Fluid Saturated Porous Layer Research Articles

Oscillatory squeeze flow through an Oldroyd-B fluid-saturated porous layer

This study deals with the analytical investigation of oscillatory squeeze film flow through a Brinkman viscoelastic Oldroyd-B fluid-saturated porous layer subject to two vertically harmonically oscillatory disks. The validity of the present proposed analytical solutions is first demonstrated for the Newtonian fluids when both Λ1 and Λ2 tend to zero by comparison with the previous literature. Results demonstrate that an increase in the elasticity parameter Λ1 correlates with a rise in axial velocities, indicating that the relaxation time Λ1 facilitates enhanced squeeze flow. In the case of squeeze film flow in porous layers, low oscillating frequencies exert minimal effects on axial velocities, independent of variations in the viscoelasticity parameter Λ1. However, at higher oscillating frequencies, axial velocities escalate with increasing the viscoelasticity parameter Λ1. Furthermore, the retardation time Λ2 of the viscoelastic fluid shows no significant effect on the axial velocity, regardless of oscillating frequency changes in both pure fluids and porous layers.

Two Numerical Methods for Thermohaline Convection in MHD Squeezing Flow of Casson Fluid Saturated Porous Layer

Two Numerical Methods for Thermohaline Convection in MHD Squeezing Flow of Casson Fluid Saturated Porous Layer

Linear and nonlinear stability of double diffusive convection in a micropolar fluid saturated porous layer with magnetic field and throughflow effects

The linear and nonlinear stability of double-diffusive convection in a porous layer saturated with micropolar fluid is examined. A transverse magnetic field is applied to the flow together with vertical throughflow. The normal mode technique is employed for linear stability analysis, whereas the energy method is used for nonlinear stability analysis. The resulting eigenvalue problems corresponding to linear and nonlinear stability theories are solved numerically by employing the bvp4c routine in MATLAB 2022(b). The critical thermal Rayleigh numbers for both linear and nonlinear analyses are computed for the different values of the governing parameters and presented graphically. A comparison is made between linear and nonlinear stability results. It is observed that the flow is more stable whenever a magnetic field is added to the flow, although the subcritical instability region also slightly increases. Increasing the Darcy number, Lewis number, coupling number, and absolute value of the throughflow parameter destabilizes the flow. On the other hand, raising the porosity of the medium and micropolar parameters stabilizes the flow. Furthermore, there is no subcritical gap in the absence of the throughflow effect, which is a good agreement between the linear and nonlinear thresholds.

Triple-diffusive instabilities in Ellis fluid-saturated porous layers: Dynamics of oscillatory convection

Triple-diffusive convection in Ellis fluid-saturated porous layers has a wide array of real-world applications, including enhanced oil recovery, optimized geothermal energy extraction, and improved food processing and drug delivery systems. It also plays a crucial role in environmental management, particularly in controlling groundwater contamination and maintaining soil health by modeling pollutant transport and nutrient dynamics. This study explores the onset of convection in an Ellis fluid-saturated porous layer, influenced by three stratifying agents with differing diffusivities. A modified Darcy porous medium, salted from below, is subjected to horizontal throughflow driven by a prescribed pressure gradient. Through normal mode analysis, a linear stability analysis is conducted, resulting in explicit threshold conditions for the onset of convection. The findings reveal that convection begins with oscillatory motion, driven by the combined effects of the pressure gradient and solute concentration gradients. Notably, the study uncovers the emergence of disconnected, closed, heart-shaped oscillatory neutral curves, indicating the presence of three critical values of the solutal Darcy-Rayleigh number required to establish linear instability criteria and novel discovery for an Ellis fluid-saturated porous medium. Moreover, the results show that increasing the solutal Darcy-Rayleigh number and the Ellis power-law index stabilizes the system, while a higher Darcy-Ellis number leads to destabilization. The results obtained in the limiting cases are found to be consistent with those reported in previous studies.

Investigation of Magneto-convection in Viscoelastic Fluid Saturated Anisotropic Porous Layer Under Local Thermal Non-equilibrium Condition

The problem of magneto-convection in viscoelastic fluid saturated anisotropic porous layer under local thermal non-equilibrium (LTNE) effect is investigated. Extended Darcy model with time derivative term for viscoelastic fluid of the Oldroyd type with an externally imposed vertical magnetic field is used to model the momentum equation. The entire investigation has been split into two parts: (i) linear stability analysis (ii) weakly non-linear stability analysis. We perform normal mode technique to examine linear stability analysis while truncated representation of Fourier series method is used for weakly non-linear stability analysis. The onset of convection is set in through oscillatory rather than stationary mode due to competition between the processes of thermal, magnetic effect and viscoelasticity. A comparative study between anisotropic and isotropic porous medium is made as a function of Q (Chandrasekhar number), 𝛤 (non dimensional inter phase heat transfer coefficient), 𝜆1 (Relaxation time) and λ2 (Retardation time). Apart from this, Q, 𝛤 and λ2 stabilize the system in oscillatory case while 𝜆1 destabilize the system. Furthermore 𝜉 (mechanical anisotropic parameter), 𝜂s (thermal anisotropic parameter for solid phase), destabilizes the system and 𝜂f (thermal anisotropic parameter for fluid phase) stabilizes the system. The effect of Q, 𝜆1, λ2, 𝛤, 𝜉, 𝜂f and 𝜂s on heat transfer is also examined.

Study of Heat and Mass transports due to modulated rotational flow in a triply diffusive Newtonian liquid saturated porous medium/fluid layer: A comparative study

Rotational modulation and the third diffusive component are investigated in relation to transports in the Rayleigh Bènard convection in the x− direction of an infinitely extended fluid layer or fluid-saturated porous layer using a weakly non-linear theory. The direction of travel for the z-axis is upward. The z-axis is interpreted as pointing upward. Temperature and concentration of both the solutes at lower plate are higher than the upper plate. The time dependent rotational speed of fluid is assumed to be modulated by small parameter ϵ2 with amplitude (δ). A linear differential matrix approach is used to examine the system’s behaviour. Ginzburg–Landau’s equation, a non-autonomous differential equation, has been derived using the Fredholm-solvability condition. The impact of dimensionless parameters on stationary convection is also discussed. The expression of the critical Rayleigh number is obtained for three different cases: clear fluid layer, Darcy porous layer, and sparsely packed porous layer (Darcy–Brinkman model). The Nusselt number (Nu) and Sherwood numbers (Sh1, Sh2) for each solute are used to quantify the convective transports. The impact of modulation and other dimensionless parameters on these convective transports has been discussed using graphical representation Furthermore, among the three models under consideration, it is discovered that the heat and mass transports are highest in the fluid layer and minimum in the densely packed porous layer.

Influence of porosity properties on natural convection heat transfer in porous square cavity

A numerical investigation was conducted to examine free convection heat transfer within a square cavity containing a fluid-saturated porous layer at the bottom under laminar flow conditions. The enclosure's left and right walls experienced heating and cooling, while the top and bottom walls remained adiabatic. The study explored the influence of the Darcy number, porosity number, and dimensionless thickness of the porous layer on heat transmission. This investigation utilized a FORTRAN computation program alongside the finite volume method, effectively solving the equations governing flow and heat exchange within porous materials through natural convection. The flow pattern is determined by the Navier–Stokes equations in the fluid region and the Darcy–Brinkman–Forchheimer formula in the porous region. The energy equation was employed to compute the thermal field. The increase in the Darcy number results in both an increase in heat transfer rate due to enhanced fluid flow through pores and an intensification of fluid flow patterns. Higher porosity leads to higher heat transfer rates due to greater fluid penetration and an increased surface area for heat exchange. The thicker porous layer reduces heat transfer rate due to increased resistance to fluid flow and decreased contact area.

Effect of Rigidity and Parabolic Irregularity on Love Wave Propagation in Transversely Isotropic Fluid-Saturated Porous Layer Lying over a Nonhomogenous Half-Space

Effect of Rigidity and Parabolic Irregularity on Love Wave Propagation in Transversely Isotropic Fluid-Saturated Porous Layer Lying over a Nonhomogenous Half-Space

Double-diffusive convection in a porous layer subjected to an inclined temperature gradient incorporating Soret effect

In several commonly occurring natural convection phenomena, the system is subjected to non-uniform heating that causes an inclined thermal gradient. As a result, the natural convection problem deviates from the classical Rayleigh–Bénard problem, in which the thermal gradient has only a vertical component. In this study, we present linear and global stability analyses results concerning thermosolutal convection in a Newtonian fluid-saturated Darcy porous layer subjected to an inclined thermal gradient in the presence of the Soret effect (associated with thermophoresis). The thermal gradient is assumed to have horizontal and vertical components, resulting in the formulation having two thermal Rayleigh numbers as system parameters, viz. horizontal and vertical Rayleigh numbers. The horizontal thermal gradient gives rise to a Hadley-type circulation. This circulation can become unstable if the vertical thermal gradient attains a certain threshold. We focus on the effect of the Soret parameter on the system’s stability under non-uniform inclined heating. The analyses reveal that the solutal Darcy–Rayleigh number and Lewis number destabilise the system, while the Soret parameter has a non-monotonic effect on the system’s stability depending on the horizontal Rayleigh number. The energy stability bounds do not coincide with linear ones for the present problem; hence, subcritical instabilities are possible.

Viscoelastic effect on the triple diffusive oscillatory flow in a fluid-saturated porous layer

The combined heat and mass transfer, the so-called thermosolutal convective problem, has become an attractive field of research in many diversified areas. In this paper, for the first time, oscillatory flow analysis has been carried out for triple diffusive viscoelastic fluid flow in a porous medium. A comprehensive model is developed for the modified Darcy–Brinkman–Oldroyd-B fluid, porous medium, Boussinesq approximation, heat and mass transfer across a finite temperature and concentration difference in the chemical potential of two salts. Triple diffusive viscoelastic fluid flows through porous media have grown significantly as this situation occurs in more than a few applications such as improved oil recovery filtration, liquid complex molding, solidification of liquid crystals, cooling of metallic plate in a bath, exotic lubricants and colloidal solutions, polymer processing, chemical and bioengineering industries, among others. The governing coupled nonlinear partial differential equations with boundary constraints represent the modeled flow problem. In addition, these equations are converted into non-dimensional form by employing suitable non-dimensionalizing quantities. The impacts of the pertinent parameters and related dimensionless numbers on the dimensionless velocity, temperature, concentrations, shear stress, heat and mass transfer are examined for both suction and injection cases. It has been found that when the injection level on the heated plate is increased, the shear rate increases for each channel plate. Furthermore, we recognized that the viscoelastic parameters exhibit an opposite kind of behavior on the velocity, temperature, and concentrations fields.

Variable gravity effects on penetrative porous convection

The effect of variable gravity on the onset of penetrative convection in a horizontal fluid-saturated porous layer is studied, performing the linear instability analysis and the nonlinear stability analysis (via the weighted energy method) of the thermal conduction solution. The linear and nonlinear critical Rayleigh numbers for the onset of penetrative porous convection are determined and their behaviour with respect to the fundamental physical parameters of the model is studied. In particular, we found that there exists a region of subcritical instabilities and that the increase of the upper bounding plane temperature and the decrease of gravity have a stabilizing effect on the onset of convection.

Temporal to spatial instability in a flow system: a comparison

AbstractThe definitions of temporal instability and of spatial instability in a flow system are comparatively surveyed. The simple model of one-dimensional Burgers’ flow is taken as the scenario where such different conceptions of instability are described. The temporal analysis of instability stems from Lyapunov’s theory, while the spatial analysis of instability interchanges time and space in defining the evolution variable. Thus, the growth rate parameter for temporally unstable perturbations of a basic flow state is to be replaced by a spatial growth rate when a coordinate assumes the role of evolution variable. Finally, the idea of spatial instability is applied to a Rayleigh-Bénard system given by a fluid-saturated horizontal porous layer with an anisotropic permeability and impermeable boundaries kept at different uniform temperatures.

Rayleigh–Bénard instability in a horizontal porous layer with anomalous diffusion

The analysis of the Rayleigh–Bénard instability due to the mass diffusion in a fluid-saturated horizontal porous layer is reconsidered. The standard diffusion theory based on the variance of the molecular position growing linearly in time is generalized to anomalous diffusion, where the variance is modeled as a power-law function of time. A model of anomalous diffusion based on a time-dependent mass diffusion coefficient is adopted, together with Darcy's law, for momentum transfer, and the Boussinesq approximation, for the description of the buoyant flow. A linear stability analysis is carried out for a basic state where the solute has a potentially unstable concentration distribution varying linearly in the vertical direction, and the fluid is at rest. It is shown that any, even slight, departure from the standard diffusion process has a dramatic effect on the onset conditions of the instability. This circumstance reveals a strong sensitivity to the anomalous diffusion index. It is shown that subdiffusion yields instability for every positive mass diffusion Rayleigh number, while superdiffusion brings stabilization no matter how large is the Rayleigh number. A discussion of the linear stability analysis based on the Galilei-variant fractional-derivative model of subdiffusion is eventually carried out.

Global stability of Bénard–Marangoni convection in an anisotropic porous medium

Surface tension is essential in many industrial applications, especially where the liquid surface is in contact with the environment, such as crystal growth, semiconductor manufacturing, and welding. The present article reports a numerical analysis of convection induced by the combined effects of buoyancy force and surface tension in an infinitely extended horizontal fluid-saturated anisotropic porous layer with high permeability. We assume that the bottom boundary is rigid and the top is exposed to the air. Biot numbers establish general thermal conditions at both ends instead of commonly used adiabatic and isothermal boundary conditions. The anisotropy of the porous structure results in thermal and mechanical anisotropy parameters while examining layer's stability. The Chebyshev Tau technique yields the critical Marangoni number, MaLc and MaEc, representing linear and energy stability boundaries. We compare the constraints obtained from linear and energy analyses and conclude that the energy bounds for the current problem are less than linear bounds, indicating subcritical instabilities may exist. It is also observed that thermal anisotropy and Biot numbers stabilize the system. In contrast, mechanical anisotropy and the Darcy number advance the onset of convection. The existing results of limiting cases of the present problem are recovered with remarkable accuracy.

Viscoelastic effects on the double-diffusive oscillatory flow in a fluid-saturated porous layer

The viscoelastic effects on the double diffusive oscillatory flow in a fluid-saturated porous layer are investigated. A modified Darcy–Oldroyd-B model is used to characterize the non-Newtonian fluid behavior flow in a porous layer. Analytic solutions of the dimensionless governing equations of fluid flow are obtained and the effects of the flow parameters on temperature, concentration, velocity profiles, skin friction and rate of heat transfer are discussed and shown graphically. It is interesting to note that skin friction increases on both channel plates as injection increases on the heated plate. Increase in the strain retardation parameter is to decrease the fluid velocity, while an opposite trend is noticed with increasing stress relaxation parameter. The study reiterates that the consideration of viscoelastic fluid is very important in proper considerate of oscillatory flow in double diffusive fluid systems.

Uniform magnetic field impact on absolute versus convective onset of Darcy–Benard convection with horizontal throughflow

PurposeThe onset of Darcy–Benard convection in a fluid-saturated porous layer within channeled walls can be through either the convectively amplified perturbations or absolutely unstable modes. The convective type route to formation of cellular forms has received much more interest in the literature than the absolute mode. This paper aims to explore the absolute instability mechanism on triggering the Benard convection in the presence of a uniform magnetic field acting perpendicular to the channel walls.Design/methodology/approachPursuing a completely theoretical linear stability approach, the locus of wavenumbers and critical Rayleigh numbers with respect to varying Peclet numbers leading to zero complex group velocity, and hence the absolute instability onset, is formulated in closed form. The formulae also incorporate the influence of fluid movement through the porous layer.FindingsWanenumbers are found to be increasing in magnitude under the effect of the magnetic field. Although the magnetic field expectedly behaves in favor of stabilizing the convection through both convective and absolute instabilities by pushing the threshold value of Rayleigh number to higher values, a peculiarity exists in such a manner that the stabilizing effect of magnetic field can no longer compete against the absolute instability mechanism within the magnetized field after some critical location possessing negative part of the wavenumber.Originality/valueThe significant outcome is attributed to the exchange of instabilities as far as the absolute instability mechanism is concerned. Magnetic field is always stabilizing and no such trend is observed regarding the convective type instability.

Onset of double diffusive surface-tension driven convection in fluid layer overlying a layer of anisotropic porous layer with soret effect

The onset of double-diffusive surface tension-driven convective motion in a fluid layer overlying a fluid-saturated anisotropic porous layer is investigated analytically in the presence of the soret effect. We considered boundaries to be insulating to temperature perturbations. The governing equation that satisfies the composite system is analyzed by the normal mode approach and solved by the regular perturbation technique for linear stability. By solving coupled equations, a mathematical expression for the critical Marangoni number is obtained. Under the effect of the anisotropy, soret parameters and the impact of various physical parameters on the start of convective motion is illustrated graphically, and the stability system is investigated.

FEEDBACK CONTROL OF CHAOTIC MOTION IN AN ANISOTROPIC POROUS MEDIUM UNDER MAGNETIC EFFECT

The main purpose of this work is to provide an innovative approach for studying the chaos control of the viscoelastic fluid-saturated anisotropic porous layer under the magnetic effect and feedback control modulation. The governing flow model partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using a powerful tool of Fourier modes and a nonlinear low-dimensional Brinkman model employed by using the truncated Galerkin method. Their results reveal the feedback gain parameter, Hartmann number, Darcy number, and the mechanical and thermal anisotropy parameters on the stabilization of thermal convection to suppress the chaos. Additionally, many real-world applications conforming to system stabilization of thermal convection are important in nuclear power energy, including turbo machinery, cooling chemical components, and electronic cooling processes. The emergence of various nonlinear flows of steady-state, periodic, and oscillatory to chaotic convection is demonstrated with the change of feedback control parameters. Also, we found that the feedback control gains parameter K value is directly proportional to the scaled Rayleigh number with the external effects on the magnetic field and anisotropic parameters. Our findings were found to be in good agreement with previous numerical results. Finally, the paper proposes the implications of using feedback control combined with magnetic effect to effectively control the chaotic 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.

Onset of triple-diffusive convective stability in the presence of a heat source and temperature gradients: An exact method

<abstract> <p>In the current work, in the presence of a heat source and temperature gradients, the onset of triple-diffusive convective stability is studied for a fluid, and a fluid-saturated porous layer confined vertically by adiabatic limits for the Darcy model is thoroughly analyzed. With consistent heat sources in both layers, this composite layer is subjected to three temperature profiles with Marangoni effects. The fluid-saturated porous region's lower boundary is a rigid surface, while the fluid region's upper boundary is a free surface. For the system of ordinary differential equations, the thermal surface-tension-driven (Marangoni) number, which also happens to be the Eigenvalue, is solved in closed form. The three different temperature profiles are investigated, the thermal surface-tension-driven (Marangoni) numbers are calculated analytically, and the effects of the heat source/sink are studied in terms of corrected internal Rayleigh numbers. Graphs are used to show how different parameters have an impact on the onset of triple-diffusive convection. The study's parameters have a greater influence on porous layer dominant composite layer systems than on fluid layer dominant composite layer systems. Finally, porous parameters and corrected internal Rayleigh numbers are stabilize the system, and solute1 Marangoni number and ratio of solute2 diffusivity to thermal diffusivity of fluid are destabilize the system.</p> </abstract>