Thermal Convective Instability Research Articles

Effect of Variable Gravity Field on Dual Component Convection in a Couple Stress Fluid Saturated Anisotropic Porous Layer With Temperature‐Dependent Heat Source

ABSTRACTThis study examines how gravity fluctuations, the couple stress parameter, anisotropic parameters, and heat source collectively influence dual‐component convection in the porous layer. The linear analysis is conducted utilizing the normal mode technique. The authors proposed three categories of gravity fluctuation, namely: (a) linear, (b) parabolic, and (c) exponential. Expressions for both stationary and oscillatory Rayleigh numbers are derived using the Galerkin approach. Neutral stability curves for both stationary and oscillatory modes are analyzed, with graphical representations to show the effects of various stability parameters, including gravity fluctuations, couple stress, anisotropy, and heat source. The results show that the mechanical anisotropy parameter and Vadasz number lead to system destabilization, while the couple stress parameter, Lewis number, gravity parameter, solute Rayleigh number, and thermal anisotropy parameter help to stabilize the system. Furthermore, the system is more stable with exponential gravity fluctuations and less stable with parabolic gravity fluctuations. This finding offers insights into thermal convective instability in porous media, impacting applications in geoscience, engineering, and environmental science.

Instability of thermal convection in an inclined fluid layer with temperature-dependent internal heat source

Instability of thermal convection in an inclined fluid layer with temperature-dependent internal heat source

Influence of defects formation on the cracking behavior of LPBFed Cu-Cr-Zr alloy: Micro-mechanism and CRITIC-WASPAS approach

Advanced strategies and techniques in the Laser Powder Bed Fusion (LPBF) process for printing Cu-Cr-Zr alloy must be created to overcome the major flaws such as cavity formation, unstable thermal capillary convection and thermodynamic instability. In this research, the significant process variables in the LPBF techniques such as Laser Power (LP) of 430, 500 and 570 W, Scanning Velocity (SV) of 550, 750 and 950 mm/s, Hatching Distance (HD) of 0.06, 0.08 and 0.10 mm were considered into account to fabricate a crack-free Cu alloy coupon with maximum Relative Density (RD), Ultimate Tensile Strength (UTS) and Reduced Elastic Modulus (REM). To optimize the process variables, a Criteria Importance Through Intercriteria Correlation (CRITIC) associated with the Weighted Aggregated Sum Product Assessment (WASPAS) approach was employed. Finally, the confirmation experiments were performed for the optimal settings (LP of 430 W, SV of 750 mm/s and HD of 0.06 mm) and the initial settings (LP of 570 W, SV of 550 mm/s and HD of 0.10 mm). The optimal settings show an 8.6 % enhancement in relative density of 99.82 %, which also reflects in 47 % improvement in UTS of 336 MPa and a 27.8 % enhancement in REM of 147.45 GPa compared with the initial settings. With the help of fracture morphology, the effect of defect development on the propagation of fractures on the printed coupons was also investigated. Moreover, the confirmation experiments aligned more with the CRITIC-integrated WASPAS approach.

Effect of Oldroyd-B fluid on thermal convection stability in a bidispersive porous media with relatively large macropores

This study investigates the effect of Oldroyd-B fluids on the thermal convection instability in a bi-disperse porous medium with relatively large macropores. The modified momentum equation of Oldroyd-B fluid in the macro- and micropores is first derived, assuming local thermal equilibrium. The Orr–Sommerfeld (O–S) equation is derived using the new modified incompressible Navier–Stokes equations of Oldroyd-B fluid. The Chebyshev collocation method is employed to solve the generalized eigenvalue problem, and the neutral stability curves and temporal growth rates are obtained. The results demonstrate that the relaxation time enhances the convective instability, while the retardation time suppresses it. Furthermore, the effect of relaxation time is generally small for smaller wave number, but the effect of relaxation time is significant for large wave number, and this effect becomes accentuated as the wave number increases. The retardation time does not have any influence when the wavenumber is small, and the influence of retardation time becomes small with the large relaxation time. Moreover, the convection instability is enhanced with the higher micropermeability and a higher ratio of momentum transfer coefficient between the macro- and microphases will suppress the instability.

On Instability of a Dusty Stellar Atmosphere in Stern’s Type Configuration

The thermal-convective instability of a stellar atmosphere in the presence of a stable solute gradient in Stern’s type configuration is studied in the presence of suspended particles. The criteria for monotonic instability are derived which are found to hold well in the presence of uniform rotation and uniform magnetic field, separately, on the thermosolutal-convective instability of a stellar atmosphere in the presence of suspended particles.

The bimodal instability of thermal convection in a tall vertical annulus

We pursue a three-dimensional linear stability analysis to investigate the convective stability in a cylindrical annulus imposed with a horizontal temperature gradient. The investigation focuses on the stability of both axisymmetric and asymmetric modes in a wide range of Prandtl number Pr and the radii ratio η between the inner to outer cylinders. Results show that, for the axisymmetric mode, the stability strongly depends on the Prandtl number. For 0≤Pr≤1.4, the instability sets in as the shear mode that the instability enhances as η increases while it is virtually independent of Pr. The critical Grashof number can be approximated by Grc(η)≈103×4η−0.68+3. For 1.5≤Pr≤12.5, the buoyant mode appears and competes with the shear mode to predominate the stability under various Pr and η, namely, the bimodal instability occurs. The transition between the two modes occurs at the specific radii ratio η1=0.21Pr0.727−0.31. For Pr≥12.6, the shear mode vanishes and the buoyant mode prevails. The asymmetric modes are less prevailing than the axisymmetric mode for small Prandtl numbers, except that the mode of an azimuthal wavenumber equal to 1 becomes dominant in two small regions of η. When the Prandtl number is large, the axisymmetric mode predominates over the asymmetric mode except when η is very small. Otherwise, the asymmetric mode of a larger azimuthal wavenumber is less prevailing.

Control of quasi-equilibrium state of annular flow through reinforcement learning

Stability control of the convection flow field has always been a focal issue. The annular flow discussed in this work is a typical research model of microgravity fluid physics, which is extracted from the industrial crystal growth by the Czochralski method. It is believed that the instability of thermal convection is the key factor affecting the quality of crystal growth. Combining the reinforcement learning algorithm with the neural network, this paper proposes a control policy that makes forced convection compete with thermocapillary convection by changing the dynamic boundary conditions of the system. This control policy is successfully applied to the control of the quasi-equilibrium state of annular flow, and the global stability of the flow field is well maintained. It first experimentally makes the annular flow field under low and medium Ma numbers achieve a quasi-equilibrium state, which is different from that before the onset of flow oscillations. Then, a simulation environment is created to imitate the experimental conditions. After training in the simulation environment, with the self-optimized algorithm, the machine learning approach can successfully maintain the simulation environment in a quasi-equilibrium state for a long period of time. Finally, the learning method is validated in the experimental environment, and a quasi-equilibrium state control policy is completely optimized by using the same optimization policy and similar neural network structure. This work demonstrates that the model can understand the physical environment and the author's control objectives through reinforcement learning. It is an important application of reinforcement learning in the real world and a clear demonstration of the research value of microgravity fluid physics.

Thermal convection instability of two miscible viscous fluids in a rotating annular Hele–Shaw cell

We investigate thermal convection instability in a system of two horizontal miscible liquid layers confined in an annular Hele–Shaw cell rotating uniformly about its axis and subjected to a radial temperature gradient. We first determine the Hele–Shaw averaged velocity field in each fluid layer by taking into account the Coriolis force. Thereafter, the linear stability analysis leads to an eigenvalue problem solved numerically by the spectral collocation method. Depending on the buoyancy number, the ratio of the stabilizing chemical density anomaly to the destabilizing thermal density anomaly, the centrifugal force gives rise to two convection regimes: the oscillating regime corresponding to single-cell convection over the entire width of the Hele–Shaw cell and the stratified regime with separate convection in each of the two layers. In the stratified regime, it turns out that the cells rotate in the same direction and, thus, only thermal coupling is dominant in the Hele–Shaw cell geometry, regardless of the value of the viscosity ratio. We show that increasing the curvature parameter of the cell has a stabilizing effect and decreases the critical Buoyancy number corresponding to the transition from the oscillatory to the stratified regime. At a low Ekman number, the Coriolis force is strongly stabilizing and has little effect on the critical buoyancy number. Moreover, the increase in the curvature parameter and the decrease in the Ekman number together cause the transition from the oscillating regime to a nearly stratified regime. The effects of fluid layer thicknesses and the ratio of kinematic viscosities on the active or passive character of a layer are also examined.

The Elbert range of magnetostrophic convection. I. Linear theory

In magnetostrophic rotating magnetoconvection, a fluid layer heated from below and cooled from above is equidominantly influenced by the Lorentz and the Coriolis forces. Strong rotation and magnetism each act separately to suppress thermal convective instability. However, when they act in concert and are near in strength, convective onset occurs at less extreme Rayleigh numbers (, thermal forcing) in the form of a stationary, large-scale, inertia-less, inviscid magnetostrophic mode. Estimates suggest that planetary interiors are in magnetostrophic balance, fostering the idea that magnetostrophic flow optimizes dynamo generation. However, it is unclear if such a mono-modal theory is realistic in turbulent geophysical settings. Donna Elbert first discovered that there is a range of Ekman (, rotation) and Chandrasekhar (, magnetism) numbers, in which stationary large-scale magnetostrophic and small-scale geostrophic modes coexist. We extend her work by differentiating five regimes of linear stationary rotating magnetoconvection and by deriving asymptotic solutions for the critical wavenumbers and Rayleigh numbers. Coexistence is permitted if and . The most geophysically relevant regime, the Elbert range, is bounded by the Elsasser numbers . Laboratory and Earth’s core predictions both exhibit stationary, oscillatory, and wall-attached multi-modality within the Elbert range.

On Instability of a Composite Rotating Stellar Atmosphere

The aim of the present work was to study the thermal-convective instability of a composite rotating stellar atmosphere in the presence of a variable horizontal magnetic field to include, separately, the effects of medium permeability and solute gradient. Following the linearized stability theory, Boussinesq approximation and normal mode analysis, the dispersion is obtained in each case. The criteria for monotonic instability in each case have been obtained which generalize the Defouw’s criterion derived for thermal-convective instability in the absence of above effects.

Thermal Convective Instabilities and Chaos in a Rotating Hybrid Nanofluid Layer with Cattaneo–Christov Heat Flux Model

The linear and nonlinear dynamics of thermal convection of a rotating hybrid nanofluid layer heated from below with the Cattaneo–Christov heat flux model are studied in this paper. Starting from the flow equations of a hybrid nanofluid and exploiting the free boundary conditions, the analytical expressions of the stationary and oscillatory Rayleigh numbers of the base fluid are determined as a function of the dimensionless parameters of the heat transfer fluid and the thermophysical properties of the hybrid nanofluid. The effects of hybrid nanoparticles and Taylor number on the onset of stationary convection in the base fluid are investigated graphically. Then, a numerical study of the transition from natural convection to chaotic behaviour of the hybrid nanofluid is made using the truncated Galerkin approximation. This approximation allowed us to find a novel six‐dimensional nonlinear system depending on the parameters of the base fluid and the thermophysical properties of the hybrid nanofluid that can be reduced to five, four, or three dimensions when we tend some parameters to zero. The different results showed that the addition of hybrid nanoparticles (alumina‐copper) to a thermal fluid (water) subjected to the rotation force in the presence or absence of the thermal relaxation time allows control of the chaotic convection in the base fluid. On the other hand, the increase of the rescaled Taylor number and the Cattaneo number widens the domain of chaos in the hybrid nanofluid with the increase of the rescaled Rayleigh number of the base fluid.

Thermosolutal-Convective Instability In Stern’s Type Configuration

The thermal-convective instability of a stellar atmosphere in the presence of stable solute gradient in Stern’s type configuration is studied in the presence of radiative transfer effect. A criterion for monotonic instability is obtained in terms of the source functions S. The criterion for monotonic instability is found to be unchanged in the presence of radiative transfer and rotation effects. The problem of thermosolutal-convective instability of a hydromagnetic composite medium is also studied to include the frictional effects with neutrals. The criterion derived for monotonic instability in terms of heat-loss function is found to be the same in the presence or absence of the collisional effects.

THERMAL CONVECTION INSTABILITY OF TWO MISCIBLE VISCOUS FLUIDS IN A HELE-SHAW CELL

THERMAL CONVECTION INSTABILITY OF TWO MISCIBLE VISCOUS FLUIDS IN A HELE-SHAW CELL

On inhibition of thermal convection instability by a magnetic field under zero resistivity

We investigate the stability and instability of the magnetic Rayleigh–Bénard problem with zero resistivity. A stability criterion is established, under which the magnetic Bénard problem is stable. The proof is mainly based on a three-layers energy method and an idea of magnetic inhibition mechanism. The stability result first mathematically verifies Chandrasekhar's physical conjecture in 1955 that the thermal instability can be inhibited by a strong (impressed) magnetic field in magnetohydrodynamic (MHD) fluids with zero resistivity (based on a linearized steady magnetic Bénard equations). In addition, we also provide an instability criterion, under which the magnetic Rayleigh–Bénard problem is unstable. The instability proof is mainly based on a bootstrap instability method by further developing new techniques. Our instability result shows that the thermal instability still occurs when the (impressed) magnetic field is weak.

Two Predictions of Supernova: GRB 130427A/SN 2013cq and GRB 180728A/SN 2018fip

Abstract On 2018 July 28, GRB 180728A triggered Swift satellites and, soon after the determination of the redshift, we identified this source as a type II binary-driven hypernova (BdHN II) in our model. Consequently, we predicted the appearance time of its associated supernova (SN), which was later confirmed as SN 2018fip. A BdHN II originates in a binary composed of a carbon–oxygen core (COcore) undergoing SN, and the SN ejecta hypercritically accrete onto a companion neutron star (NS). From the time of the SN shock breakout to the time when the hypercritical accretion starts, we infer the binary separation ≃3 × 1010 cm. The accretion explains the prompt emission of isotropic energy ≃3 × 1051 erg, lasting ∼10 s, and the accompanying observed blackbody emission from a thermal convective instability bubble. The new neutron star (νNS) originating from the SN powers the late afterglow from which a νNS initial spin of 2.5 ms is inferred. We compare GRB 180728A with GRB 130427A, a type I binary-driven hypernova (BdHN I) with isotropic energy >1054 erg. For GRB 130427A we have inferred an initially closer binary separation of ≃1010 cm, implying a higher accretion rate leading to the collapse of the NS companion with consequent black hole formation, and a faster, 1 ms spinning νNS. In both cases, the optical spectra of the SNe are similar, and not correlated to the energy of the gamma-ray burst. We present three-dimensional smoothed-particle-hydrodynamic simulations and visualizations of the BdHNe I and II.

Thermal convection instability of two miscible viscous fluids in a Hele-Shaw cell

The onset of convection in two superimposed miscible fluid layers is investigated in the configuration of a geometric Hele-Shaw cell using linear stability analysis. The two fluids have different densities. We neglect the surface tension and chemical diffusion at the interface which is assumed of small amplitude. We consider only the asymptotic case, where the Prandtl number’s order is of the order of unity or larger than unity. We show, in the Hele-Shaw configuration, which can simulate convection in porous media, that the onset of convection can be either stationary or oscillatory depending on the Buoyancy number, B (the ratio of the stabilizing chemical density anomaly to the destabilizing thermal density anomaly), which depends on the viscosity and layer height ratios. When the buoyancy number is lower than a critical value, Bc, oscillating convection occurs in the whole cell height, however beyond Bc, the stratified regime develops without deformation of the interface and convection occurs separately in each layer. In this paper, the transition from oscillatory regime to stratified regime is visualised by using the streamlines at the onset of convection

Effect of composition gradient on magnetothermal instability modified by shear and rotation

We model the intracluster medium as a weakly collisional plasma that is a binary mixture of the hydrogen and the helium ions, along with free electrons. When, owing to the helium sedimentation, the gradient of the mean molecular weight (or equivalently, composition or helium ions' concentration) of the plasma is not negligible, it can have appreciable influence on the stability criteria of the thermal convective instabilities, e.g., the heat-flux-buoyancy instability and the magnetothermal instability (MTI). These instabilities are consequences of the anisotropic heat conduction occurring preferentially along the magnetic field lines. In this paper, without ignoring the magnetic tension, we first present the mathematical criterion for the onset of composition gradient modified MTI. Subsequently, we relax the commonly adopted equilibrium state in which the plasma is at rest, and assume that the plasma is in a sheared state which may be due to differential rotation. We discuss how the concentration gradient affects the coupling between the Kelvin--Helmholtz instability and the MTI in rendering the plasma unstable or stable. We derive exact stability criterion by working with the sharp boundary case in which the physical variables---temperature, mean molecular weight, density, and magnetic field---change discontinuously from one constant value to another on crossing the boundary. Finally, we perform the linear stability analysis for the case of the differentially rotating plasma that is thermally and compositionally stratified as well. By assuming axisymmetric perturbations, we find the corresponding dispersion relation and the explicit mathematical expression determining the onset of the modified MTI.

Thermal Instability of a Power-Law Fluid Flowing in a Horizontal Porous Layer with an Open Boundary: A Two-Dimensional Analysis

A two-dimensional analysis of the onset of thermal convective instability in a horizontal porous layer with open upper boundary is carried out. The saturating fluid is non-Newtonian of power-law behaviour, and its flow is represented through a suitable extension of Darcy’s law. A model of temperature-dependent viscosity is employed where the consistency index is considered as variable, while the power-law index is assumed to be constant. Numerical data for the neutral stability and for the critical values of a modified Darcy–Rayleigh number have been obtained. The feasibility of an experimental validation of the theoretical results predicted by the stability analysis is discussed in detail. An experimental set-up based on a Hele-Shaw cell is described, and preliminary results relative to the onset of convective cells are described. Observed hysteretic effects and deviations from the rheological model are identified as potential sources of uncertainty.

Thermohaline instability and the formation of glacial North Atlantic super polynyas at the onset of Dansgaard‐Oeschger warming events

AbstractLate Quaternary rapid warming events inferred on the basis of oxygen isotopic data from Greenland ice cores are the most prominent characteristic of millennial‐scale Dansgaard‐Oeschger oscillations. In a coupled climate model simulation which has accurately reproduced this oscillatory behavior for the first time, we show that formation of a glacial North Atlantic super polynya characterizes the initial stage of transition from cold stadial to warm interstadial conditions. The winter polynya forms within the otherwise sea ice‐covered North Atlantic as a consequence of the onset of a thermohaline convective instability beneath an extensive stadial sea ice lid. Early in the stadial period, the tendency for thermal convective instability of an extensive warm pool beneath the sea ice lid is strongly inhibited by a stabilizing vertical salinity gradient, which gradually diminishes until a thermohaline convective instability occurs that leads to polynya formation and the rapid retreat of North Atlantic sea ice cover.

Experimental investigation on effects of crystal and crucible rotation on thermal convection in a model Czochralski configuration

A series of experiments are presented to understand the effects of crystal and crucible rotations on the thermal convection in a model Czochralski (Cz) configuration which consists of a crucible filled with the transparent 0.65cSt silicone oil (Pr=6.7) and a model crystal. The thermal convection is induced by the temperature difference between the crucible sidewall and the crystal sidewall. The results show that the critical Rayleigh number for the onset of instability of thermal convection increases with the increase of the crystal rotation rate without the crucible rotation. When the crucible rotates, the critical Rayleigh number is higher than that with standing crucible at small crystal rotation rates. After the flow destabilizes, a three-dimensional oscillatory convection is characterized by traveling spoke patterns at small crystal rotation rates. With the increase of the crystal rotation rate, the azimuthal propagating velocity of the spoke pattern increases. Furthermore, the spoke pattern dims gradually and gives way to the wave pattern. The crystal rotation has a slight effect on the spoke number until the spoke pattern disappears. Compared with the shallow pool, the crystal rotation makes the flow more likely to be disturbed in the deeper pool. On the contrary, the crucible rotation is more conducive to suppressing the oscillatory flow in the deeper pool.