Oscillatory Convection Research Articles

Stability Analysis of Binary Casson Nanofluid Convection With Viscosity and Conductivity Variations Using Darcy–Brinkman Model

Abstract The onset of binary/double-diffusive convection with conductivity and viscosity variations has been investigated for Casson nanofluids using Darcy–Brinkman model. Nanoparticle conductivity and viscosity are used as linear functions of volume fraction. The normal mode approach, linearized stability theory, and one-term Galerkin method are used to obtain the expressions of Darcy–Rayleigh number for stationary and oscillatory convection. Different base-fluids (water, blood, honey) for different porous phases (glass, limestone, sand) have been examined numerically using the software mathematica (version 12.0). When Darcy parameter, conductivity, and viscosity variation parameters are combined, the layer's stability is significantly enhanced. The top-heavy layer of fluid instability state is shown to be dominated by stationary mode. It is observed that non-Newtonian Casson parameter and solute Lewis number destabilize the system while porosity parameter, Darcy number, and solute Rayleigh number postpone the same. Interestingly, thermal capacity ratio, conductivity, and viscosity parameters have stabilizing effects. A comparison of stability patterns of Newtonian and non-Newtonian nanofluids is carried out numerically by taking different base fluids like water (Newtonian fluid), blood, and honey (non-Newtonian Casson fluids). The system is found to be more stable for non-Newtonian fluids. It is observed that conductivity variation pattern for different porous media is: glass < limestone < sand for all the base fluids. As far as base fluids are concerned, they follow the conductivity pattern as water < honey < blood for different porous phases.

Role of the intraseasonal IPCO in the absence of typhoons in July 2020

The influence of the intraseasonal Indo-western Pacific convection oscillation (IPCO) on the absence of typhoons in July 2020 over the western North Pacific (WNP) was explored. While observation analysis shows that necessary conditions such as sea surface temperature (SST) and vertical wind shear in July 2020 meet the basic requirement of or even are conducive to the formation of typhoon, the unprecedented absence of typhoon over the WNP occurred in July 2020, and it is the first time that no typhoon in July since 1951. Additionally, significant differences were found in the number of typhoons in July between the different phases of the intraseasonal IPCO, and the number in the positive phase of the intraseasonal IPCO was significantly higher than that in the negative phase of the intraseasonal IPCO. In July 2020, the intraseasonal IPCO was in a strong negative phase, with the third lowest index in history and had the strongest inhibition effect on convection over the WNP on record, leading to large-scale circulation anomalies. The strongest descending movement on record inhibited the upward transport of water vapor and the development of cumulus convection, thereby reducing the release of latent heat of condensation and making it difficult to form a typhoon warm-core structure. In addition, the geopotential height increased over the WNP, and the western Pacific subtropical high moved southerly, which inhibited typhoon formation. Simultaneously, the South China Sea monsoon trough weakened significantly, with increased negative vorticity anomaly in the response scale, which hindered disturbance generation. The lowest genesis potential index confirmed that the large-scale circulation anomaly caused by the intraseasonal IPCO had an unprecedented restraining effect on typhoon generation, leading to the absence of typhoons over the WNP in July 2020.

Total Solar Irradiance during the Last Five Centuries

The total solar irradiance (TSI) varies on timescales of minutes to centuries. On short timescales it varies due to the superposition of intensity fluctuations produced by turbulent convection and acoustic oscillations. On longer timescales, it changes due to photospheric magnetic activity, mainly because of the facular brightenings and dimmings caused by sunspots. While modern TSI variations have been monitored from space since the 1970s, TSI variations over much longer periods can only be estimated either using historical observations of magnetic features, possibly supported by flux transport models, or from the measurements of the cosmogenic isotope (e.g., 14C or 10Be) concentrations in tree rings and ice cores. The reconstruction of the TSI in the last few centuries, particularly in the 17th/18th centuries during the Maunder minimum, is of primary importance for studying climatic effects. To separate the temporal components of the irradiance variations, specifically the magnetic cycle from secular variability, we decomposed the signals associated with historical observations of magnetic features and the solar modulation potential Φ by applying an empirical mode decomposition algorithm. Thus, the reconstruction is empirical and does not require any feature contrast or field transport model. The assessed difference between the mean value during the Maunder minimum and the present value is ≃2.5 W m−2. Moreover it shows, in the first half of the last century, a growth of ≃1.5 W m−2, which stops around the middle of the century to remain constant for the next 50 years, apart from the modulation due to the solar cycle.

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.

Thermal Convection for an Oldroyd-B Fluid in an Anisotropic Porous Medium Underlying a Fluid Layer

Abstract We investigate the thermal convection in a fluid layer overlying an anisotropic porous medium with Oldroyd-B fluids in the paper. The linear stability analysis and the Chebyshev pseudo-spectral method are used to obtain the numerical results. We found that the neutral curves are bimodal at some depth ratios. The proper values of the permeability ratio and the thermal diffusivity ratio are found to stabilize the stationary convection and the oscillatory convection. Furthermore, the variation of permeability ratio does not affect the bimodal nature of the neutral curves. In addition, the increase in the stress relaxation time has an unstable effect on the oscillatory convection, but the strain retardation time has the opposite effect.

An Analytical Study of Thermal Instability in a Nanofluid Layer with a Vertical Magnetic Field

The paper re-examines analytically the work of Yadav et al. ([43], [44]) (referred to as Y hereafter) wherein they have examined the combined effect of vertical magnetic field and the free-free, rigid-rigid and rigid-free boundaries on the onset of convection in an electrically conducting nanofluid layer heated from below. The key feature of the present paper is that it explains that the case M=0 ([43], [44]) is not justified either on physical or on mathematical grounds. Moreover, a number of sufficient conditions regarding the non-existence of oscillatory convection have been found.

Micropolar nanofluid overlying a porous layer: Thermosolutal convection

An investigation of the stability of an micropolar nanofluid overlying a sparsely packed porous medium and implanted in a parallel conduit is reviewed. Linear and also nonlinear terms are incorporated for the study. A Darcy-Brinkman-Forchheimer drag force model is deployed. To evaluate nanoscale effects the Buongiorno model is employed. The equations for mass, momentum, angular momentum, energy and nanoparticle species conservation with correlated wall conditions are non-dimensionalized. Modified diffusivity ratio and Lewis number stable the system, the micropolar parameters concentration Rayleigh number destable system for stationary convection. Concentration Rayleigh number, micropolar parameters stabilize and Lewis number destabilizes the system for oscillatory convection. Applications of the study include micro/nano-fluidic devices, nano-doped energy systems and packed beds in chemical engineering.

Effects of throughflow on thermosolutal penetrative convection in a fluid layer with variable gravity field

AbstractIn this study, the start of thermosolutal penetrative convection in a horizontal fluid layer heated and salted from below was investigated analytically and graphically in the presence of throughflow and changeable gravity field effects. The normal mode technique is used to test the system's stability properties. The mathematical expressions for stationary and oscillatory Rayleigh numbers are obtained as a function of the governing parameters. The analysis demonstrates that the vertical throughflow, gravity parameter, and heat source effect all have a considerable influence on the beginning of convective motion in double‐diffusive flow. The impacts of variable gravity, vertical throughflow, and heat source parameters, as well as other physical parameters such as Solutal Rayleigh numbers and Lewis numbers, on stationary and oscillatory convection, are studied and illustrated graphically, and some previously published results are recovered in the limiting cases.

Linear stability analysis of electro‐convection in dielectric Oldroydian nanofluid

AbstractThis study deals with an analytical and computational study for the initiation of oscillatory convection in a rheological nanofluid permeated with an alternating current electric field using stress‐free boundary conditions. The rheological properties of the nanofluid are described using the Oldroyd model. The used model for nanofluid permeated with electric field integrates the additional effect of electrophoresis, Brownian motion, and thermophoresis in the conservation of momentum equations. The coupled partial differential equations are simplified to a nondimensional ordinary linear differential equation using infinitesimal perturbations, Boussinesq approximation, normal mode technique, and linearized stability theory. The characteristic equation is solved analytically for stress‐free boundary conditions and the expressions for Rayleigh number of non‐oscillatory and oscillatory modes initiation are determined with regard to various nondimensional governing variables. The oscillatory modes are found to occur for both the cases of top‐/bottom‐heavy nanoparticle distributions. The thermal Rayleigh number are presented graphically to investigate the influence of involved variables on the stability of the considered system. The results show that the electric Rayleigh number, Prandtl number, and stress‐relaxation parameter advance whereas the strain‐retardation parameter delays the initiation of both stationary and oscillatory convection.

Magnetized Oscillatory Double-diffusive Convection

We study the properties of oscillatory double-diffusive convection (ODDC) in the presence of a uniform vertical background magnetic field. ODDC takes place in stellar regions that are unstable according to the Schwarzschild criterion and stable according to the Ledoux criterion (sometimes called semiconvective regions), which are often predicted to reside just outside the core of intermediate-mass main-sequence stars. Previous hydrodynamic studies of ODDC have shown that the basic instability saturates into a state of weak wave-like convection, but that a secondary instability can sometimes transform it into a state of layered convection, where layers then rapidly merge and grow until the entire region is fully convective. We find that magnetized ODDC has very similar properties overall, with some important quantitative differences. A linear stability analysis reveals that the fastest-growing modes are unaffected by the field, but that other modes are. Numerically, the magnetic field is seen to influence the saturation of the basic instability, overall reducing the turbulent fluxes of temperature and composition. This in turn affects layer formation, usually delaying it, and occasionally suppressing it entirely for sufficiently strong fields. Further work will be needed, however, to determine the field strength above which layer formation is actually suppressed in stars. Potential observational implications are briefly discussed.

Study of primary and secondary instabilities arising due to a chemical reaction in a two-component Rayleigh–Bénard system

Manifestation of stationary and oscillatory convection and secondary instabilities due to a chemical reaction in a two-component convective fluid system is reported in the paper by considering idealistic as well as physically realistic boundaries. Using a normal mode solution, analytical expression of the critical Rayleigh number for a stationary and oscillatory disturbances, and the natural frequency are reported. The range of parameters is identified where oscillatory motion happens. Further, the parameters’ range for existence of oscillatory regime is found to be larger for rigid boundaries compared to that of free boundaries. Furthermore, for both the boundaries, parameters’ range for this regime increases when the chemical reaction rate increases, leading to the conclusion that the oscillatory motion emerges as the most preferred mode in the two-component system due to the presence of a chemical reaction and the size of this domain is directly proportional to the chemical reaction rate. The marginal stability plots depict that the oscillatory and stationary regimes respectively correspond to Hopf and direct pitchfork bifurcations. The critical Rayleigh number and the wave number where codimension two bifurcation exists are documented in the paper for fixed values of parameters. It is shown that the codimension two bifurcation that arose in the problem is not a Takens–Bogdanov bifurcation. In a stationary regime, the domain for secondary instabilities of Eckhaus and zigzag is obtained using the spatio-temporal Newell–Whitehead–Segel equation. These instabilities grow with increasing chemical reaction rate. In the oscillatory regime, the complex Ginzburg–Landau equation is used to predict the appearance of the Benjamin–Feir instability.

Double-Diffusive Convection in Bidispersive Porous Medium with Coriolis Effect

In this paper, the thermal instability of rotating convection in a bidispersive porous layer is analyzed. The linear stability analysis is employed to examine the stability of the system. The neutral curves for different values of the physical parameters are shown graphically. The critical Rayleigh number is evaluated for appropriate values of the other governing parameters. Among the obtained results, we find: the Taylor number has a stabilizing effect on the onset of convection; the Soret number does not show any effect on oscillatory convection, as the oscillatory Rayleigh number is independent of the Soret number; there exists a threshold, Rc* ∈ (0.45, 0.46), for the solute Rayleigh number, such that, if RC > Rc*, then the convection arises via an oscillatory mode; and the oscillatory convection sets in and as soon as the value of the Soret number reaches a critical value, (∈(0.6, 0.7)), and the convection arises via stationary convection.

Oscillatory natural convection of Al2O3-water nanofluid near its density maximum in a narrow horizontal annulus

In order to reveal the oscillatory characteristics of the natural convection of nanofluid, this paper presents a comprehensive numerical work on the oscillatory natural convection of Al2O3-water nanofluid near its density maximum in a narrow horizontal annulus. The influences of nanoparticle volume fraction, Rayleigh number and density inversion parameter on the flow pattern evolution and heat transfer ability are analyzed. Results show that the density inversion of the working fluid affects the velocity and temperature distributions of the natural convection of Al2O3-water nanofluid significantly. Adding nanoparticles is beneficial to stabilizing the flow of nanofluid and keeping the symmetry of the flow structure. The convective heat transfer is enhanced with the increase of the volume fraction of nanoparticles. Furthermore, the evolution of the flow regime with the Rayleigh number at different volume fractions of nanoparticles is summarized.

Thermal Instability and Chaos in a Hybrid Nanofluid Flow

In this work, the linear and nonlinear dynamics of thermal convection in an incompressible Newtonian (alumina-copper)/water hybrid nanofluid each confined in an infinite rectangular cavity and heated from below via the Cattaneo–Christov heat flux model are studied for volume fractions fixed between 0 and 0.05. Firstly, using the governed flow equations and free boundary conditions, we proceed to the classical theory of stationary and oscillatory convection which help us to find the expressions of critical Rayleigh numbers, Cattaneo numbers and wavenumber of base fluid as a function of mono or hybrid nanofluid thermophysical properties. The results show that when the Cattaneo number increases, the critical Rayleigh number is constant in the case of stationary convection but decreases in the case of oscillatory convection for pure base fluid and hybrid nanofluids. It is noted that beyond the threshold Cattaneo number, the critical Rayleigh number of stationary convection is greater than those of oscillatory convection and the critical wavenumber shifts discontinuously from stationary to oscillatory convection. Secondly, the use of the truncated Galerkin approximation made it possible to find a five low-dimensional system in order to study numerically the transition from natural convection to chaotic behavior of nanofluid. We noticed that the addition of hybrid nanoparticle in the heat fluid transfer increases the domain of stationary convection by delaying the oscillatory convection with increasing normalized Rayleigh number. Also, the bifurcation diagrams show that the use of hybrid nanoparticles allows further control of the chaos in base fluid by expanding the convective flow. Furthermore, in the presence of thermal relaxation time, the chaos in the hybrid nanofluid lasts longer compared to the ordinary fluid.

Internal flow structure and dynamic free-surface deformation of oscillatory thermocapillary convection in a high-Prandtl-number liquid bridge

Internal flow structure and dynamic free-surface deformation of oscillatory thermocapillary convection in a high-Prandtl-number liquid bridge

Linear and weakly non-linear stability analysis of oscillatory convection in rotating ferrofluid layer

In the present paper, the problem of ferroconvection in the presence of uniform vertical rotation is considered to investigate the linear and weakly non-linear oscillatory stability. Two-dimensional convective roll instability is discussed with finite-amplitude disturbances. For linear stability, as a first-order problem, the expressions for Rayleigh numbers for stationary and oscillatory convection are derived and the effects of Coriolis force and magnetic parameters on the onset of ferromagnetic convection are studied, numerically. In weakly nonlinear oscillatory analysis, the second-order and third-order stability problems are discussed and the complex Ginzburg-Landau equation describing the amplitude of convection cell in rotating ferrofluid is derived and consequently, the expression for Nusselt number representing the heat transfer rate is obtained. From the present analysis, we observed that the rotation has the usual stabilizing effect on the linear stability in ferroconvection, however, the magnetic number (M1) and the measure of nonlinearity of magnetization (M3) both have a destabilizing effect on the onset of linear instability. Also, we found that for non-linear convection, the heat transfer rate (the Nusselt number) increases with increasing values of Taylor number, magnetic number, and the measure of nonlinearity of magnetization.

Convection in a Ferromagnetic Fluid Layer Influenced by Changeable Gravity and Viscosity

The motive of this work is to numerically evaluate the effect of changeable gravitational fields and varying viscosity on the beginning of convection in ferromagnetic fluid layer. The fluid layer is constrained by two free boundaries and varying gravitational fields that vary with distance across the layer. The authors hypothesized two categories of gravitational field variation, which can be subdivided into six distinct cases: (i) f(z)=z, (ii) f(z)=ez, (iii) f(z)=log(1+z), (iv) f(z)=−z, (v) f(z)=−z2, and (vi) f(z)=z2−2z. The normal mode method was applied, and the single term Galerkin approach was used to solve the ensuing eigenvalue problem. The results imply that, in the first three cases, the gravity variation parameter speeds up the commencement of convection, while, in the last three cases, the viscosity variation parameter and gravity variation parameter slow down the onset of convection. It was also observed that, in the absence of the viscosity variation parameter, the non-buoyancy magnetization parameter destabilizes the impact on the beginning of convection but, in the presence of the viscosity variation parameter, it destabilizes or stabilizes impact on the beginning of convection. In the case of oscillatory convection, the results illustrate that oscillatory modes are not permitted, suggesting the validity of the theory of exchange of stabilities. Additionally, it was also discovered that the system is more stable for case (vi) and more unstable for case (ii).

Oscillatory natural convection in a square enclosure containing a PCM suspension

In this study, a numerical simulation is performed to explore oscillatory natural convection in a square enclosure with a phase change material (PCM) suspension using the implicit finite difference method. The following parameters are considered: aspect ratio of the physical model = 1; ratio of the buoyancies caused by temperature and concentration gradients = 1; Rayleigh number = 103-106; initial mass fraction (or concentration) of PCM particles = 0–0.1; Stefan number = 0.005–0.1; and subcooling factor = 0–1.0. The results show that high Rayleigh numbers can easily cause oscillations in the flow field and temperature distribution. However, even under low Rayleigh number conditions, when the initial mass fraction or subcooling is increased or the Stefan number is decreased, oscillations occur.

Gravitational Modulation Effect on Double-Diffusive Oscillatory Convection in a Viscoelastic Fluid Layer

The complex Ginzburg-Landau model has been employed to derive the temporal amplitude of convection in a viscoelastic fluid layer under gravity modulation. The finite amplitude is based on a weakly nonlinear thermal convection. The perturbation technique is applied to simplify the nonlinear system of partial differential equations into a non-autonomous amplitude equation. Heat and mass transfer obtained in terms of the Nusselt and Sherwood numbers, and the corresponding results are presented for the small amplitude of modulation. The moderate values of amplitude and frequencies of gravity modulation are considered, their effect is to enhance the heat and mass transfer in the layer. Thus, the modulation plays dual role in heat and mass transfer. The variations of Nusselt and Sherwood numbers with slow time becomes rapid on either increasing the parameters Rs, Pr, λ, δ or decreasing the parameters Γ, ε, Ω. Each parameter effect has been presented graphically with their effect on Nu and Sh. Further, it is found that an oscillatory mode of convection enhances the heat and mass transfer than a stationary mode.

Numerical investigation of thermocapillary convection instability for large Prandtl number nanofluid in rectangular cavity

Oscillation characteristics and evolution process of large Prandtl number (Pr = 58) nanofluid thermocapillary convection is first reported in this work, and the variation of critical Marangoni number and flow instability under different nanoparticle concentrations is revealed. The results show that, nanofluid thermocapillary oscillatory convection consists of multiple vortices and these vortices migrate periodically from cold wall to hot wall, meanwhile, periodic temperature wave and stream function fluctuation cell exist in the oscillation process. As nanoparticle volume fraction increases, the critical Marangoni number decreases obviously, the oscillatory amplitude first increases and then decreases, and the oscillatory period almost increases linearly. This discovery can effectively promote the active control of thermocapillary convection instability.