Onset Of Rayleigh-Benard Convection Research Articles

Onset of Rayleigh-Benard Convection with Periodic Boundary Temperatures Using Weakly Nonlinear Theory

This paper investigates the Rayleigh Benard instability of a viscous, Newtonian, Boussinesq fluid with time-periodic boundary temperature modulation using the framework of weakly nonlinear theory. Critical Rayleigh number is computed for asymptotic stability criterion using the energy method accompanied by variational algorithm. Subcritical instability is found to occur under two conditions: when modulation is in anti-phase and when modulation is imposed only on the lower boundary. Supercritical stability is witnessed during in-phase modulation. In all the three cases of the relative phase of two boundary temperatures, the effect of modulation is found to be weaker for infinitesimal disturbances. The findings of the present study could be referred in several applications where appropriate temperature modulation is of prime concern.

Bursting dynamics in Rayleigh-Bénard convection

We report bursting dynamics in a parametrically driven Rayleigh-Benard convection (RBC) model of low Prandtl-number fluids with free-slip boundary conditions. A four dimensional RBC model [P. Pal, K. Kumar, P. Maity, S.K. Dana, Phys. Rev. E 87, 023001 (2013)] is used for this study. The dynamical system shows pitchfork, Hopf and gluing bifurcations near the onset of RBC of low Prandtl-number fluids. Around the bifurcation points, when the Rayleigh number of the system is slowly modulated periodically, two unknown kinds of bursting appears, namely, Hopf/Hopf via pitchfork bifurcation and Hopf/Hopf via gluing bifurcation besides the conventional Hopf/Hopf (elliptical) and pitchfork/pitchfork bursting.

Linear stability analysis of Rayleigh-Bénard convection of cold water near its density maximum in a vertically heated annular container

In order to understand the onset of Rayleigh-Benard convection of cold water near its density maximum in a vertical annular container heated from below and cooled from above, the instability of the static diffusive state was investigated by linear stability analysis. Two kinds of thermal boundary conditions, perfect insulating and conducting sidewalls, were used. The aspect ratio and radius ratio of the annular container varied from 0.5 to 4.5 and 0.1 to 0.8, respectively. Results indicate that the critical Rayleigh number and the critical wave number increase with the increase of density inversion parameter. There are some new flow modes with large azimuthal wave number near the convection onset for cold water with density maximum, which are not observed in Rayleigh-Benard convection of the Boussinesq fluids. The stratified flow phenomenon in cold water with density maximum is certified. The larger the density inversion parameter is, the more obvious the stratified flow phenomenon becomes. With the increase of the aspect ratio, the critical Rayleigh number decreases, but the critical wave number increases. However, with the increase of the radius ratio, both the critical Rayleigh number and the critical wave number increase continuously. Furthermore, the effect of thermal boundary conditions at the sidewalls on the convection stability is also validated.

Effects of Gravity Modulation and Internal Heat Generation on the onset of Rayleigh-Benard convection in a Micropolar Fluid

The effect of gravity modulation (time periodic body force or g-jitter) on the onset of Rayleigh-Bénard convection in a micropolar fluid with internal heat generation is investigated by making a linear stability analysis. The stability of a horizontal layer of fluid heated from below is examined by assuming time periodic body force in the presence of internal heat source. A regular perturbation method is used to arrive at an expression to compute the critical Rayleigh number for small amplitude of modulation and dimensionless internal heat source. The Venezian approach is adopted to obtain the eigen value of the problem. The results obtained during the analysis have been presented graphically.

Implications of the Marangoni effect on the onset of Rayleigh–Benard convection in a two-layer system with a deformable interface

The paper deals with the investigation of the implications of the Marangoni effect on the onset of Rayleigh-Benard convection in a two-layer system with deformable fluid interface. The study of the conductive state stability to the longwave perturbations shows that in the case of heating from above the thermocapillary effect leads to the increase of instability domain to the monotonic longwave perturbations. In the case of heating from below, the thermocapillarity makes stabilizing effect on the longwave perturbations and at some values of the parameters the configuration where more dense fluid is located above less dense one turns out to be stable. However, the analysis of the perturbations with finite wavelength in the presence of thermocapillary effect shows that in the case of heating from below the Rayleigh-Taylor instability is not suppressed. For any values of the parameters the perturbations with finite wavelength turn out to be more dangerous. In this situation the instability domain becomes wider with the increase of the Marangoni number modulus. In the case of heating from above, for any values of the Marangoni number, at the Rayleigh numbers small in the modulus, long-wave monotonic perturbations are most dangerous whereas at the Rayleigh numbers large in the modulus, the most dangerous mode is cellular monotonic instability.

Effect of imposed time-periodic boundary temperature on on the onset of rayleigh-benard convection in a dielectric couple stress fluid

The effect of imposed time-periodic boundary temperature of small amplitude on electroconvection under AC electric field in dielectric couple stress liquids is investigated by making a linear stability analysis. A regular perturbation method is used to arrive at an expression for the correction Rayleigh number that throws light on the possibility of sub-critical motions. The Venezian approach is adopted for obtaining eigen value of the problem. Three cases of oscillating temperature field are examined: (a) symmetric, so that the wall temperatures are modulated in phase, (b) asymmetric, corresponding to out-of phase modulation and (c) only the lower wall is modulated. It is shown that the system is most stable when the boundary temperatures are modulated out-of-phase.

On Rayleigh Bènard Convection with Porous Boundaries

In this paper, we utilize a combination of analytical and computational techniques to study the onset of Rayleigh Benard convection in a horizontal layer of fluid heated from below. It is established mathematically that the principle of exchange of stabilities is valid. The characteristic value problem is solved and results are computed numerically for a wide range of values of the boundary parameters characterizing the nature of porous boundaries. Under a situation where in the value of the parameter characterizing the nature of the permeability of the upper boundary varies inversely to the value of parameter that characterize the nature of the lower boundary, we find a specific range of values of the permeability parameter of the lower boundary in which the increasing values of this parameter has destabilizing effect. In addition, existing results are obtained as the limiting cases of the boundary parameters, namely when both the bounding surfaces are either dynamically free or rigid, and either one of them is dynamically free while the other one is rigid.

Effects of Internal Heat Generation and Variable Viscosity on Onset of Rayleigh-Benard Convection

In the present study, onset of stationary Rayleigh-Benard convective instability in a fluid layer, with internal heating and thermally dependent viscosity has been investigated by means of linear stability analysis. The dependence of viscosity is assumed to be exponential. The resulting eigen value problem is solved using a regular perturbation technique with wave number a as a perturbation parameter. The viscosity parameter and the presence of internal heat source play a decisive role on the stability characteristics of the system. It is observed that both stabilizing and destabilizing factors can be enhanced because of the simultaneous presence of a volumetric heat source and variable viscosity so that a more precise control (suppress or augment) of thermal convective instability in a fluid layer is possible.

Effect of Non-Uniform Temperature Gradient on the Onset of Rayleigh-Bénard Electro Convection in a Micropolar Fluid

The effects of electric field and non-uniform basic temperature gradient on the onset of Rayleigh-Benard convection in a micropolar fluid are studied using the Galerkin technique. The eigenvalues are obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations and for isothermal and/or adiabatic temperature boundaries. The microrotation is assumed to vanish at the boundaries. A linear stability analysis is performed. The influence of various micropolar fluid parameters and electric Rayleigh number on the onset of convection has been analyzed. One linear and five non-uniform temperature profiles are considered and their comparative influence on onset is discussed.

The Effects of Radiation on the Linear Stability of a horizontal layer in a Fluidsaturated Media heated from below

The effect of radiation on the onset of Rayleigh-Benard convection is studied in the case of a radiating Newtonian fluid in a fluid-saturated horizontal porous layer heated from below. The radiative heattransfer is treated using the differential approximation for optically thin limiting case. The linear stability theory is employed to predict the onset of buoyancy-driven convective motion. It is seen that neither radiation on thestatic temperature nor on the disturbances can be neglected. In addition, radiation delayed the onset of instability, and higher radiation values led to greater stabilization of a gravity-driven flow in a fluid-saturated porous medium heated from below

Effect of Second Sound on the Onset of Rayleigh-Benard Convection in a Coleman - Noll Fluid

This paper deals with linear stability analysis of the effects resulting from the substitution of the classical Fourier law by the non-classical Maxwell - Cattaneo law in Rayleigh - Benard convection in second order fluid is studies. Coleman-Noll constitutive equaion is used to give a viscoelastic correction. The eigenvalue is obtained for free - free isothernal boundary combination. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical eigenvalues are less than the classical ones.

Effects of Magnetic Field and Non-uniform Basic Temperature Gradient on the Onset of Rayleigh-Benard Convection in a Micropolar Fluid

The effects of magnetic field and non-uniform basic temperature gradient on the onset of Rayleigh-Benard convection in an electrically conducting micro polar fluid are studied using the Garlerkin technique. The eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal and adiabatic temperature conditions on the spin-vanishing boundaries. The eigenvalues are also obtained for lower rigid isothermal and upper free adiabatic boundaries with vanishing spin. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the electrically conducting fluid layer with suspended particles heated from below is more stable compared to the classically electrically conducting fluid without suspended particles. The critical wave number is found to be insensitive to the changes in the parameters but sensitive to the changes in the Chandrasekhar number.

Atomistic simulation of heat and mass transfer near the convection threshold.

The detailed behavior at the onset of Rayleigh-Benard convection is examined using molecular-dynamics simulation of a hard-disk fluid in which the vertical temperature difference is increased gradually. The dependence of thermal flux and mass transfer rate on Rayleigh number just above onset is shown to be consistent with the assumption that the convective bifurcation is the analog of a second-order phase transition

Critical Rayleigh numbers for cryogenic experiments

We give critical Rayleigh numbers, Rc, and the corresponding critical wavevectors, ac, for the onset of Rayleigh-Benard convection for thermal conditions on the horizontal boundaries that model physical experiments, particularly those carried out at low temperatures with liquid helium. We assume that a fluid layer, satisfying the Boussinesq approximation, is bounded above and below by rigid plates with finite, nonzero vertical thicknesses and finite thermal conductivities. The effect of sidewalls on Rc is not likely to be important for many experiments and so is not considered here; specifically, we assume a horizontally infinite layer. At the top of the top plate and the bottom of the bottom plate, we consider boundary conditions for which a linear combination of the convective temperature field and its vertical derivative vanishes. For these boundary conditions, the growth rates of the linear stability problem are necessarily real. We find that Rc only deviates significantly from 1708 and ac only deviates significantly from 3.11, when the thermal conductivity of the fluid is comparable to or larger than that of the boundaries, or when the plates are exceptionally thin. In particular a fixed heat flux applied to highly conducting plates (a configuration frequently used in cryogenic experiments) does not cause Rc to vary much from the standard value, 1708.

Mean flows and the onset of chaos in large-cell convection.

Numerical simulations of two-dimensional model equations show that a coupling between amplitude and vertical-vorticity fields allows chaotic flows near the onset of Rayleigh-Benard convection in large-aspect-ratio domains. In cylindrical cells, mean flows arising from this coupling lead to a chaotic nucleation of dislocations that is remarkably similar to recent observations in convection experiments.

Precise measurements of the wavelength at the onset of Rayleigh-Benard convection in a long rectangular duct

WHEN a fluid layer is heated uniformly from below, the state of rest becomes unstable when the critical Rayleigh number Ra” (the non-dimensional temperature gradient) exceeds a certain value. At the onset of convection, the shape of the convective motion depends on the nature and the geometry of the boundaries. In the case of a rectangular channel, various theoretical works have been achieved; they all show that convection appears under the form of rolls aligned with their axis perpendicular to the axis of the channel [l-5]. The results concerning the onset of free convection in an infinite rectangular duct with four rigid boundaries, two perfectly conducting horizontal plates and two insulating lateral walls have been given elsewhere [S]. There the stability of the following cases was studied : (i) infinite longitudinal rolls [with their axis parallel to the axis of the channel (V, = 0 in Fig. l)]. (ii) finite transverse rolls (V, = 0), (iii) 3-dim. rolls (V,, V,, V, # 0). Three-dimensional perturbations lead to the lowest critical Rayleigh numbers. At the onset of convection, the existence of a y-component of the velocity leads to a z-symmetrical ycurvature of the trajectories of fluid particles. The dependence of the critical wavenumber (related to the size of convective rolls at the critical point), on the width-to-height ratio is very characteristic of the 3-dim. structure: in the case of longitudinal rolls as’ is obviously equal to zero; for finite transverse rolls, it decreases monotonically when the width-to-height ratio increases (curve a, Fig. 2) and for three-dimensional rolls one obtains the particular curve bon Fig. 2. This characteristic shape does not depend on the nature of the horizontal walls since it has been sketched as well as for ‘free-free’ boundary conditions [3], and for ‘rigid-rigid’ ones [5]. Concerning the experimental point of view, Oertel and Biihler [6] quoted,via a differential interferometry technique, the presence of a three-dimensional convective motion in a duct with a length-to-width ratio (y) of 2.5 and Rayleigh numbers not less than 1.5 times the critical Rayleigh number. In this work we intend to measure the wavelength of convective cells as a function of the width-to-height ratio in a very long apparatus (y 2 17.5) and as close as possible to the threshold of Rayleigh-Bthrard convection. For that, we use the same experimental apparatus and the same shadowgraph method described earlier [7] in a paper about the influence of a superimposed basic flow on the shape of thermoconvective rolls in a long duct.