Oscillatory Convection Research Articles

Thermal Convection of Rivlin-Ericksen Fluid Governed by the Brownian Motion and Thermophoresis of Nanoparticles with Passive Behaviour of Nanoparticles at the Parallel Boundaries

Stability of Rivlin-Ericksen category of nanofluid saturated in a continuous medium bounded by infinite horizontal plates has been studied. Energy equation has been supplemented with the variables belonging to the Brownian motion and thermophoresis of nanoparticles. For the linear and the non-linear stability analyses, other than the specific boundary conditions appraised with the physical situation, the boundary conditions for the flux of nanoparticle mass, in analogy with the passive behaviour of temperature at the boundaries have been explored. The novelty of the paper is that the stationary convection exists for both positive as well as negative Rn (concentration Rayleigh number) and the convection sets in earlier in comparison to a porous medium. It is also shown that the non-existence of the oscillatory convection in a Newtonian nanofluid has been ruled out for Rivlin-Ericksen nanofluid, though it exists only for negative Rn, the situation when the density of the fluid is greater than the density of nanoparticle. The viscoelastic parameter of Rivlin-Ericksen nanofluid annihilates the instability of oscillatory convection. Under non-linear stability analysis, the truncated representation of Fourier series approach has been used and the parameters belonging to the heat and mass transfer have been evaluated. It is shown that corresponding to certain parameters, the rate of heat and mass transfer rises rapidly. The valuable results are shown graphically and verified numerically.

Thermal instability of rotating Jeffrey nanofluids in porous media with variable gravity

It is investigated how changes in gravity affect the thermal instability rotating Jeffrey nanofluids in porous media. Along with the Galerkin method and normal mode approach, the Darcy model is used. The distinct variable gravity parameters taken in this paper are: h(z)=z2-2z, h(z)=-z2, h(z)=-z and h(z)=z and their effects on the Jeffrey parameter, Taylor number, moderated diffusivity ratio, porosity of porous media, Lewis number and nanoparticle Rayleigh number on stationary convection have been scrutinized and graphically shown. Our finding demonstrates that varying gravity parameter h(z)=z2-2z has more stabilising impact on stationary convection. We have also discovered the necessary condition for overstability in the instance of oscillatory convection for this problem.

Effect of Vadasz term on the onset of convection in a Darcy–Brinkman anisotropic rotating porous medium in LTNE

In the present paper, the effect of the Vadasz inertia term on the onset of convective motions for a Darcy–Brinkman model is investigated. It is proved that this term leads to the possibility for oscillatory convection to occur. Hence, convection can occur via either oscillatory or steady motions. It is proved analytically that the onset of steady convection is not affected by the Vadasz term, while oscillatory convection is favoured by it. Moreover, conditions to rule out the occurrence of oscillatory convection are determined numerically. The influence of rotation, interaction coefficient and mechanical and thermal anisotropies on the onset of instability is investigated, both analytically and numerically.

Free Electrothermo-Convective Instability in a Dielectric Oldroydian Nanofluid Layer in a Porous Medium

For the last few years, thermal instability of non-Newtonian nanofluids becomes a prominent field of research because it has various applications in automotive industries, energy-saving, nuclear reactors, transportation, electronics etc. and suspensions of nanoparticles are being developed in medical applications including cancer therapy. In this paper, a free electrothermo-convective instability in a dielectric nanofluid layer in a porous medium is studied. An Oldroyd’s constitutive equation is used to describe the behaviour of nanofluid and for porous medium, the Darcy model is employed. The equation of conservation of momentum of fluid is stimulated due to the presence of an AC electric field, stress-relaxation parameter and strain-retardation parameter. The stability of the system is discussed in stationary and oscillatory convections for free–free boundaries. For the case stationary convection, it is found that the Oldroydian Nanofluid behaves like an ordinary nanofluid as the stationary Rayleigh number is independent of the stress-relaxation parameter, the strain-retardation parameter and Vadasz number. The effect of stress-relaxation-time parameter, strain-retardation-time parameter, Vadasz number, nanoparticles Rayleigh number, modified diffusivity ratio, medium porosity, Lewis number and electric Rayleigh number examined numerically and graphs have been plotted to analyse the stability of the system. It is observed that the electrical Rayleigh number has destabilizing influence whereas nanoparticles Rayleigh number, porosity and modified diffusivity ratio have stabilizing effect on the system. The oscillatory convection is possible for the values of the stress-relaxation parameter less than the strain-retardation parameter for both top-heavy/bottom-heavy distributions of nanoparticles.

Dependency of transition in thermocapillary convection on volume ratio in annular pools of large-Pr fluid in microgravity

Thermocapillary convection driven by the horizontal temperature gradient is a typical nonlinear dynamical system. As the applied temperature difference increases, the flow undergoes a series of transitions into turbulence. Volume ratio of the liquid layer Vr (liquid volume/volume of the container) is a critical parameter that affects transition behaviors of the convection. Direct numerical simulations on thermocapillary convection in annular liquid pools with various volume ratios are carried out. Characteristics of the oscillatory convection are detected by time series and frequency spectrum analyses. The dynamic mode decomposition (DMD) method is also adopted to investigate inherent structures of the flow field. Effect of Vr on oscillation characteristics under a wide range of temperature differences from 10K to 90K is discussed. Results show that in annular pools with lager volume ratios, the thermocapillary convection is chaotic under very large ΔT and its transition behaviors are more complicated.

Darcy–Brinkman Double Diffusive Convection in an Anisotropic Porous Layer with Gravity Fluctuation and Throughflow

The influence of the throughflow and gravity fluctuation on thermosolutal convection in an anisotropic porous bed with the Darcy–Brinkman effect is considered numerically. The critical Rayleigh numbers for the onset of stationary and oscillatory modes have been found via linear instability analysis. The impact of various gravitational functions in the presence of throughflow on stability is studied. The analysis has been carried out for decreasing and increasing gravity fluctuations. The convective problem has been numerically analyzed using a single-term Galerkin approach. The results show that the mechanical anisotropy parameter and Lewis number have a destabilizing effect, while the thermal anisotropy parameter, Darcy number, solutal Rayleigh number, throughflow parameter, and gravity parameter have a stabilizing effect on stationary and oscillatory convection. It is clear that the system changes in a way that makes it more stable for case (iii) gravity fluctuation and more unstable for case (iv) gravity fluctuation.

Predicting the effect of inertia, rotation, and magnetic field on the onset of convection in a bidispersive porous medium using machine learning techniques

Effects of the magnetic field and inertia on the onset of thermal convection in a horizontal bidispersive porous layer, rotating about a vertical axis, are analyzed. The Darcy equation with same temperature in the micro- and macrophases is used to characterize the fluid motion. The Vadasz number is taken into account in a generalized Darcy equation for the macrophase. The eigenvalue problem obtained from the linear stability analysis is solved analytically for free–free boundaries. Moving one step further from the traditional linear stability analysis, machine learning tools are introduced in this paper to include the effect of multiple parameters on the marginal state of the system. Machine learning techniques have been implemented to identify the mode of instability with respect to different parameters. In particular, classification algorithms, namely, Artificial Neural Networks (ANN) and Support vector machine, are used to examine the onset of oscillatory convection and stationary convection. The required data for training of the algorithms are generated from the results of linear stability analysis. It is found that ANN with the sufficient number of hidden layers along with good choice of training dataset can predict the mode of instability even on the small variation in a given parameter. The combined effect of rotation, magnetic field, and inertia is to reduce the oscillatory mode of instability; hence, the system exhibits the steady mode of instability for a significant region in the three dimensional space comprising the Taylor number, the Hartman number, and the Vadasz number.

Finite Amplitude Oscillatory Convection of Binary Mixture Kept in a Porous Medium

In the present study, the double-diffusive oscillatory convection of binary mixture, 3He–4He, in porous medium heated from below and cooled from above was investigated with stress-free boundary conditions. The Darcy model was employed in the governing system of perturbed equations. An attempt was made, for the first time, to solve these equations by using the nonlinear analysis-based truncated Fourier series. The influence of the Rayleigh number (R), the separation ratio (ψ) due to the Soret effect, the Lewis number (Le), and the porosity number (χ) on the field variables were investigated using the finite amplitudes. From the linear stability analysis, expressions for the parameters, namely, R and wavenumbers, were obtained, corresponding to the bifurcations such as pitchfork bifurcation, Hopf bifurcation, Takens–Bogdnanov bifurcation and co-dimension two bifurcation. The results reveal that the local Nusselt number (NL) increases with R. The total energy is enhanced for all increasing values of R. The deformation in the basic cylindrical rolls and the flow rate are enhanced with R. The trajectory of heat flow was studied using the heatlines concept. The influence of R on the flow topology is depicted graphically. It is observed that the intensity of heat transfer and the local entropy generation are increased as R increases.

Study on Oscillatory Mechanism of Solutocapillary Convection and Influence of Aspect Ratio on Flow Characteristics during Crystal Growth

A numerical simulation has been conducted to investigate the oscillatory mechanism of a solutocapillary convection and the influence of different aspect ratios on the flow characteristics in a liquid bridge. The SIMPLE algorithm is applied to figure out the Navier-Stokes equation and the concentration diffusion equation on the staggered grids, and the level set approach with the conservation of the mass is used to acquire the surface deformation of the liquid bridge. The flow characteristics of the oscillatory solutocapillary convection are analyzed in detail, including the distributions of the concentration, velocity, and transverse displacement of the free surface at the upper corner and intermediate height of the liquid bridge. Moreover, the effects of the aspect ratio on the flow stability and onset time of the oscillations for the concentration and velocity have also been investigated. The results show that the essence of the oscillatory solutocapillary convection is the result of the coupling oscillation of the concentration, velocity and free surface. The upper corner is the origin region of the oscillation, which has an important impact on the overall flow characteristics. Within a definite height range of the liquid bridge, the lower the height, the more stable the flow and the weaker the oscillation. There is a complex relationship between the onset time of the concentration and velocity oscillations and the aspect ratio of the liquid bridge.

Bi-stability Bifurcation in Convection Double Diffusion Through a Shallow Horizontal Layer Saturated with a Complex Fluid

The onset of non-linear convection in a porous layer saturated by a shear-thinning liquid is studied. The Carreau-Yasuda model is utilized for modeling the behavior of the working medium. Constant fluxes of heat and mass are defined on the horizontal surfaces of the cavity, while the vertical sides are assumed adiabatic. The parallel flow approximation and the finite difference approach are used to conduct the investigation analytically and numerically, respectively. The linear stability inspection of the convective and diffusive circumstances is carried out by taking into account an infinitesimal perturbation. The theory of linear stability is employed to determine the critical Rayleigh number for the motion from the rest state, Hopf bifurcation, and the transition from the stationary to oscillatory convection. Overall, the Carreau-Yasuda rheological parameters have a significant impact on the thresholds of convection. The most interesting findings of this study is highlighting the existence of a bi-stability phenomenon, i.e., the existence of two steady-state solutions, which was not observed before in non-Newtonian fluids convection.

Oscillatory convection in viscoelastic ferrofluid layer: Linear and non-linear stability analyses

The problem of ferroconvection in a viscoelastic fluid layer is studied with the aim to investigate oscillatory motions. In this article, a stability analysis for both linear and nonlinear systems is carried out. In the linear stability analysis, the expressions for steady and oscillatory Rayleigh numbers are obtained and the effects of magnetic as well as viscoelastic parameters on the onset of viscoelastic ferromagnetic convection are investigated numerically. From the analysis, we found that the magnetic number (M_1), the stress relaxation time (lambda_1) and the nonlinearity of magnetization (M_3) have destabilizing influences on the onset of ferroconvection, whereas the strain retardation time (lambda_2) has stabilizing influence. In the weakly nonlinear stability analysis, the formula for heat transfer rate in terms of the Nusselt number is derived for oscillatory convection. From the analyses, we found that for increasing values of the magnetic number, stress relaxation time and nonlinearity of magnetization, the heat transfer rate rises, whereas it decreases for larger values of the strain retardation time. Moreover, the pitchfork bifurcation analysis yields that in order to reach the stable positions, the value of amplitude increases as the stress relaxation time increases, whereas a reverse trend is observed for the strain retardation time.

Stationary and oscillatory convection in bidisperse colloidal suspension

Stationary and oscillatory convection in bidisperse colloidal suspension

Mantle thermochemical variations beneath the continental United States through petrologic interpretation of seismic tomography

The continental lithospheric mantle plays an essential role in stabilizing continents over long geological time scales. Quantifying spatial variations in thermal and compositional properties of the mantle lithosphere is crucial to understanding its formation and its impact on continental stability; however, our understanding of these variations remains limited. Here we apply the Whole-rock Interpretive Seismic Toolbox For Ultramafic Lithologies (WISTFUL) to estimate thermal, compositional, and density variations in the continental mantle beneath the contiguous United States from MITPS_20, a joint body and surface wave tomographic inversion for Vp and Vs with high resolution in the shallow mantle (60–100 km). Our analysis shows lateral variations in temperature beneath the continental United States of up to 800–900°C at 60, 80, and 100 km depth. East of the Rocky Mountains, the mantle lithosphere is generally cold (350–850°C at 60 km), with higher temperatures (up to 1000°C at 60 km) along the Atlantic coastal margin. By contrast, the mantle lithosphere west of the Rocky Mountains is hot (typically >1000°C at 60 km, >1200°C at 80–100 km), with the highest temperatures beneath Holocene volcanoes. In agreement with previous work, we find that the chemical depletion predicted by WISTFUL does not fully offset the density difference due to temperature. Extending our results using Rayleigh-Taylor instability analysis, implies the lithosphere below the United States could be undergoing oscillatory convection, in which cooling, densification, and sinking of a chemically buoyant layer alternates with reheating and rising of that layer.

Pattern selection and heat transfer in the Rayleigh–Bénard convection near the vicinity of the convection onset with viscoelastic fluids

The effect of viscoelasticity on the flow and heat transport in the Rayleigh–Bénard convection (RBC), a frequently encountered phenomenon in nature and industry, in a rectangular enclosure with horizontal periodic boundary is investigated via direct numerical simulation. The working fluid is described by a finitely extensible nonlinear elastic-Peterlin constitutive model almost all important features of viscoelastic fluid flow. Numerical simulations are conducted at a low concentration β=0.9, where β=μs/μ0, μs is the solvent viscosity, and μ0=μs+μp is the sum of μs and the polymer viscosity μp. A parametric analysis is performed to understand the influence of the Weissenberg number Wi, the viscosity ratio β, and the extension length L on the oscillating mode of the viscoelastic RBC. The results indicate that both Wi and β weakly inhibit the convection onset and the transition from steady to oscillatory convection. The amplitude and frequency of the oscillations in the oscillatory flow regime are both suppressed. However, the strongly elastic nonlinearity makes the flow transition irregular and even brings about the relaminarization or lead to the convection cells traveling in the horizontal direction. The increasing extension length L induces multiple pairs of roll flow patterns at a specific setting of (Ra, Wi). Heat transport is reduced (up to 8.5%) by elasticity but still obeys the power law with Ra if the flow pattern has one pair of rolls. However, heat transfer enhancement occurs if multiple pairs of rolls are induced.

The combined effects of rotation and anisotropy on double diffusive bi-disperse convection

In the present paper, double-diffusive convection, taking into account Coriolis effects, in a horizontal layer of Brinkman-anisotropic bi-disperse porous medium is analysed. Via linear instability analysis, we find that convection can set in through stationary or oscillatory motions and the critical Rayleigh numbers for the onset of stationary secondary flow (steady convection) and overstability (oscillatory convection) are determined.

On oscillatory rotating convection of a couple‐stress fluid with helical force

AbstractLinear and weakly nonlinear stability analyses of thermosolutal convection in a couple‐stress fluid with effects of helical force and rotation are performed. The governing nondimensional equations are solved using the normal modes. We have shown the effect of the helical force parameter, solutal Rayleigh number, Couple stress parameter, Lewis number, Taylor number, and Prandtl number on stationary and oscillatory convection regions and presented graphically. Solutal Rayleigh number, Couple stress parameter, Lewis number, and Taylor number have a stabilizing effect on the system whereas the helical force parameter has a destabilizing effect on the system. To study heat transport by convection we have derived the Ginzburg–Landau equation.

Oscillations of convective flow around a continuous optical discharge in high-pressure xenon

Laser-sustained plasma or continuous optical discharge (COD), predicted and first obtained in pioneering works initiated and inspired by Professor Raizer et al (1970 JETP Lett. 11 120–3; 1970 JETP Lett. 11 302–4; 1972 Sov. Phys.—JETP 34 763–9), is still a unique method of sustaining localized dense plasma in the laboratory and some special devices such as high-brightness broadband radiation sources [6–10]. Although the parameters determining the COD state can be stabilized, in practice, COD tends to regular oscillations. As stated in the paper, the oscillations may be attributed to the regular pulsing of thermal gravitational convective plumes around the COD. Application problems arising from instability of this type is pulsing of the emission from promising radiation sources utilizing COD plasma. This paper presents a detailed analysis of the experimental data on COD convective plume radii and oscillation frequencies depending on the plasma-forming gas pressure. The analysis leads to a similarity relation for the oscillation frequency. The similarity relation turns out to be common for optical discharges and laminar flames under conditions of prevailing buoyancy forces. This indicates the hydrodynamic nature of the instability considered, regardless of whether the energy input method is in the form of absorbed laser radiation or a chemical reaction. To support the idea of a hydrodynamic origin of the pulsations, a numerical simulation of a convective plume from a concentrated heat source was carried out. The thermal dissipation power of the heat source was equal to that of the COD. The results of numerical simulations demonstrate good agreement with those of the experiments. The dynamic temperature, density and gas velocity distributions obtained show that the direct cause of the oscillations is the dynamics of the toroidal vortices developed in the convection plume. The pulsing frequency equal to the frequency of the vortex formation may be increased under incoming additional forced gas flow that may also suppress the convective oscillations. The results obtained may be useful for studying optical discharges, and improving the parameters of high-brightness broadband laser-plasma radiation sources based on them.

Nonlinear system stabilization in an anisotropic porous medium with Oldroyd-B fluid based on an actuator and sensor array

In this research, the authors precisely focus on the analysis of the chaotic behavior in an Oldroyd-B fluid saturated anisotropic porous medium via a feedback control technique. A four-dimensional (4D) weakly nonlinear system emerging from a Galerkin method of the constitutive and preservation equations is developed to accord with a convective stabilization with various Darcy numbers (Da) and feedback control gain value [Formula: see text]. The chaotic dynamic convection is governed by the Darcy–Rayleigh number ([Formula: see text]) and feedback control, while the Da has a significant impact on system stabilization. Their results reveal the effects of the feedback gain parameter [Formula: see text], stress relaxation parameter ([Formula: see text]), strain retardation parameter ([Formula: see text]), Darcy number (Da), mechanical ([Formula: see text]) and thermal ([Formula: see text]) anisotropy parameter on the stability and destabilization of thermal convection. Stabilization of thermal convection are important in cooling, nuclear power, and a range of technical, biological and engineering processes. In particular, feedback control gain values are discovered to be the preferred mode for the controlled onset of oscillatory convection. Finally, a graphical representation is presented to demonstrate that the feedback control approach is more effective in regulating the entire system when aperiodic external disturbances occur.

Modified stability analysis of double‐diffusive convection in viscoelastic fluid layer saturating porous media

AbstractThe present analysis mathematically investigates the thermohaline convection problem in viscoelastic fluid layer saturating porous media by utilizing the modified Boussinesq approximation. By performing linear stability analysis, the Darcy–Rayleigh numbers for stationary and oscillatory modes of convection are derived. The effects of different parameters describing the problem are studied numerically. In nonlinear stability analysis, the heat and mass transfer rates in the form of Nusselt and Sherwood numbers, respectively, are obtained for oscillatory convection using the derived Ginzburg–Landau equation. From the results, it is observed that overstability is the preferred mode of instability in linear stability. It is found that in linear double‐diffusive convection problems, the stress relaxation imparts a destabilizing effect whereas the strain retardation time, the coefficient of specific heat variation due to temperature, and the concentration gradient have a stabilizing effect on the system's stability. The numerical values of heat and mass transfer rates varied with the coefficient of specific heat showing that the heat transport decreases while the mass transport increases. Also, the stress relaxation time, the concentration gradient, and the gravity modulation's amplitude increase while the strain retardation time decreases the heat and mass transfer rates. The wavelength of oscillations remains unaltered with the variation of specific heat variation due to temperature. The modulation frequency does not affect the heat/mass transfer rate; though, the wavelength of oscillations decreases with increasing frequency.

Thermal convection in a Brinkman–Darcy–Kelvin–Voigt fluid with a generalized Maxwell–Cattaneo law

We investigate thoroughly a model for thermal convection of a class of viscoelastic fluids in a porous medium of Brinkman–Darcy type. The saturating fluids are of Kelvin–Voigt nature. The equations governing the temperature field arise from Maxwell–Cattaneo theory, although we include Guyer–Krumhansl terms, and we investigate the possibility of employing an objective derivative for the heat flux. The critical Rayleigh number for linear instability is calculated for both stationary and oscillatory convection. In addition a nonlinear stability analysis is carried out exactly.