Convection In Fluid Layer Research Articles

Onset of double diffusive surface-tension driven convection in fluid layer overlying a layer of anisotropic porous layer with soret effect

The onset of double-diffusive surface tension-driven convective motion in a fluid layer overlying a fluid-saturated anisotropic porous layer is investigated analytically in the presence of the soret effect. We considered boundaries to be insulating to temperature perturbations. The governing equation that satisfies the composite system is analyzed by the normal mode approach and solved by the regular perturbation technique for linear stability. By solving coupled equations, a mathematical expression for the critical Marangoni number is obtained. Under the effect of the anisotropy, soret parameters and the impact of various physical parameters on the start of convective motion is illustrated graphically, and the stability system is investigated.

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.

Conditional and unconditional stability for double diffusive convection when the viscosity has a maximum

We here analyse two models of double-diffusive convection in fluid layer when viscosity depends on temperature quadratically. However, to a linearized instability analysis, conditional and global (unconditional) nonlinear stability theories are applied. For the first model, we establish an unconditional nonlinear energy stability. Moreover, in the second model the standard energy method does not yield unconditional stability so a conditional energy analysis is employed to achieve nonlinear results. In addition, the nonlinear stability bounds is found to be independent of the salt field and a presentation of the region of possible subcritical instabilities is given.

Control of Rayleigh-Bénard Convection in a Fluid Layer with Internal Heat Generation

The control of the onset of convection in a horizontal fluid layer with internal heat generation is studied. The horizontal boundaries of the system are cooled isothermally. The stability of the fluid layer is investigated on the basis of the linear stability theory and the resulting eigenvalues problem is solved numerically. Upon using a feedback proportional control, the heating power of the system is modulated in order to counteract any deviations of the temperature of the fluid from its conductive value. As a result, it is possible to postpone (or advance) significantly the onset of motion. The optimal positions of the thermal sensors can be predicted on the basis of the linear stability theory. The linear stability analysis also reveals the possible existence of Hopf’s bifurcations at the onset of motion. This type of bifurcation can be delayed using differential controllers. Two-dimensional numerical simulations of the full governing equations are carried out and found to agree well with the prediction of the linear stability theory.

Heat and mass transfer driven by stratified viscosity and thermal diffusion

The transfer of heat and mass by convection in fluid layers is a challenging task as it can be driven by different factors. In the present paper the coupled action of viscosity and thermal diffusivity, both stratified, is investigated. The thermal conduction steady state is found and it is shown that: (1) steady convection occurs; (2) linear stability guarantees nonlinear asymptotic exponential energy stability and global attractivity.

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 analysis for penetrative convection in a fluid layer with throughflow

The problem of penetrative convection in fluid layer with vertical throughflow effect is studied by using methods of linear instability theory and unconditional and conditional nonlinear energy theories. Then, the accuracy of the linear instability thresholds are tested using a three-dimensional simulation. For small values of throughflow, the results support the assertion that the linear theory is a good prediction to the onset of convective motion, and thus, regions of stability. However, for large values of throughflow, we found that the actual threshold move from the linear instability threshold with increasing the positive and negative effect of throughflow.

Penetrative Marangoni Convection in Fluid Layer with Soret Effect

Penetrative Marangoni Convection in Fluid Layer with Soret Effect

Effects of a magnetic field on chaotic convection in fluid layer heated from below

Features of nonlinear dynamics of thermal convection in an electrically conducting fluid layer heated from below and cooled from above subjected to a constant magnetic field are studied theoretically. The Galerkin truncated approximation is employed to derive a low dimensional Lorenz-like model. Numerical analysis was performed to examine the influence of magnetic field on the phase space trajectory of various chaotic regimes. The result indicates that it is possible to suppress or enhance the chaotic convection.

CORRELATION METHODS OF RAYLEIGH-BÉNARD CONVECTION IN A FLUID LAYER WITH PHASE CHANGE MATERIAL PARTICLES

Two new methods for correlating experimental data of Rayleigh-Bénard convection in a fluid layer dispersed with phase-change-material particles have been proposed. Instead of the conventional arithmetic mean temperature method, two new methods for evaluating the intensity of convection in a horizontal fluid layer with strongly temperature-dependent specific heat were given. One method is by introducing a modified Stefan number in a Nu-Ra correlation or using the integrally averaged specific heat across the layer for calculating the Rayleigh number. The other method is by using the supercriticality (Ra/Rac) as an intensity parameter, in which the critical Rayleigh number Rac can be calculated by using the linear stability theory. Two models of non-dimensionalized apparent specific heat functions with respect to temperature were introduced. Results show that the two proposed methods are more rational comparing with the convectional 1/2-height rule method.

The onset of buoyancy-driven convection in fluid layers with temperature-dependent viscosity

A theoretical analysis of thermal instability driven by buoyancy forces under a time-dependent temperature field of conduction is conducted in an initially quiescent, horizontal liquid layer. The dependency of viscosity on temperature is considered and the propagation theory is employed for the stability analysis. For large Prandtl number systems, the critical condition of the onset of buoyancy-driven convection is obtained as a function of the Rayleigh number and also the viscosity contrast and it is compared with available experimental data. It is evident that the growth period is required until the growing instabilities are detected experimentally, which is dependent upon the viscosity contrast.

Effects of throughflow and internal heat generation on the onset of convection in a fluid layer

The throughflow and internal heat generation effects on the onset of convection in an infinite horizontal fluid layer are investigated. The boundaries are considered to be rigid (however permeable) and perfectly conducting. The resulting eigenvalue problem is solved by using the Galerkin method, and the effects of various parameters in the stability results are analyzed. The results indicate that the stability of the system is significantly affected by both throughflow and internal heat generation in the fluid layer. The Prandtl number comes into play due to the presence of throughflow and it has a profound effect on the stability of the system. It is found that, in the presence of internal heating, throughflow in one direction supresses convection while throughflow in the other direction encourages it.

Phase and amplitude instabilities for Bénard-Marangoni convection in fluid layers with large aspect ratio.

Pattern formation in fluids heated from below is examined in the presence of a free flat surface. On that surface, the Marangoni effect is taken into account as a second instability mechanism. It is shown that phase instabilities already known from Rayleigh-B\'enard convection confine the region of stable hexagons and shrink the band of stable wavelengths considerably. The problem is attacked from two sides: amplitude equations are derived explicitly from the basic hydrodynamic equations and are analyzed with regard to secondary instabilities. This results in stability diagrams analogous to earlier calculations obtained for parallel rolls in simple Rayleigh-B\'enard convection. On the other hand, we developed a numerical scheme that allows for a direct integration of the fully-three-dimensional hydrodynamic equations. This method is described in detail and time series for pattern evolution are presented, showing phase and amplitude instabilities as expected from the formalism of amplitude equations. Finally we show the connection between amplitude equations and two-dimensional generalized Ginzburg-Landau equations. These models may reproduce pattern formation near convective threshold in a quantitative way. They have the advantage of being more general than the basic equations and they can be treated numerically in a much easier way. This allows the computation of pattern evolution in very-large-aspect-ratio systems.

Two-dimensional convection in a horizontal fluid layer with spatially periodic boundary temperatures

Two-dimensional thermal convection in a fluid layer confined between two horizontal rigid walls kept at spatially periodic temperatures is investigated by direct numerical simulations. With increasing the Rayleigh number, convection evolves from a steady state to a temporally chaotic flow. It is observed that the transition to the chaos occurs via quasi-periodic states with two or three basic frequencies or via sequences of period-doubling bifurcations, according to the boundary temperature distributions.

Penetrative convection in fluid layers with internal heat sources

The stability problem for penetrative convection in a fluid layer that is heated internally is analyzed using the methods of linear instability theory and unconditional nonlinear energy theory. Critical Rayleigh numbers in the case of a constant heat source are determined numerically from both theories. Although it is not known whether exchange of stabilities holds for this problem, a comparison between the linear and nonlinear results suggests that for top temperatures close to 4°C stationary convection is predominant when the heat source is not too large. The nonlinear results delimit a band of Rayleigh numbers where possible subcritical instabilities could arise.

Numerical modeling of thermocapillary convection in a fluid layer with local heating of the free surface

Thermocapillary convection in a plane horizontal fluid layer with concentrated heating of the free surface is modeled numerically using the Navier-Stokes equations and the heat transport equation. This makes it possible to examine the structure of the convection throughout the fluid volume, in particular in the region where the motion is weak. The deformation of the free surface is assumed to be negligibly small. In the case of a ponderable fluid this assumption is justified given certain upper and lower constraints on the temperature difference and the thickness of the layer, respectively, [9, 10]. Under conditions of weightlessness a fluid layer of constant thickness in a rectangular channel can be realized at a contact angle of 90° [7].

The onset of convection in fluid layers heated rapidly in a time-dependent manner

We treat the onset of convective motions for the case in which the base-state density profile is evolving in time. The formulation is in terms of random forcing which we take to be thermodynamic in origin, following our earlier work (see Jhaveri & Homsy 1980). Experimental evidence is reviewed which clearly demonstrates the need for such a stochastic formulation. The randomly forced initial-value problem is solved numerically at high Rayleigh numbers in the mean-field approximation for both a step change and linear temporal increase in surface temperature. The numerical results give both an expected value for the onset time for which convection is measurable and the variance of that expected value. The results are in good agreement with available experiments.

Onset of Convection in Fluid Layers with Non-uniform Volumetric Energy Sources

The thermal stability of a fluid layer with non-uniform distribution of the volumetric energy sources is studied. The conditions leading to the onset of convective motions in the fluid are determined analytically by linear stability theory. The system considered consists of a fluid layer of infinite horizontal extent which is confined between two rigid parallel boundaries and subjected to general convective boundary conditions. The fluid is heated internally by way of absorption of the external radiation penetrating in the fluid body. The effects of the stabilizing and destabilizing temperature differences at the boundaries and the properties of the bounding surfaces are investigated. Optically thicker layers are found to be more stable.

Instability and convection in fluid layers: A report on Euromech 106

The 106th Euromech Colloquium on instability and convection driven by body forces in fluid layers was held in Grenoble from 11 to 14 September 1978 with the first two authors acting as chairmen. There were sixty-five participants coming from fifteen different countries and having widely different backgrounds. Fifty-seven papers were presented during the four full days of the meeting and are discussed in this report with the purpose of giving an up-to-date view of current research in convection.

On the interaction of two scales of convection in the mantle

A system in which convection takes place in the upper mantle on two distinct horizontal length scales is proposed. This is consistent with the existence of the plates themselves, the relatively constant heat flux background in older ocean basins, and the knowledge of convection in fluid layers gained from laboratory and numerical experiments. The large-scale circulation consists of the plates themselves and the return flow necessary to conserve mass. The small-scale flow, analogous to Rayleigh-Benard convection or variants of this, which have been the main target of numerical study, provides the necessary vertical heat transport in the upper mantle that supplies the required heat flux at the base of the lithosphere. The depth of convection is taken to be down to the 650-km seismic discontinuity, and this depth characterizes the horizontal length scale of the small-scale convection. This system is studied by means of a set of laboratory experiments that explore the interaction of the small-scale convection with the large-scale flow. The experiments show the plausibility of convection on two scales. Furthermore, they suggest that beneath fast-moving plates (absolute velocities around 10 cm y−1) the small-scale convection will align itself as rolls in the direction of the large-scale flow in geologically short times. However, beneath very slow moving plates the times required for the alignment of convective rolls are long in comparison with times over which no changes in plate motions are to be expected. Here the convective planform is more likely to take the form of upwelling and downwelling spouts. Thus this simple system of a convecting layer beneath a moving boundary contains the possibility of explaining a wide variety of surface features. Observational tests of the consequences of the two-scale idea are suggested, and the assumptions on which this idea is based are critically discussed.