigh–Darcy number at which the convective motion occurs increased nearly 3% with a 15% increase in the value of the Kuvshiniski parameter. Furthermore, the convective heat and mass transfers are reduced by growing the Kuvshiniski parameter and the heat capacity ratio, while both are enhanced by increasing the thermal Rayleigh–Darcy number and the solute Rayleigh–Darcy number.

Rayleigh-Benard convection in a binary fluid-saturated anisotropic porous layer with variable viscosity effect

Rayleigh-Benard convection due to buoyancy that occurred in a horizontal binary fluid layer saturated anisotropic porous media is investigated numerically. The system is heated from below and cooled from above. The temperature-dependent viscosity effect was applied to the double-diffusive binary fluid and the critical Rayleigh number for free-free, rigid-free, and rigid-rigid representing the lower-upper boundary were obtained by using the single-term Galerkin expansion procedure. Both boundaries are conducted to temperature. The effect of temperature-dependent viscosity, mechanical anisotropy, thermal anisotropy, Soret, and Dufour parameters on the onset of stationary convection are discussed and shown graphically.

THERMAL INSTABILITY OF A MAXWELL FLUID SATURATED POROUS LAYER WITH CHEMICAL REACTION

THERMAL INSTABILITY OF A MAXWELL FLUID SATURATED POROUS LAYER WITH CHEMICAL REACTION

Influence of Boundary Roughness on Magnetohydrodynamic Kelvin-Helmholtz Instability in Couple-stress Fluid

The Kelvin-Helmholtz instability (KHI) occurs at the interface amongst two fluids, which are in relative motion with a common boundary. The growth rate of waves occurs whenever the relative velocity is greater as compared with the critical relative velocity. In the present paper, the influence of boundary roughness on KHI under the impact magnetic field in a couple-stress fluid layer bounded by a rigid surface at the lower side and upper side by a fluid saturated porous layer. Using suitable surface and boundary conditions, we have derived the dispersion relation and results are depicted graphically. As observed in presence of sharp interface, magnetic field exhibits stabilizing effect however, destabilizing effect is shown by the buoyancy force on KHI. Also, noted that the growth rate of interface reduces, as there is a rise in roughness parameter value.

Thermal convection for a Darcy-Brinkman rotating anisotropic porous layer in local thermal non-equilibrium

The onset of natural convection in a fluid-saturated anisotropic porous layer, which rotates about the vertical axis, under the hypothesis of local thermal non-equilibrium, is analysed. Since the porosity of the medium is assumed to be high, the more suitable Darcy-Brinkman model is adopted. Linear instability analysis of the conduction solution is carried out. Nonlinear stability with respect to L^2-norm is performed in order to prove the coincidence between the linear instability and the global nonlinear stability thresholds. The effect of both rotation and thermal and mechanical anisotropies on the critical Rayleigh number for the onset of instability is discussed.

Anisotropy and the Onset of the Thermoconvective Instability in a Vertical Porous Layer

Abstract The thermoconvective instability of the parallel vertical flow in a fluid saturated porous layer bounded by parallel open boundaries is studied. The open boundaries are assumed to be kept at constant uniform pressure while their temperatures are uniform and different, thus forcing a horizontal temperature gradient across the layer. The anisotropic permeability of the porous layer is accounted for by assuming the principal axes to be oriented along the directions perpendicular and parallel to the layer boundaries. A linear stability analysis based on the Fourier normal modes of perturbation is carried out by testing the effect of the inclination of the normal mode wavevector to the vertical. The neutral stability curves and the critical Rayleigh number for the onset of the instability are evaluated by solving numerically the stability eigenvalue problem.

Reflection and transmission phenomena of SH waves in fluid saturated porous medium with corrugated interface

This article deals with the behavior of reflection/transmission phenomena on the propagation of SH waves in a corrugated fluid-saturated porous layer sandwiched between heterogeneous viscoelastic and orthotropic half-spaces. Various mathematical tools such as Rayleigh’s method of approximation, Snell’s law, Crammer’s law are applied to get the analytical expression for the reflection/transmission coefficient and energy ratio for each scattered wave. A numerical treatment has been performed for a particular model to study the nature of various affecting parameters such as heterogeneity, viscosity, porosity, angle of incidence, and wave number. A comparative study has been made for the graphical observation to show the effect of the various affecting parameters in the presence and absence of porosity. The reflection/transmission coefficient, energy ratio for each wave (regularly and irregularly reflected/transmitted wave) are calculated analytically and given a graphical representation for a particular model. It has been shown that the conservation of energy rule holds very well in the model. The finding of this article may be valuable in the field of seismology and geophysics to enhance the knowledge about the structure of rock in the interior of the Earth and its elastic property.

Cross Diffusion Effect on Linear and Nonlinear Double Diffusive Convection in a Viscoelastic Fluid Saturated Porous Layer with Internal Heat Source

Double diffusive convection in a binary viscoelastic fluid saturated porous layer in the presence of a cross diffusion effect and an internal heat source is studied analytically using linear and nonlinear stability analysis. The linear stability theory is based on the normal mode technique, while the nonlinear theory is based on a minimal representation of truncated double Fourier series. The modified Darcy law for the viscoelastic fluid of the Oldroyd type is considered to model the momentum equation. The onset criterion for stationary and oscillatory convection and steady heat and mass transfer have been obtained analytically using linear and nonlinear theory, respectively. The combined effect of an internal heat source and cross diffusion is investigated. The effects of Dufour, Soret, internal heat, relaxation and retardation time, Lewis number and concentration Rayleigh number on stationary, oscillatory, and heat and mass transport are depicted graphically. Heat and mass transfer are presented graphically in terms of Nusselt and Sherwood numbers, respectively. It is reported that the stationary and oscillatory convection are significantly influenced with variation of Soret and Defour parameters. An increment of the internal heat parameter has a destabilizing effect as well as enhancing the heat transfer process. On the other hand, an increment of internal heat parameter has a variable effect on mass transfer. It is found that there is a critical value for the thermal Rayleigh number, below which increasing internal heat decreases the Sherwood number, while above it increasing the internal heat increases the Sherwood number.

Bidispersive double diffusive convection with relatively large macropores and generalized boundary conditions

This paper is concerned with the question of the beginning of convective motion in a fluid saturated porous layer, containing a salt in solution, heated below and salted above and below. This model has a single temperature and employs the Darcy theory in the micropores, the Brinkman theory, however, being utilized in the macropores. The effect of slip boundary conditions on the stability of the model is also studied. General boundary conditions regarding temperature and salt are also taken into account. It will be shown that the linear instability threshold is the same as that of nonlinear stability if the layer is salted from above, indicating that the linear theory entirely captures the physics of the onset of thermal convection. In the case of salting from below, the behavior of the transition from stationary to oscillatory convection is investigated in detail, as the boundary conditions change from prescribed temperature and salt concentration toward those of prescribed heat flux and salt flux. The nonlinear stability threshold does not coincide with that of linear instability; thus, regions of possible subcritical instability are still present. We believe that the problem presented in this paper has not been addressed before and that its study will have great scientific value and impact.

Magnetic field and Rotation effect on thermal stability in an Anisotropic couple-stress fluid saturated Porous Layer under presence of Cross-Diffusion

The present paper is based on the investigation of thermal stability problem under the influence of rotation, solute, heat and magnetic field on electrically conducting fluid saturated rotating horizontal porous media under local thermal non-equilibrium effect. We have considered a rotating horizontal anisotropic porous medium saturated with binary fluid. Process of Heating and salting is made from above to the fluid layer.Governing equations is followed by Darcy Brinkman model for characterizing the convection through porous media under the above said physical configuration. Normal mode technique and Application of Linear stability analysis has been made under the consideration of free-free boundary conditions. Thereafter the characteristic graphs between critical Darcy-Rayleigh number and corresponding wave number for beginning of convection in stationary case has been drawn and the effect of rotation, magnetic and couple stress parameters has been illustrated.At last it has been observed the non-dimensonalise parametres regarding singnificant components like rotation magnetic field and anisotropic properties of the physical configuration in present study has stabilizing effect.

Effects of variable heat source on convective motion in an anisotropic porous layer

The onset of convective motion in a fluid saturated anisotropic porous medium layer is examined analytically in the occurrence of the qualitative effect of the source of variable internal heat. Three different kinds of heat source functions: (i) N (z) = z (linear) (ii)N(z) = z2 (parabolic) and (iii) N (z) = z 3 (cubic) are considered. The resulting eigenvalue problem was analytically solved using regular perturbation technique. A parametric study is carried out by varying the following parameters: the heat source parameter (X), thermal anisotropy parameter(n), and mechanical anisotropy parameter(ξ). Results indicates that the effects of the increasing values of λ and ξ will enhance the convection of a anisotropic porous layer system while the increasing of n will help to stabilize the system. It is also noted that for case (iii) the system is more stable, while for case (i) the system is more unstable

Influence of an impulsive source on shear wave propagation in a mounted porous layer over a foundation with dry sandy elastic stratum and functionally graded substrate under initial stress

The present paper articulates a mathematical model for the propagation of horizontally polarised shear (SH) wave in an initially stressed composite layered structure under the influence of an impulsive line source. The initially stressed composite structure is comprised of a transversely isotropic fluid saturated porous layer over a foundation with dry sandy elastic stratum and functionally graded substrate (semi-infinite medium) in which the bonding between the interfaces of the layers and semi-infinite medium are considered to be imperfect. Green's functions are derived for the composite layered structure by taking a line force/charge density (Dirac delta function) at the lower interface of intermediate stratum into the account. An efficient analytical treatment involving Green's function technique along with Fourier's transform has been employed to establish the closed form of dispersion equation for the propagating wave. As a special case of the problem, the closed form of dispersion equation has been deduced for a structure with a single layer overlying a semi-infinite medium. These deduced results are validated with pre-established results and classical Love wave equation. Numerical computation has been carried out to demonstrate graphically the effect of various affecting parameters, viz. wave number, initial stress, porosity, sandiness parameter, width ratio, imperfect bonding parameters and functional gradient parameters on the phase velocity of shear wave. Some remarkable results regarding the propagation behaviour of shear wave in the considered composite layered structure due to various affecting parameters serve as the major highlights of the present work which has significant relevance to field of geophysics, earthquake engineering and civil engineering.