Inclined Fluid Layer Research Articles

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

Thermal instability in an inclined fluid layer subjected to Couette–Poiseuille flow

The present work deals with the onset of thermal instability in an inclined fluid layer subjected to Couette–Poiseuille flow. We consider the configuration in which one boundary is maintained at a constant temperature and the other boundary is imposed with a constant heat flux. The collocation method, based on Chebyshev polynomials, is used to discuss the instability of the flow with respect to the thermal Rayleigh number. It is found that there exists a value of the angle of inclination below which the instability sets in as longitudinal rolls, and the critical value of the Rayleigh number remains unaffected by superimposed Couette–Poiseuille flow. However, for angles of inclination greater than this threshold value, the critical mode of instability is transverse mode, and the critical value of the Rayleigh number is significantly affected by the superposition of Couette–Poiseuille flow. Further, the onset of instability also depends upon the Prandtl number of the fluid.

Energy stability of thermally modulated inclined fluid layer

The stability of natural convection in thermally modulated inclined fluid layer is analyzed using linear instability analysis and generalized energy stability theory. A sufficient condition for the global stability of the fluid layer is obtained. The stability boundaries are found in terms of the Rayleigh number. Shooting method is used to find the stability limits numerically. Uncertain stability region is observed between the linear and the nonlinear stability boundaries. The onset of instability depends upon the frequency and the amplitude of modulation.

Global stability of natural convection in internally heated inclined fluid layer

Energy stability theory is applied to the study of the nonlinear stability of natural convection in an inclined fluid layer having a uniform internal heat source (sink), with the boundaries of the layer maintained at constant temperatures. The stability limit is found in terms of the thermal Rayleigh number $$R_{1}$$ and the internal Rayleigh number $$R_{2}$$ . The region of stability is found in $$R_{1}$$ – $$R_{2}$$ plane where the base state is stable against arbitrary perturbations. The Prandtl number Pr of the fluid and the angle of inclination of the fluid layer play an important role in determining the stability region.

Stability of transient natural convection in impulsively heated inclined fluid layer

The stability of the transient state of convection in an inclined fluid layer on heating one of the boundaries impulsively has been discussed. The closed form time dependent basic solutions for the velocity and the temperature are obtained. The non-linear stability of the transient state is investigated by using the energy method. The stability limit for the Rayleigh number Ra is found at different times. The competition between the buoyancy and the shear forces determines a value of the angle of inclination corresponding to which the layer is the least stable. The effect of the Prandtl number Pr on the stability boundary is investigated.

Nonlinear Stability of Natural Convection in an Inclined Fluid Layer

A nonlinear stability analysis of convection in an inclined layer of a viscous, incompressible fluid is carried out using energy method. The nonlinear stability boundary determined by the Rayleigh number $$\text {Ra}$$ for the underlying dynamical system is found to depend upon the inclination of the layer with respect to the horizontal and Prandtl number of the fluid. A comparison with the linear instability boundary for the considered hydrodynamic system indicates a parametric region where the nonlinear stability of the basic flow is uncertain.

Áp dụng hệ Navier-Stokes trong nghiên cứu ảnh hưởng của từ trường lên sự đối lưu nhiệt của dung dịch sắt từ

This study is devoted to evaluating the effect of magnetic field on thermoconvection in a layer of ferrofluids. The linear and weakly nonlinear flow stability analyses that are presented here illustrate an intricate interplay between thermogravitational and thermomagnetic mechanisms of convection in one of the practically important geometrical setups, an inclined fluid layer heated from below. The low-dimensional amplitude evolution equations of Landau type are derived to model the physical phenomena of interest. The solutions of the so-obtained dynamical system show that the application of magnetic field can indeed trigger convection in regimes where natural convection cannot exist, thus enhancing heat transfer.

The influence of magnetic field on convection in an inclined ferrofluid layer heated from below

Ferrofluids are strongly magneto-polarisable nanofluids. Their flows can be non-intrusively controlled by applying an external magnetic field. One of their prospective applications is as a heat carrier in thermal management systems operating in conditions where natural convection is suppressed due to extreme confinement (microelectronics) or reduced gravity (orbital stations). The linear and weakly nonlinear flow stability analyses that are presented here illustrate an intricate interplay between thermogravitational and thermomagnetic mechanisms of convection in one of the practically important geometrical setups, an inclined fluid layer heated from below. The low-dimensional amplitude evolution equations of Landau type are derived to model the physical phenomena of interest. The solutions of the so-obtained dynamical system show that the application of magnetic field can indeed trigger convection in regimes where natural convection cannot exist, thus enhancing heat transfer. At the same time in regimes where both magnetic and gravitational buoyancy mechanisms are active the competition between the two may suppress the overall heat exchange, which has to be kept in mind in designing practical heat management systems.

Long-wave instability of an advective flow in an inclined fluid layer with perfectly heat-conducting boundaries

We investigate the stability of the steady convective flow in a plane tilted layer with ideal thermal conductivity of solid boundaries in the presence of uniform longitudinal temperature gradient. Analytically found the stability boundary with respect to the long-wave perturbations, find the critical Grashof number for the most dangerous among them of even spiral perturbation.

Two-Dimensional Thermal Convection in a Parallelogram-Shaped Cavity with Inclined Sidewalls

The effect of inclination of sidewalls on two-dimensional thermal convection of a fluid in a parallelogram-shaped cavity is investigated under the assumption that all walls are rigid, with perfect thermal conductance and with a vertically linear temperature profile connecting the temperatures on the horizontal top and bottom walls. The critical Rayleigh number R c , at which a motionless state becomes unstable, is calculated numerically for several values of inclination angle φ of sidewalls from the vertical direction and aspect ratio A . As φ increases from 0, the increase in R c and the exchange of most unstable eigenmode are observed for all A satisfying 0.3≤ A ≤3. Moreover, we find numerically that two steady convection states bifurcating from the motionless state at R c become unstable at different Rayleigh numbers for non-zero φ. Furthermore, the stability of the motionless state in an inclined fluid layer of infinite length is examined along with its relevance to stability in a parallelogram-shaped...

Vibrational Convection in an Inclined Fluid Layer Heated from Below

The stability of mechanical equilibrium of an inclined fluid layer with respect to three-dimensional perturbations under the action of high-frequency vibration is studied. It is shown that under heating from below the spiral perturbations are always the most dangerous for vibration transverse to the layer. For vertical vibration the stability limit is determined by three-dimensional perturbations whose shape depends in a complicated way on the angle of inclination of the layer and the vibrational Rayleigh number. In the limiting case of a thin vertical layer supercritical vibrational-convective motions are calculated numerically and analytically and scenarios of transition from quasi-equilibrium to irregular motions are studied.

Defect turbulence and generalized statistical mechanics

We present experimental evidence that the motion of point defects in thermal convection patterns in an inclined fluid layer is well described by Tsallis statistics with an entropic index q≈1.5. The dynamical properties of the defects (anomalous diffusion, shape of velocity distributions, power-law decay of correlations) are in good agreement with typical predictions of nonextensive models, over a range of driving parameters.

Statistics of defect motion in spatiotemporal chaos in inclined layer convection.

We report experiments on defect-tracking in the state of undulation chaos observed in thermal convection of an inclined fluid layer. We characterize the ensemble of defect trajectories according to their velocities, relative positions, diffusion, and gain and loss rates. In particular, the defects exhibit incidents of rapid transverse motion which result in power law distributions for a number of quantitative measures. We examine connections between this behavior and Levy flights and anomalous diffusion. In addition, we describe time-reversal and system size invariance for defect creation and annihilation rates.

Bursts in inclined layer convection

A new instability of longitudinal rolls in an inclined fluid layer heated from below is analyzed in the case of the Prandtl number P=0.71. The instability assumes the form of subharmonic undulations and evolves into a spatially chaotic pattern when the angle of inclination is of the order of 20°. The chaotic state rapidly decays and longitudinal rolls recover until the next burst of chaotic convection occurs. The theoretical findings closely correspond to recent experimental observations by Daniels et al. [Phys. Rev. Lett. (to be published)].

Hysterisis effect on thermosolutal convection with opposed buoyancy forces in inclined enclosures

The onset of double diffusive convective flows in an inclined fluid layer, when constant fluxes of heat and mass are applied on the two oposing boundaries of the layer, is investigated. The case of equal and opposing buoyancy forces is considered. A numerical linear stability theory is used to determine the critical Rayleigh number for the onset of convection. The existence of a subcritical Rayleigh number, for the onset of finite amplitude convection, is demonstrated on the basis of the parallel flow approximation.

Thermovibrational convective instability of mechanical equilibrium of an inclined fluid layer

The convective instability of mechanical equilibrium of an inclined plane layer of fluid developing under the action of a static gravity field and high-frequency vibration is studied. Configurations corresponding to four directions of the equilibrium temperature gradient — vertical, longitudinal, horizontal, and transverse — are considered for an arbitrary orientation of the vibration axis. The stability limits and the characteristics of the critical perturbations are determined.

The stability of natural convection in an inclined fluid layer in the presence of a temperature gradient and an a.c. electric field

Linear stability theory is applied to examine the effect of a normal a.c. electric field on the stability of the natural convection that occurs in a dielectric fluid layer between two inclined plates that are maintained at different temperatures. The power-series method is used to obtain the eigenvalue equation which is then solved numerically to obtain the stable and unstable solutions. Factors affecting the stability are discussed.

The stability of natural convection in an inclined fluid layer in the presence of a temperature gradient and an a.c. electric field

The stability of natural convection in an inclined fluid layer in the presence of a temperature gradient and an a.c. electric field

The Stability of Natural Convection in an Inclined Fluid Layer in the Presence of AC Electric Field

Linear stability theory is applied to the problem of the natural convection that occurs in an inclined fluid layer with uniformly distributed internal heat sources and subjected to the action of a normal ac electric field. It is assumed that the two plates between which the fluid layer is confined are maintained at constant and equal temperature. Both the dielectric constant and density of the fluid are assumed to be functions of temperature. The power series method is used to obtain the eigenvalue equation which is then solved numerically to obtain the stable and unstable solutions.

Mechanical quasi-equilibrium and thermovibrational convective instability in an inclined fluid layer

The linear stability of mechanical quasi-equilibrium of a long inclined plane fluid layer, in the presence of a constant temperature gradient, subject to a static gravity field and high frequency vibration is investigated theoretically. The layer is oriented in an arbitrary respect to the vertical. The boundaries of the layer are assumed to be rigid and highly conducting. Each of two vectors-the temperature gradient and the axis of vibration-can have one of the four orientations: vertical ( v), longitudinal ( l), horizontal ( h), and transversal ( t). Thus a total of sixteen situations are studied. The consideration is based on the equations system describing mean (averaged) fields in the frame of an averaging method. The possibility and necessary conditions of mechanical quasi-equilibrium existance are studied. The spectral amplitude problem for small two-dimensional normal disturbances is formulated. In the case of long-wave instability, the spectral problem is solved asymptotically using the wave number as a small parameter for expansion. In the case of an arbitrary value of wave number, the spectral problem is solved numerically. The boundaries of stability and critical disturbance characteristics are determined for all the sixteen cases mentioned before.