Fluid Saturated Anisotropic Porous Layer Research Articles

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.

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.

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.

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.

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 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.

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

Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer

The nonlinear stability of thermal convection in a layer of an Oldroyd-B fluid-saturated Darcy porous medium with anisotropic permeability and thermal diffusivity is investigated with the perturbation method. A modified Darcy-Oldroyd model is used to describe the flow in a layer of an anisotropic porous medium. The results of the linear instability theory are delineated. The thresholds for the stationary and oscillatory convection boundaries are established, and the crossover boundary between them is demarcated by identifying a codimension-two point in the viscoelastic parameter plane. The stability of the stationary and oscillatory bifurcating solutions is analyzed by deriving the cubic Landau equations. It shows that these solutions always bifurcate supercritically. The heat transfer is estimated in terms of the Nusselt number for the stationary and oscillatory modes. The result shows that, when the ratio of the thermal to mechanical anisotropy parameters increases, the heat transfer decreases.

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.

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.

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.

Effect of Gravity Modulation on Electrothermal Convection in a Dielectric Fluid Saturated Anisotropic Porous Layer

This paper deals with linear and nonlinear stability analyses of thermal convection in a dielectric fluid saturated anisotropic Brinkman porous layer subject to the combined effect of AC electric field and time-periodic gravity modulation (GM). In the realm of linear theory, the critical stability parameters are computed by regular perturbation method. The local nonlinear theory based on truncated Fourier series method gives the information of convection amplitudes and heat transfer. Principle of exchange of stabilities is found to be valid and subcritical instability is ruled out. Based on the governing linear autonomous system several qualitative results on stability are discussed. The sensitive dependence of the solution of Lorenz system of electrothermal convection to the choice of initial conditions points to the possibility of chaos. Low frequency g-jitter is found to have significant stabilizing influence which is in turn diminished by an imposed AC electric field. The role of other governing parameters on the stability threshold and on transient heat transfer is determined.

Dispersion of Love Wave Propagating in Irregular Anisotropic Porous Stratum under Initial Stress

AbstractPropagation of a Love wave in an initially stressed fluid-saturated anisotropic porous layer with an irregular boundary sandwiched between two isotropic half-spaces has been studied. The irregularity is assumed to be rectangular, and the perturbation method is used to obtain the displacement field in the porous layer. Finally, the dispersion relation for the assumed model is obtained, and the result is compared with those derived for the flat layer theory. The effect of porosity, initial stress, and irregularity of the porous layer in phase velocity is studied and shown graphically.

Effect of Internal Heat Generation on the Onset of Marangoni Convection in a Fluid Layer Overlying a Layer of an Anisotropic Porous Medium

Linear stability analysis has been performed to investigate the effect of internal heat generation on the criterion for the onset of Marangoni convection in a two-layer system comprising an incompressible fluid-saturated anisotropic porous layer over which lies a layer of the same fluid. The upper non-deformable free surface and the lower rigid surface are assumed to be insulated to temperature perturbations. The fluid flow in the porous layer is governed by the modified Darcy equation and the Beavers–Joseph empirical slip condition is employed at the interface between the two layers. The resulting eigenvalue problem is solved exactly. Besides, analytical expression for the critical Marangoni number is also obtained by using regular perturbation technique with wave number as a perturbation parameter. The effect of internal heating in the porous layer alone exhibits more stabilizing effect on the system compared to its presence in both fluid and porous layers and the system is least stable if the internal heating is in fluid layer alone. It is found that an increase in the value of mechanical anisotropy parameter is to hasten the onset of Marangoni convection while an opposite trend is noticed with increasing thermal anisotropy parameter. Besides, the possibilities of controlling (suppress or augment) Marangoni convection is discussed in detail.

Onset of surface tension driven convection in a fluid layer overlying a layer of an anisotropic porous medium

The paper deals with the criterion for the onset of surface tension-driven convection in the presence of temperature gradients in a two-layer system comprising a fluid saturated anisotropic porous layer over which lies a layer of fluid. The lower rigid surface is assumed to be insulated to temperature perturbations, while at the upper non-deformable free surface a general thermal condition is invoked. Both the Beavers–Joseph and the Jones conditions have been used at the interface to know their preference and prominence in the study of the problem. The resulting eigenvalue problem is solved exactly and also by regular perturbation technique when both the boundaries are insulating to temperature perturbations. It is found that the depth of the relative layers, mechanical and thermal anisotropy parameters have a profound effect on the stability of the system. Decreasing the mechanical anisotropy parameter and increasing the thermal anisotropy parameter leads to stabilization of the system. Besides, the possibility of control of Marangoni convection by suitable choice of physical parameters is discussed in detail.

The Onset of Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Layer

The double diffusive convection in a horizontal couple stress fluid saturated anisotropic porous layer, which is heated and salted from below, is studied analytically. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. The effect of anisotropy parameter, solute Rayleigh number, Lewis number, couple stress parameter, and Vadasz number on the stationary, oscillatory, and finite amplitude convection is shown graphically. It is found that the thermal anisotropy parameter, couple stress parameter, and solute Rayleigh number have stabilizing effect on the stationary, oscillatory, and finite amplitude convection. The mechanical anisotropy parameter has destabilizing effect on stationary, oscillatory, and finite amplitude convection. The Lewis number has stabilizing effect in the case of stationary and finite amplitude modes, with dual effect in the case of oscillatory convection. Vadasz number advances the onset of oscillatory convection. The heat and mass transfer decrease with an increase in the values of couple stress parameter, while both increase with an increase in the value of solute Rayleigh number and mechanical anisotropy parameter. The thermal anisotropy parameter and Lewis number have contrasting effect on the heat mass transfer.

The onset of convection in a binary fluid saturated anisotropic porous layer

The double diffusive convection in a horizontal fluid saturated anisotropic porous layer, which is heated and salted from below, is studied analytically. The generalized Darcy model is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes and frequency of oscillations are obtained analytically using linear theory. The effect of anisotropy parameters, solute Rayleigh number, Lewis number and Prandtl number on the stationary, oscillatory and finite amplitude convection is shown graphically. The transient behavior of the Nusselt and Sherwood numbers is studied, by solving numerically a fifth order Lorenz type system using Runge–Kutta method. Some of the convection systems previously reported in the literature are shown to be special cases of the system presented in this study.

The onset of double diffusive convection in a binary viscoelastic fluid saturated anisotropic porous layer

The onset of double diffusive convection in a binary viscoelastic fluid saturated anisotropic porous layer is studied using a linear and a weak nonlinear stability analyses. The modified Darcy law for the viscoelastic fluid of the Oldroyd type is used to model the momentum equation. The onset criterion for stationary and oscillatory convection is derived analytically. There is a competition between the processes of thermal, solute diffusions, and viscoelasticity that causes the convection to set in through oscillatory rather than stationary. The effect of anisotropy parameters, Darcy–Prandtl number, relaxation, and retardation parameters on the stability of the system is investigated. The nonlinear theory based on the truncated representation of Fourier series method is used to find the transient heat and mass transfer. The effect of various parameters on heat and mass transfer is also brought out.

Linear and Non-linear Double Diffusive Convection in a Fluid-Saturated Anisotropic Porous Layer with Cross-Diffusion Effects

The double diffusive convection in a horizontal anisotropic porous layer saturated with a Boussinesq binary fluid, which is heated and salted from below in the presence of Soret and DuFour effects is studied analytically using both linear and non-linear stability analyses. The linear analysis is based on the usual normal mode technique, while the non-linear analysis is based on a minimal representation of double Fourier series. The generalized Darcy model including the time derivative term is employed for the momentum equation. The critical Rayleigh number, wavenumbers for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. The effects of anisotropy parameter, solute Rayleigh number, and Soret and DuFour parameters on the stationary, oscillatory convection, and heat and mass transfer are shown graphically. Some known results are recovered as special cases of the present problem.