Onset Of Double-diffusive Convection Research Articles

Onset of Double-Diffusive Convection with a Kelvin-Voigt Fluid of variable order

Onset of Double-Diffusive Convection with a Kelvin-Voigt Fluid of variable order

The onset of double diffusive convection in a rotating bi-disperse porous medium

It is well known that when a horizontal layer of fluid is heated from below, a thermal boundary layer of less dense and hot fluid rises up. When this boundary layer becomes unstable, convective motion in the fluid above sets in. Forecasting when instabilities take place is essential. When a salt dissolved in a fluid saturating a porous medium heated from below is considered, simultaneous mass diffusion and thermal diffusion occur. Unlike the diffusion of heat, the diffusion of salt can take place only through the fluid phase, so an additional physical effect has to be considered: the Soret effect, that is the mass flux created by a temperature gradient. In the present paper the onset of convection in a rotating layer of bi-disperse porous medium saturated by a binary fluid mixture, taking into account the Soret effect, is analysed. Linear stability analysis is performed in order to determine the instability thresholds for the onset of convection via a steady state (stationary convection) and via an oscillatory state (oscillatory convection). Nonlinear stability analysis is performed to obtain the global stability threshold with respect to the L^2-norm.

Impact of Throughflow and Coriolis Force on the Onset of Double-Diffusive Convection with Internal Heat Source

The present research examines the joint influence of throughflow and Coriolis force on the onset of double-diffusive convection with an internal heat source modelled by Darcy’s law. The BVP4C routine in MATLAB R2020a is used to solve the eigenvalue problem numerically. Critical Rayleigh numbers are obtained for designated values of governing parameters. The effect of the internal heat source parameter, Taylor number, Darcy number, and Peclet number on the system’s stability is investigated. The internal heat source parameter has a destabilizing influence on the system, according to our findings. The reason behind this observation is that the presence of an internal heat source in the porous medium may cause more molecular diffusion inside the medium. The Taylor number, on the other hand, stabilizes the system for both upward and downward throughflow because rotation introduces vorticity into the fluid. Thus, the fluid moves with higher velocity in horizontal planes. The velocity of the fluid perpendicular to the planes reduces as a result of this motion. Thus, the onset of convection is delayed.

Study on linear and nonlinear stability analysis of double diffusive electro-convection in couple stress anisotropic fluid-saturated rotating porous layer

The influence of rotation and electric field on the onset of double-diffusive convection in rotating anisotropic couple stress fluid embedded porous media, which is caused by the combined action of external AC electric field and heating from below, has been investigated in this study. The associated equations were solved using the normal mode technique in conjunction with the modified Brinkman model, with free-free and rigid-rigid boundary conditions. Solute concentration and temperature are treated as independent parameters for the two diffusive components. Finally, neutral stability curves have been sketched to show how various flow parameters affect neutral stability. It is noticed that electric field has destabilizing effect on thermodynamic convection while rotation couple stress parameters have a tendency to stabilize the physical system under consideration. Furthermore, heat and mass transport have been studied using non-linear analysis in unsteady case. It is found that rotation, couple stress, porous parameters has influence of declining heat and mass transport while electric and anisotropic parameters have effect of boosting up heat and mass transport.

Onset of double-diffusive convection in water and ester based magnetic nanofluids

The present paper studies the onset of double diffusive convection in water based magentic nanofluids (WMNF) and ester based magnetic nanofluids (EMNF) for a thin horizontal layer. The fluid is heated and salted from below. The effect of three important slip mechanisms viz., Brownian diffusion, thermophoresis and magnetophoresis has been incorporated. The Eigen value problem is solved by the numerical method. The results are presented for rigid-rigid boundaries in the gravity environment. Critical Rayleigh number is determined in terms of the governing non-dimensional parameters like solutal Rayleigh number, solutal Lewis number and nanoparticle concentration Rayleigh number.

The Onset of Double-Diffusive Convection in a Two-Layer System With a Viscoelastic Fluid-Saturated Porous Medium Under High-Frequency Vibration

Abstract The effect of high frequency vibration in the gravity field on the double-diffusive convection in a two-layer system with a viscoelastic fluid-saturated porous layer is studied. The averaging method is employed to split the unknown functions into a periodic rapidly varying part and a slower mean part. Then, the governing equation of perturbations is numerically solved by the Chebyshev tau method and QZ decomposition method. The influence of physical parameters on the stability of system is investigated. It is shown that the neutral stability curves are bimodal under high frequency vibration. The parameter of the high frequency vibration mainly stabilizes the pure fluid layer for greater wave numbers and has a weak impact on the whole system for smaller wave numbers.

The Effect of Magnetic Field on the Stability of Double-Diffusive Convection in a Porous Layer with Horizontal Mass Throughflow

The onset of double-diffusive convection in an electrically conducting fluid-saturated porous layer is studied. The convective flow in the porous medium is induced by horizontal temperature and concentration gradients with net horizontal mass throughflow. The effect of magnetic field on the instability of convection is taken into consideration. The stability of the steady-state solution is investigated in two different approaches, namely the linear instability analysis and nonlinear stability analysis. The nonlinear stability analysis is performed by constructing the energy functional. The eigenvalue problems which are derived from the stability analyses are numerically integrated using the shooting and Runge–Kutta methods. The variation in the critical thermal Rayleigh number against each flow governing parameter is shown graphically. It is observed that Hartman number $$Ha^{2}$$ delays the onset of convection to commence and helps to reduce the region of subcritical instabilities. When the solute is concentrated at lower boundary of the porous layer, the onset of convection is in the form of stationary modes, but it switches to oscillatory mode of convection when the solute is concentrated at upper boundary. Interestingly, Hartman number $$Ha^{2}$$ plays an important role in delaying this transition from stationary mode to oscillatory mode of convection.

Linear and non-linear analyses of double-diffusive-Chandrasekhar convection coupled with cross-diffusion in micropolar fluid over saturated porous medium

PurposeThe problem aims to find the effects of coupled cross-diffusion in micropolar fluid oversaturated porous medium, subjected to Double-Diffusive Chandrasekhar convection.Design/methodology/approachNormal mode and perturbation technique have been employed to determine the critical Rayleigh number. Non-linear analysis is carried out by deriving the Lorenz equations using truncated Fourier series representation. Heat and Mass transport are quantified by Nusselt and Sherwood numbers, respectively.FindingsAnalysis related to the effects of various parameters is plotted, and the results for the same are interpreted. It is observed from the results that the Dufour parameter and Soret parameter have an opposite influence on the system of cross-diffusion.Originality/valueThe effect of the magnetic field on the onset of double-diffusive convection in a porous medium coupled with cross-diffusion in a micropolar fluid is studied for the first time.

The study of effects of surface tension, magnetic field and non-uniform salinity gradients on the onset of double diffusive convection in composite system

The study of effects of surface tension, magnetic field and non-uniform salinity gradients on the onset of double diffusive convection in composite system

Soret phenomenon in porous Magneto-Hydrodynamics

The onset of double-diffusive convection in horizontal porous layers filled by an electrically conducting fluid embedded in a magnetic field, is investigated on taking into account of Soret phenomenon. Sufficient conditions guaranteeing the onset of steady or oscillatory convection in a closed algebraic form are obtained. Conditions guaranteeing that Hopf convection in the absence of Soret phenomenon, turns into steady convection by the Soret parameter, have been found.

The onset of double-diffusive convection in a Brinkman porous layer with convective thermal boundary conditions

The onset of double-diffusive convection in a highly permeable porous medium with a horizontal throughflow is investigated considering the convective thermal boundary conditions. The convection occurring inside the medium is mainly due to the basic temperature difference between the two boundaries and the heat supplied from external sources at these boundaries. However, the effect of viscous dissipation and the changing mass flux due to temperature gradient (Soret effect), on the convection, is also considered. Due to the consideration of the viscous dissipation inside the medium, a nonlinear basic flow profile is obtained. The disturbances in the base flow are assumed in the form of two-dimensional oblique structures, which are inclined to the base flow at an angle γ(0≤γ≤π2). The effect of the coefficients of external heating at the two boundaries (the associated non-dimensional parameters are the Biot numbers, B0 and B1, respectively) is discussed extensively. The cases with various combinations of the limiting values of B0 and B1 are also discussed. Viscous dissipation has a stabilizing effect on the flow, as long as the external heating at the bottom boundary is higher than that at the upper boundary. The system stabilizes with the increase in the coefficient of external heating at the lower boundary. The solute concentration gradient has a linearly destabilizing effect on the flow, for all Le(<, =, > 1). The Soret parameter has a linearly destabilizing effect on the flow, when the direction of solute concentration gradient opposes the direction of thermal buoyancy.

Onset of double-diffusive convection in near-critical gas mixtures.

Near the thermodynamic critical point, the physical properties of binary fluids exhibit large variations in response to small temperature and concentration differences, whose effects on the onset of double-diffusive convection are reported here. The vertical symmetry is broken, irregular penetrative instability occurs, and cat's eye patterns are identified in the fingering regime and oscillatory regime, respectively. A new parameter Θ is defined which indicates how the variations of physical properties influence flow fields. It is seen through numerical simulations that the Boussinesq approximation with constant physical properties has limited applicability, and that the Boussinesq equations with variable properties and density will describe all features seen. This conclusion is based on comparisons with the fully compressible, variable-property system.

Double-diffusive Soret convection phenomenon in porous media: effect of Vadasz inertia term

The onset of double-diffusive convection in horizontal porous layers for the thermo-diffusive Soret phenomenon in the case of a generalized Darcy model including inertia term is investigated. Via a linearization principle recently introduced in Rionero (Atti Accad Naz Lincei Rend Cl Sci Fis Mat Natur 28:21–47, 2017) the coincidence between linear and nonlinear (global) stability thresholds of the thermo-solutal conduction solution, is proved. Necessary and sufficient conditions guaranteeing the onset of steady or oscillatory convection in a closed algebraic form are obtained.

On the Onset of Double-diffusive Convection in a Couple Stress Nanofluid in a Porous Medium

Double-diffusive convection in a horizontal layer of nanofluid in a porous medium is studied. The couple-stress fluid model is considered to describe the rheological behavior of the nanofluid and for porous medium Darcy model is employed. The model applied for couple stress nanofluid incorporates the effect of Brownian motion and thermophoresis. We have assumed that the nanoparticle concentration flux is zero on the boundaries which neutralizes the possibility of oscillatory convection and only stationary convection occurs. The dispersion relation describing the effect of various parameters is derived by applying perturbation theory, normal mode analysis method and linear stability theory. The impact of various physical parameters, like the couple stress parameter, medium porosity, solutal Rayleigh Number, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have been examined on the stationary convection. It is observed that the couple stress parameter, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have stabilizing effects on the stationary convection whereas the solutal Rayleigh number and Dufour parameter have very small effect on the system.

The Onset of Double-Diffusive Convection in a Superposed Fluid and Porous Layer Under High-Frequency and Small-Amplitude Vibrations

We numerically simulate the initiation of an average convective flow in a system composed of a horizontal binary fluid layer overlying a homogeneous porous layer saturated with the same fluid under gravitational field and vibration. In the layers, fixed equilibrium temperature and concentration gradients are set. The layers execute high-frequency oscillations in the vertical direction. The vibration period is small compared with characteristic timescales of the problem. The averaging method is applied to obtain vibrational convection equations. Using for computation the shooting method, a numerical investigation is carried out for an aqueous ammonium chloride solution and packed glass spheres saturated with the solution. The instability threshold is determined under two heating conditions—on heating from below and from above. When the solution is heated from below, the instability character changes abruptly with increasing solutal Rayleigh number, i.e., there is a jump-wise transition from the most dangerous shortwave perturbations localized in the fluid layer to the long-wave perturbations covering both layers. The perturbation wavelength increases by almost 10 times. Vibrations significantly stabilize the fluid equilibrium state and lead to an increase in the wavelength of its perturbations. When the fluid with the stabilizing concentration gradient is heated from below, convection can occur not only in a monotonous manner but also in an oscillatory manner. The frequency of critical oscillatory perturbations decreases by 10 times, when the long-wave instability replaces the shortwave instability. When the fluid is heated from above, only stationary convection is excited over the entire range of the examined parameters. A lower monotonic instability level is associated with the development of perturbations with longer wavelength even at a relatively large fluid layer thickness. Vibrations speed up the stationary convection onset and lead to a decrease in the wavelength of most dangerous perturbations of the motionless equilibrium state. In this case, high enough amplitudes of vibration are needed for a remarkable change in the stability threshold. The results of numerical simulation show good agreement with the data of earlier works in the limiting case of zero fluid layer thickness.

Linear and Nonlinear Stability of Double-Diffusive Convection with the Soret Effect

The onset of double-diffusive convection in a horizontal fluid-saturated porous layer is examined by taking the Soret effect into consideration. The linear and nonlinear stability analyses are derived, and the corresponding eigenvalue problems are solved. The nonlinear stability analysis is achieved by using the energy method. In both the cases of linear and nonlinear stability theories, the onset criterion for all possible modes is derived analytically. For numerical computations of the eigenvalue problem, the Chebyshev tau method is employed. It is observed that the effect of stabilization or destabilization caused by the Soret parameter is significant for the Soret parameters which are less than \(Sr = 2\). In the absence of the Soret effect, the linear and nonlinear stability thresholds coincide.

Control strategy on the double-diffusive convection in a nanofluid layer with internal heat generation

The influences of feedback control and internal heat source on the onset of Rayleigh–Bénard convection in a horizontal nanofluid layer is studied analytically due to Soret and Dufour parameters. The confining boundaries of the nanofluid layer (bottom boundary–top boundary) are assumed to be free–free, rigid–free, and rigid–rigid, with a source of heat from below. Linear stability theory is applied, and the eigenvalue solution is obtained numerically using the Galerkin technique. Focusing on the stationary convection, it is shown that there is a positive thermal resistance in the presence of feedback control on the onset of double-diffusive convection, while there is a positive thermal efficiency in the existence of internal heat generation. The possibilities of suppress or augment of the Rayleigh–Bénard convection in a nanofluid layer are also discussed in detail.

The onset of double-diffusive convection in a nanofluid saturated porous layer: Cross-diffusion effects

The onset of double-diffusive convection in a horizontal porous layer saturated with a nanofluid with the Soret and Dufour effects is studied using both linear and nonlinear stability analyses in a three-dimensional way. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis, and the modified Darcy model is used for the porous medium that includes the time derivative term to describe the momentum transport. The thermal energy equation includes the diffusion and cross-diffusion terms. The linear theory depends on the normal mode technique, and the nonlinear analysis depends on the minimal representation of double Fourier series. The effects of the Soret and Dufour parameters, solutal Rayleigh number, viscosity ratio, and conductivity ratio on the stationary and oscillatory convections are presented graphically. It is found that for the stationary mode, the Soret and Dufour parameters, viscosity ratio, and thermal conductivity ratio have a stabilizing effect, while the solutal Rayleigh number destabilizes the system. For the oscillatory mode, the Soret and Dufour parameters, viscosity ratio, and Vadász number have a stabilizing effect, while the solutal Rayleigh number and the thermal conductivity ratio destabilize the system. We also study the effects of time on transient Nusselt number, which is found to be oscillatory when the time is small. However, when the time becomes very large, all three transient Nusselt number values approach the steady-state values.

Stability Control in a Binary Fluid Mixture Subjected to Cross Diffusive Coefficients

The effect of feedback control on the onset of double-diffusive convection in a horizontal binary fluid layer is studied analytically subjected to cross diffusion coefficients which are the Soret and Dufour parameters. The confined boundaries of the binary fluid layer are considered to be free-free, rigid-free and rigid-rigid which described the lower and upper surfaces respectively. The linear stability theory is applied and the eigenvalue solution is obtained numerically using Galerkin technique. Focusing on the stationary convection, it is shown that there is a positive thermal resistance in the presence of feedback control on the onset of double-diffusive convection in binary fluid mixture.

Effect of Vertical Magnetic Field on the Onset of Double Diffusive Convection in a Horizontal Porous Layer with Concentration Based Internal Heat Source

Effect of Vertical Magnetic Field on the Onset of Double Diffusive Convection in a Horizontal Porous Layer with Concentration Based Internal Heat Source