Vertical Fluid Layer Research Articles

Convection instability in a vertical porous Brinkman fluid layer with uniform horizontal throughflow

The present paper examines the effect of a uniform horizontal throughflow on the linear stability of buoyancy-driven convection in an infinite vertical fluid layer saturating a Brinkman porous medium. Two different constant temperature distributions are assigned on the rigid-permeable boundaries, so that there exists a horizontal temperature gradient. The resulting eigenvalue problem is solved numerically using the Chebyshev collocation method. The neutral stability curves are presented, and the critical values of the Rayleigh number are calculated for various prescribed values of the governing parameters. The onset of convection relies on several dimensionless parameter values of Darcy number Da, Péclet number Pe (it determines the strength of the horizontal throughflow), and Darcy-Prandtl number PrD. It is shown that there exists a critical value of the throughflow parameter Pe, which will increase with Da. Below the critical value of Pe, critical Rayleigh number Rac becomes smaller with the increase of Pe, which means the horizontal throughflow has a destabilizing effect. However, when Pe is larger than the critical value, an opposite conclusion can be drawn and the horizontal throughflow has a stabilizing effect. Moreover, the influence of the PrD on convection instability exhibits a dual behavior depending on Pe. The PrD stabilizes the system when Pe is small, and it destabilizes the system when Pe is large.

Convection instability of linear Oldroyd-B fluids in a vertical channel with non-Fourier heat flux model

Owing to the importance of non-Fourier heat flux model in several natural and engineering processes, the convection of binary viscoelastic fluid in a vertical channel with non-Fourier heat flux model is investigated. The linear Oldroyd-B constitutive equation is used to model viscoelasticity. The presence of the basic flow in the vertical y-direction makes the problem challenging compared with the case in Rayleigh–Bénard convection. We use the Chebyshev collocation method to explore the instability characteristics of the linear Oldroyd-B fluid under a wide variety of physical parameters. Results show that the non-Fourier effect and relaxation time contribute to destabilize the system for oscillatory convection. The retardation time can inhibit the instability of the convective system. In the absence of the non-Fourier effect, the vertical fluid layer cannot support oscillatory motions. Oscillatory motion is possible, and the neutral stability curve branches when the non-Fourier effect is taken into account in the fluid. In addition, a new interesting phenomenon can be found: under the coupling action of viscoelastic fluids and the non-Fourier effect, the neutral stability curve would change from single to two branches and then to a single branch with the increase in relaxation time.

Magnetic field influence on Casson fluid flow in rotating convection

The stability of buoyant flow in an infinite extended vertical fluid layer bounded by impermeable conducting isothermal rigid walls, known as magnetic field influence on Casson fluid flow in rotating convection, is investigated. A system of governing equations (Navier–Stokes, heat, and induction ones) is solved with isothermal rigid boundary conditions. When the majority of electrically conducting fluids are extremely small, the stability of governing equations can be simplified by taking the smallness of magnetic Prandtl number into account. In linear stability, the Chebyshev collocation method is used to solve numerically the system of eigenvalue problems. The Casson fluid parameter, Chandrasekhar number, magnetic Prandtl number, and Taylor number all have destabilizing effects on the system's basic velocity and basic magnetic field, resulting in instability. The critical Rayleigh number (Rc), critical wave number (ac), and critical wave speed (cc) are calculated using the influence of governing parameters. The Casson fluid parameter and magnetic Prandtl number were found to stabilize stationary disturbances in neutral stability curves.

Imperfectly conducting eigenflows in a vertical fluid layer

The stability of buoyant flow in an infinite vertical fluid layer bounded by imperfectly conducting rigid walls, called imperfectly conducting eigenflows, is discussed. The third kind boundary conditions describing heat transfer to the external environment are applied to perturbations in temperature. The linear stability analysis is carried out numerically by employing the Chebyshev collocation method. Instability arises when the Grashof number G exceeds its critical value, which depends on the Prandtl number Pr and the Biot number Bi. It is found that the onset of instability changes dramatically depending on the magnitude of Prandtl and Biot numbers particularly when the instability is through the traveling-wave mode. The numerical results show that the Biot number plays a pivotal role in determining the transition Prandtl number PrT at which the instability switches over from one mode to another mode. The novel outcomes suggest the presence of a single PrT for Bi<2.1739 while three distinct values of PrT for Bi≥2.1739. The departure from the conventional single value typically observed at isothermal boundaries signifies the complexity of the instability mechanism.

On the Stability of a Convective Flow with Nonlinear Heat Sources

The linear stability of a convective flow in a vertical fluid layer caused by nonlinear heat sources in the presence of cross-flow through the walls of the channel is investigated in this paper. This study is relevant to the analysis of factors that affect the effectiveness of biomass thermal conversion. The nonlinear problem for the base flow temperature is investigated in detail using the Krasnosel’skiĭ–Guo cone expansion/contraction theorem. It is shown that a different number of solutions can exist depending on the values of the parameters. Estimates for the norm of the solutions are obtained. The linear stability problem is solved numerically by a collocation method based on Chebyshev polynomials. It is shown that the increase in the cross-flow intensity stabilizes the flow, but there is also a small region of the radial Reynolds numbers where the flow is destabilized.

Stability of natural convection in a vertical layer of Navier-Stokes-Voigt fluid

The stability of natural convection in a vertical layer of viscoelastic fluid confining between rigid-isothermal side walls held at different temperatures is investigated numerically using the Chebyshev collocation method. The viscoelastic behavior is modelled by means of a constitutive equation encompassing the Navier-Stokes-Voigt fluid or the Kelvin-Voigt fluid of order zero. The onset of convective instability is examined by linearizing the governing equations for the perturbations and an appropriate extension of Squire's theorem is given making a case to consider only two-dimensional perturbation stability equations. The numerical solution of the stability eigenvalue problem leads to the determination of the neutral stability condition. The dependence of the Kelvin-Voigt parameter on the critical stability parameters and also on the Prandtl number at which the point of transition from stationary to travelling-wave mode occurs is thoroughly analysed. The Kelvin-Voigt parameter shows an important role on the travelling-wave mode instability where it inducts both stabilizing and destabilizing effects on the base flow depending on the values of Prandtl number, while its impact on the stationary mode is found to be very weak. Furthermore, the streamlines and isotherms of the perturbation modes presented herein demonstrate the development of complex dynamics at the critical state. The results of a Newtonian fluid are obtained as a particular case.

Stability of double-diffusive natural convection in a vertical fluid layer

The stability of basic buoyant flow in a vertical fluid layer induced by temperature and solute concentration differences between the vertical boundaries is investigated. The linear dynamics of the perturbed flow is formulated as an eigenvalue problem and solved numerically by employing the Chebyshev collocation method. The validity of Squire's theorem is proved, and therefore, two-dimensional motions are considered. The neutral stability curves defining the threshold of linear instability and the critical values of the thermal Grashof number and wave number at the onset of instability are determined for various values of the Prandtl number Pr, the solute Grashof number GS, and the Lewis number Le. The magnitude of the Prandtl number at which the transition from stationary to travelling-wave mode occurs can be either increased or decreased by tuning the values of GS and Le. For certain combinations of the parameters, there exist one or two closed disconnected travelling-wave neutral curves emphasizing the necessity of multiple thermal Grashof numbers to embark upon the stability of fluid flow, a result of contrast to that of the single-diffusive fluid layer. The mechanism of modal instability is deciphered by using the method of energy budget and four different modes of instability are identified, one of which is new and due entirely to the presence of solutal buoyancy.

On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for Thermotherapy

We consider the effect of gold nanoparticles on the stability properties of convection in a vertical fluid layer saturated by a Jeffreys fluid. The vertical boundaries are rigid and hold at uniform but different temperatures. Brownian diffusion and thermophoresis effects are considered. Due to numerous applications in the biomedical industry, such a study is essential. The linear stability is investigated through the normal mode disturbances. The resulting stability problem is an eighth-order ordinary differential complex eigenvalue problem that is solved numerically using the Chebyshev collection method. Its solution provides the neutral stability curves, defining the threshold of linear instability, and the critical parameters at the onset of instability are determined for various values of control parameters. The results for Newtonian fluid and second-grade fluid are delineated as particular cases from the present study. It is shown that the Newtonian fluid has a more stabilizing effect than the second-grade and the Jeffreys fluids in the presence of gold nanoparticles and, Jeffreys fluid is the least stable.

Instability of natural convection in a vertical fluid layer with net horizontal throughflow

The implication of a uniform horizontal throughflow on the linear stability of buoyancy-driven convection in a vertical fluid layer is studied. The vertical boundaries of the fluid layer are rigid-permeable and holding at uniform but different temperatures. The instability to small-amplitude perturbations is tested by parameterizing the basic stationary flow through the Peclet number and the Prandtl number (representative of liquid mercury, air, water and oil). A modal analysis is performed, and the stability eigenvalue problem is solved numerically using the Chebyshev collocation method. The neutral stability curves are presented, and the critical values of the wave number, wave speed as well as the Grashof number are computed for different prescribed values of the governing parameters. The effect of horizontal throughflow on the stability of fluid flow is found to be dependent on the values of Prandtl number, and their intricacies have been discussed in detail. The results for the case of no throughflow are also highlighted as a particular case from the present study.

Effects of flexible fin on natural convection in enclosure partially-filled with porous medium☆

A numerical study is conducted to analyze the effects of a flexible fin on unsteady convective flow in a square enclosure composed of a vertical fluid layer and a porous layer. The fin is attached to the heated left wall of the enclosure. The Brinkman-Forchheimer-extended Darcy flow model is assumed in the porous layer. The governing equations are written in the Arbitrary Lagrangian–Eulerian (ALE) formulation in the fluid and structure domains and then solved using the FEM. The result shows that the fin oscillation impacts the area below the fin rather than the area above the fin or the area in the center. The overall rate of heat transfer is improved as the Darcy number, the fluid layer thickness, and the fin elasticity increase. The overall rate of heat transfer increases exponentially with the rise of the oscillation amplitude. An oscillation amplitude of 0.1 could result in 3.4 percent improvement in the heat transfer rate.

Bicritical states in a vertical layer of fluid under two-frequency temperature modulation.

In this paper, the effect of two-frequency modulation of boundary temperatures on the onset of natural convection in a layer of fluid (with Prandtl number <12.5) between two vertical parallel planes is considered. The ratio of the two forcing frequencies and the mixing angle for the amplitude of modulation provide an efficient way of controlling the underlying instability. At the onset of instability, the fluid layer executes harmonic and subharmonic oscillations. The transition between harmonic and subharmonic responses is found to occur through an intermediate bicritical state. In addition to bicritical states, the instability is found to exhibit an almost tricritical state for a particular combination of the modulation parameters. The onset of the instability depends upon the modulation parameters and Prandtl number of the fluid.

Stability of mixed convection in a differentially heated vertical fluid layer with internal heat sources

The linear stability of mixed convection caused by a constant external pressure gradient, buoyancy force and a uniform internal heating in a vertical incompressible fluid layer whose vertical walls are kept at different constant temperatures is studied. The ensuing eigenvalue problem is solved numerically using the Chebyshev collocation method for two-dimensional motions after ensuring the validity of Squire’s theorem. The presence of internal heating introduces the point of inflection as well as reverse flow and increasing in its strength is found to amplify the back flow. The stability characteristics of the system are discussed for three values of Prandtl number representative of liquid mercury, water and oil. Multiple local minimum wave numbers are observed even in the presence of internal heating which facilitates instability of the system for all the values of Reynolds number and the Prandtl number considered. Additionally, the streamlines and isotherms of the perturbation modes are presented for different values of internal heat source strength, the Reynolds number and the Prandtl number. An energy budget analysis is embarked upon to understand the physical mechanisms involved in the flow transition.

Experimental and Numerical Analysis of Mixing Process of Two Component Gases in a Vertical Fluid Layer in a VHTR

When a depressurization accident of a very-high-temperature reactor (VHTR) occurs, air is expected to enter into the reactor pressure vessel from the breach and oxidize in-core graphite structures. Therefore, in order to predict or analyze the air ingress phenomena during a depressurization accident, it is important to develop a method for the prevention of air ingress during an accident. In particular, it is also important to examine the influence of localized natural convection and molecular diffusion on the mixing process from a safety viewpoint. Experiment and numerical analysis using a three-dimensional (3D) computational fluid dynamics code have been carried out to obtain the mixing process of two-component gases and the flow characteristics of localized natural convection. The numerical model consists of a storage tank and a reverse U-shaped vertical rectangular passage. One sidewall of the high-temperature side vertical passage is heated, and the other sidewall is cooled. The low-temperature vertical passage is cooled by ambient air. The storage tank is filled with heavy gas and the reverse U-shaped vertical passage is filled with a light gas. The result obtained from the 3D numerical analysis was in agreement with the experimental result quantitatively. The two component gases were mixed via molecular diffusion and natural convection. After some time elapsed, natural circulation occurred through the reverse U-shaped vertical passage. These flow characteristics are the same as those of phenomena generated in the passage between a permanent reflector and a pressure vessel wall of the VHTR.

Laminar-turbulent transitions at natural convection in flat and annular vertical fluid layers

The evolution of the local characteristics of natural convective boundary layers along the longitudinal coordinate is studied experimentally. The spatial forms of secondary flows in boundary layers on the walls of the plane and annular vertical liquid layer heated to different temperatures and in the core of the layers are studied. Hot walls are transparent, which allows video recording in two planes. In the regions of the laminar, transition, and turbulent boundary layer, local fields of velocity and temperature and local heat fluxes are measured.

Stability of temperature modulated convection in a vertical fluid layer

• Time-periodic modulation of boundary temperatures on natural convection is considered. • Floquet analysis of the basic flow is done leading to a generalized eigenvalue problem. • The numerical results are computed using MATLAB programming. • The instability appears in form of harmonic or subharmonic oscillations . • Transition between these oscillations occurs through a bicritical state. We investigate the effect of time periodic oscillations of the boundary temperatures on the onset of natural convection in a fluid layer bounded by two vertical planes. The fluids with Prandtl number up to 12.5 are considered. For these fluids, the mode of instability with constant temperature gradient is the steady convection mode. The parametric instability of the modulated fluid layer is found to appear either in the form of harmonic oscillations or in the form of subharmonic oscillations, depending upon the modulation parameters and the Prandtl number. The transition of the instability between harmonic and subharmonic oscillations occurs via an intermediate bicritical state in which the fluid layer oscillates with coexistence of distinct harmonic and subharmonic wave numbers. A proper tuning of the modulation parameters offers a good control over the mode of instability in the fluid layer.

Stability of natural convection in a vertical non-Newtonian fluid layer with an imposed magnetic field

A numerical study has been conducted to analyze the influence of a uniform horizontal magnetic field on the stability of buoyancy driven parallel shear flow in a differentially heated vertical layer of an electrically conducting couple stress fluid; a type of non-Newtonian fluid. Within the framework of linear stability theory, the resulting complex generalized eigenvalue problem is solved numerically using the Chebyshev collocation method with QZ algorithm. The critical Grashof number $$G_{c}$$ and the corresponding wave number $$\alpha_{c}$$ and wave speed $$c_{c}$$ are computed for a wide range of couple stress parameter $$\varLambda_{c}$$ , Prandtl number $$Pr$$ and Hartmann number $$M$$ . It is found that the value of $$Pr$$ at which the instability switches over from stationary to travelling-wave mode increases with increasing $$M$$ and decreasing $$\varLambda_{c}$$ . The effect of magnetic field is to delay the onset of instability while an opposite kind of behavior is observed with increasing $$\varLambda_{c}$$ . The streamlines presented herein demonstrate the development of complex dynamics at the transition mode.

Effect of Horizontal AC Electric Field on the Stability of Natural Convection in a Vertical Dielectric Fluid Layer

The stability of buoyancy-driven parallel shear flow of a dielectric fluid confined between differentially heated vertical plates is investigated under the influence of a uniform horizontal AC electric field. The resulting generalized eigenvalue problem is solved numerically using Chebyshev collocation method with wave speed as the eigenvalue. The critical Grashof number Gc, the critical wave number αc and the critical wave speed cc are computed for wide ranges of AC electric Rayleigh number Rea and the Prandtl number Pr. Based on these parameters, the stability characteristics of the system are discussed in detail. It is found that the AC electric Rayleigh number is to instill instability on convective flow against both stationary and travelling-wave mode disturbances. Nonetheless, the value of Prandtl number at which the transition from stationary to travelling-wave mode takes place is found to be independent of AC electric Rayleigh number. The streamlines and isotherms presented demonstrate the development of complex dynamics at the critical state.

鉛直流体層内の2成分気体混合過程に関する研究

The purpose of this study is to investigate the effect of natural convection and molecular diffusion on the mixing process under the stable density stratified fluid layer of two component gas. An experiment has been carried out to investigate a control method of natural circulation of air by injection of helium gas. The experimental apparatus consists of a reverse U-sharped vertical slot and a storage tank. The left side vertical slot consists of the heated wall and cooled wall. The right side vertical slot does not insert anything. Experimental results regarding mixing process of two component gases in vertical fluid layer were as follows. The heavy gas was transported to the slot by the molecular diffusion and natural convection. As time elapses, natural circulation of heavy gas suddenly occurs through the reverse U-shaped slot. As a result of experiments, the onset time of natural circulation is affected by not only molecular diffusion coefficient but also the strength of natural convection. When the helium gas is injected into the channel, it is possible to control the natural circulation of air. The onset time of the reproduction of the natural circulation can be varied by changing the injection rate of the helium gas.

The influence of an oblique magnetic field on convection in a vertical layer of magnetic fluid

The influence of an oblique magnetic field on convection in a vertical layer of magnetic fluid

The influence of an oblique magnetic field on convection in a vertical layer of magnetic fluid

The influence of an oblique magnetic field on convection in a vertical layer of magnetic fluid