Small Rayleigh Numbers Research Articles

Conjugate free convection in a non-uniform heating walled enclosure filled by ternary hybrid nanofluid under magnetic field

A study was conducted using numerical simulations to analyse the behaviour of heat transfer in a square enclosure filled with a ternary hybrid nanofluid in the occurrence of a magnetic field. The flow in the enclosure is characterised by steady and laminar conjugate-free convection. The enclosure has a vertical border with a finite thickness, while the other three borders are assumed to be very thin. The investigation aims to analyse the impact of several key factors on the average Nusselt number using the finite element method. These parameters include the volume fraction of ternary hybrid type nanoparticles (ranging from 0 to 0.03), Rayleigh number (varying from 103 to 106), solid wall thickness (changing from 0.1 to 0.3), Hartmann number (varying from 0 to 100), and the ratio of thermal conductivities (ranging from 0.1 to 10). A notable enhancement in heat transfer is found by employing a ternary hybrid nanofluid. This enhancement becomes more significant for small Rayleigh numbers, where heat conduction governs the primary means of heat transfer. Also, at low levels of Ra, the development of energy transfer strength becomes insignificant in the existence of a magnetic field. This magnetic field effect is primarily controlled by high values of Ra, which consequently leads to an enhancement in the strength of energy transmission.

Multi-fuel combustion performance analysis and operating characteristics of a vortex-tube combustor

In this work, an ultra-steady combustion technique was attempted to achieve fuel adaptability combustion. The combustion performances of five representative gaseous fuels in a stratified vortex-tube combustor were investigated in terms of the stability limit, pressure fluctuation, and flame topology. Results show that the lean stability limit of the global equivalence ratio for the five fuels can always be less than 0.15 with a uniform flame front, whilst the amplitude of pressure fluctuations is always below 2300 Pa, indicating a super-steady combustion process. The non-premixed flame structure guarantees a high mass concentration near the reaction zone, whilst the vortex flow also decreases the local flow velocity, inhibiting flame blow-out, and suggesting good self-adjusting capacity under various global equivalence ratios. The synergistic action of the flow and flame structures transports the interior high-enthalpy burnt gas and exterior unburnt gas to the exterior unburnt gas and reaction zones to promote the ignition and reaction procedures, resulting in an intensified combustion. The large tangential velocity and density gradient result in the large values of Richardson number, which indicates that laminarization of the flow arises and results in good aero-dynamic and thermo-dynamic stabilities. The resultant good self-adjusting capacity and three types of dynamic stabilities are the intrinsic causes of the ultra-steady combustion process in this combustor. Ultimately, the generalized criterion of stabilization can be defined by the combination of Richardson and Rayleigh numbers, for which large Richardson and small Rayleigh numbers are required for a highly steady combustion process.

Fingering Convection in the Stably Stratified Layers of Planetary Cores

AbstractStably stratified layers may be present at the top of the electrically conducting fluid layers of many planets either because the temperature gradient is locally subadiabatic or because a stable composition gradient is maintained by the segregation of chemical elements. Here we study the double‐diffusive processes taking place in such a stable layer, considering the case of Mercury's core where the temperature gradient is stable but the composition gradient is unstable over a 800 km‐thick layer. The large difference in the molecular diffusivities leads to the development of buoyancy‐driven instabilities that drive radial flows known as fingering convection. We model fingering convection using hydrodynamical simulations in a rotating spherical shell and varying the rotation rate and the stratification strength. For small Rayleigh numbers (i.e., weak background temperature and composition gradients), fingering convection takes the form of columnar flows aligned with the rotation axis and with an azimuthal size comparable with the layer thickness. For larger Rayleigh numbers, the flows retain a columnar structure but the azimuthal size is drastically reduced leading to thin sheet‐like structures that are elongated in the meridional direction. The azimuthal size decreases when the thermal stratification increases, following closely the scaling law expected from the linear planar theory (Stern, 1960, https://doi.org/10.1111/j.2153-3490.1960.tb01295.x). We find that the radial flows always remain laminar with local Reynolds number of order 1–10. Equatorially symmetric zonal flows form due to latitudinal variations of the axisymmetric composition. The zonal velocity exceeds the non‐axisymmetric velocities at the largest Rayleigh numbers. We discuss plausible implications for planetary magnetic fields.

On the differential effect of temperature on the Nusselt-Rayleigh relationship in free convection

The aim of and inspiration behind this paper was to explain the reasons, also observed by other researchers, of the discrepancy in the results of experimental free convection, which for small Rayleigh and Nusselt numbers in the initial phase of research can sometimes reach several hundred percent. These discrepancies decrease with increasing heating power and plate surface temperature, in proportion to the increase in Ra and Nu, reaching typical values for this type of research. To explain this phenomenon, a comprehensive theoretical and experimental analysis of the influence of the physical properties of a fluid (air and water) as well as primary (tw and t∞) and secondary (tav and Δt) temperatures on the Rayleigh number was carried out. The impact was found to be unequal. The plate temperature tw is of greater importance, which is much higher than the much lower and almost constant temperature t∞ of the undisturbed area, especially since it causes convective movement, generating differences in fluid density and thus driving the phenomenon. Similarly, the direct contribution of the temperature difference Δt to Ra suggests that it has a greater influence on convective heat transfer than the average temperature of the medium tav.By analysing the effect of each of these temperatures separately, it was possible to show that their mutual, compatible or opposite interaction (tw/t∞) causes a different scattering of results, or may even lead to unusual Rayleigh numbers (Ra temperature dualism). This study led not only to a better understanding of the phenomenon, but even to a prediction of its unusual behaviour, unheard of in typical experimental studies of free convection.For example, if we consider the theoretical convective heat transfer from a plate l = 0.15 m in air in the context of the interaction of tav and Δt, it turns out that for the same Δt = 40 K, the Rayleigh number may assume, depending on tav = (tw + t∞)/2, different values. So, for tw = 50 °C, t∞ = 10 °C and tav = 30 °C, Ra = 1.213.107, whereas for tw = 90 °C, t∞ = 50 °C and tav = 70 °C it is ≈ 1.7 times smaller (Ra = 0.687.107). This hypothetical phenomenon, unheard of in typical experimental studies, which could occur, and maybe even does occur in smelting, thermal energy, etc., forces us to think about the values of Nusselt numbers, heat transfer coefficients and heat fluxes for these two cases. This lies beyond the scope of the present paper, but it is a topic for possible future research.

Rayleigh–Bénard flow for a Carreau fluid in a parallelepiped cavity

A continuation method is used to study Rayleigh–Bénard convection in a non-Newtonian fluid inside a parallelepiped cavity. The cavity has its length equal to twice the side of the square cross-section. Shear-thinning and shear-thickening Carreau fluids are considered. The focus is put on the two stable branches which exist in the Newtonian case, a stable primary branch of transverse rolls $B_1$ and a primary branch of longitudinal roll $B_2$ , stabilized beyond a secondary bifurcation point $S_2$ . Although the primary bifurcation points are unchanged, the non-Newtonian properties strongly modify the bifurcation diagram. Indeed, for a shear-thinning fluid, the stable solutions can exist at much smaller Rayleigh numbers ${Ra}$ , on subcritical branches beyond saddle-node points $SN_1$ and $SN_2$ , and small perturbations can be sufficient to reach them. In agreement with Bouteraa et al. (J. Fluid Mech., vol. 767, 2015, pp. 696–734), the change of the primary bifurcations from supercritical to subcritical occurs at given values of what they define as the degree of shear-thinning parameter $\alpha$ . Moreover, the value of the Rayleigh number at the saddle-node points can be approximated by a simple expression, as proposed by Jenny et al. (J. Non-Newtonian Fluid Mech., vol. 219, 2015, pp. 19–34). In the case of a shear-thickening fluid, the branches remain supercritical, but the secondary point $S_2$ is strongly moved towards larger ${Ra}$ , making it more difficult to reach the longitudinal roll solution. Energy analyses at the bifurcations $SN_1$ , $SN_2$ and $S_2$ show that the changes of the corresponding critical thresholds ${Ra}_c$ are connected with the changes of the viscous properties, but also with changes of the buoyancy effect.

Period bubbling bifurcation and transition to chaotic state of convective flow on a top-open cylinder

Period bubbling bifurcation and transition to chaotic state of a convective flow on the top-open cylinder beneath heating are investigated using direct numerical simulation owing to its fundamental significance and extensive application. Numerical results show that a primary convective flow on the cylinder is axisymmetric and dominated by the effect of baroclinicity for small Rayleigh numbers. There exists a complex route of the transition to chaotic state involving a succession of bifurcations when the Rayleigh number is increased; that is, the pitchfork bifurcation occurs between Ra = 2.7 × 103 and Ra = 2.8 × 103 for which an axisymmetric convective flow is broken, and the first Hopf bifurcation occurs between Ra = 3.3 × 105 and Ra = 3.4 × 105. An interesting phenomenon is that the convective flow may change from periodic back to steady state with the increase in the Rayleigh number for 7.0 × 105 ≤ Ra ≤ 1.5 × 106, termed as a period bubbling bifurcation. The whole route of the transition to chaotic state can be described by a steady, a periodic, a steady again, a period doubling, a quasiperiodic, and a chaotic state as the Rayleigh number is increased. Further, the convective flow in the transition is discussed by employing the topologic index, the spectral analysis, the attractor, and the fractal dimension. Additionally, heat transfer is also quantified.

Numerical study of energy transmission through copper-based nanofluid contained in a partially heated isosceles triangular cavity in the presence of heat source/sink

This study reports computational simulation of natural convective energy transport through copper-based nanofluid contained in partially heated isosceles triangular conduit in the presence of invariable magnetic field under the influence of energy source/sink. Inclined sides of the enclosure are retained cold and horizontal boundary is supposed thermally insulated. Heat source of a particular length is placed on the horizontal wall. Relations expressing the energy transport and fluid flow are first dealt by penalty scheme and then composed expressions are assembled through Galerkin approximation scheme. Pertinent physical parameters governing the flow are the solid volume increment of nanoparticles (0.0 < < 0.06), Hartmann number (0 < Ha < 100), Rayleigh number (105 < Ra < 108) and coefficient of heat source/sink (−10 < Q < 10). It has been noted through this investigation that in consequence of magnetic force, reduction in heat transport occurs. Conduction and convection regimes are dominant for small and large Rayleigh numbers respectively. Energy transport rate is found zero on corners of the cold inclined walls. Obtained computational results reveal that the flow pattern relies considerably on the concentration of nanoparticles, coefficient of energy source/sink, Rayleigh and Hartmann numbers. Computed solutions are expressed through plots of streamlines, isothermal lines, and rate of local and overall energy flow. The current results are also validated through graphical comparison with the existing literature.

Transition from steady to chaotic flow of natural convection on a section-triangular roof

Flow phenomena on a roof are investigated by employing direct numerical simulation. A sequence of pitchfork bifurcations of steady plumes on the roof occurs for small Rayleigh numbers, which is analyzed using a topological method. Furthermore, a Hopf bifurcation followed by periodic doubling, quasiperiod bifurcations, and a transition to chaos appear as the Rayleigh number is increased.

Convection in viscoplastic fluids in rectangular cavities at lateral heating

The paper is devoted to the study of convective motions of viscoplastic fluids in closed two-dimensional rectangular domains with different aspect ratios under lateral heating. The problem was solved numerically using the ANSYS Fluent software. The Herschel-Bulkley model was chosen for describing the rheological behavior of the fluid. Under certain rheological parameters, this model was transformed into a Newtonian fluid model, whose behavior was also simulated as a limiting case. Based on the calculated results, the dependences of the maximum value of the stream function in the cavity on the Rayleigh number are plotted. It was found that at small Rayleigh numbers the intensity of motion is close to zero. At a certain value of the Rayleigh number there is a sharp increase in the intensity of motion, and a further increase in the Rayleigh number causes an almost linear growth of the maximum value of the stream function. For each of the considered ratios of cavity sides, the threshold values of the Rayleigh number, at which a sharp increase in the intensity of motion of liquid is observed, were determined. The obtained values of Rayleigh numbers turned out to be close to the threshold values of the Rayleigh number for the Bingham fluid found in the works of other authors earlier. The fields of the stream function and the square root of the second invariant of the viscous stress tensor were obtained for different values of the Rayleigh number and different aspect ratios. The scenarios of rearrangement of quasisolid motion zones with increasing Rayleigh number were compared with the available results for the Bingham fluid.

Heat transport bounds for a truncated model of Rayleigh–Bénard convection via polynomial optimization

Upper bounds on time-averaged heat transport are obtained for an eight-mode Galerkin truncation of Rayleigh’s 1916 model of natural thermal convection. Bounds for the ODE model—an extension of Lorenz’s three-ODE system—are derived by constructing auxiliary functions that satisfy sufficient conditions wherein certain polynomial expressions must be nonnegative. Such conditions are enforced by requiring the polynomial expressions to admit sum-of-squares representations, allowing the resulting bounds to be minimized using semidefinite programming. Sharp or nearly sharp bounds on mean heat transport are computed numerically for numerous values of the model parameters: the Rayleigh and Prandtl numbers and the domain aspect ratio. In all cases where the Rayleigh number is small enough for the ODE model to be quantitatively close to the PDE model, mean heat transport is maximized by steady states. In some cases at larger Rayleigh number, time-periodic states maximize heat transport in the truncated model. Analytical parameter-dependent bounds are derived using quadratic auxiliary functions, and they are sharp for sufficiently small Rayleigh numbers.

Thermal Analysis of a Microhotplate - An Experimental Study

In the present work, experimental and numerical thermal analysis of a microhotplate were performed to evaluate the heat transfer mechanism at small Rayleigh number ( $Ra$ ). The convective and radiative heat transfer coefficient values were evaluated for microhotplate mounted over two different mounting positions (namely model-1 & model-2). At different heat generation ( $Q$ ) values, it was found that the average convective coefficient value was less than $10\frac {W}{m^{2}K}$ , irrespective of the microhotplate mounting position. Comparison of both models at a similar $Q$ ( $\simeq 0.69W$ ) value, reveals that the radiative heat transfer contribution was 33% & 68% for model-1 and model-2 respectively. Based on the results obtained in the present study, a correlation was developed using regression analysis for the convective Nusselt number in terms of Rayleigh number ( $8.84\times 10^{-4}\le \:Ra\:\le 4.94\times 10^{-3}$ ), and the convective Nusselt number obtained from the correlation and present study are within ±17%.

Propagating fronts in fluids with solutal feedback.

We numerically study the propagation of reacting fronts in a shallow and horizontal layer of fluid with solutal feedback and in the presence of a thermally driven flow field of counterrotating convection rolls. We solve the Boussinesq equations along with a reaction-convection-diffusion equation for the concentration field where the products of the nonlinear autocatalytic reaction are less dense than the reactants. For small values of the solutal Rayleigh number the characteristic fluid velocity scales linearly, and the front velocity and mixing length scale quadratically, with increasing solutal Rayleigh number. For small solutal Rayleigh numbers the front geometry is described by a curve that is nearly antisymmetric about the horizontal midplane. For large values of the solutal Rayleigh number the characteristic fluid velocity, the front velocity, and the mixing length exhibit square-root scaling and the front shape collapses onto an asymmetric self-similar curve. In the presence of counterrotating convection rolls, the mixing length decreases while the front velocity increases. The complexity of the front geometry increases when both the solutal and convective contributions are significant and the dynamics can exhibit chemical oscillations in time for certain parameter values. Last, we discuss the spatiotemporal features of the complex fronts that form over a range of solutal and thermal driving.

Melting Behavior of Phase Change Material in Honeycomb Structures with Different Geometrical Cores

Honeycomb structure with phase change material (PCM) is frequently used in passive thermal management devices. The geometrical shape of the honeycomb core greatly influences the melting rate of the PCM. This paper investigates the melting rates of PCM in honeycomb cores of non-hexagonal cells in comparison with that of hexagonal cell in three Rayleigh numbers. The objective is to find the optimal shape in order to reduce the melting time of the PCM. The constrained melting behaviors of PCM in triangular, quadrilateral, hexagonal, and circular honeycomb cores are numerically studied. The enthalpy porosity technique and finite volume method are used in this paper. The instantaneous liquid fraction and energy absorption of PCM in different honeycomb cores are discussed in detail. The influences of the placed orientation and aspect ratio of different cores on melting rates of PCM are considered. Results show that the melting rate of PCM in a rectangular core is always higher than the hexagonal core for the given aspect ratio and Rayleigh number. The geometrical factor (GF), which indicates the cross-sectional area per unit perimeter, is found to be an important index on the melting rate. At a small Rayleigh number, it takes a longer melting time of the PCM for the core with a larger GF. As the Rayleigh number is large, the melting time of the PCM is affected by both the GF and the orientation of the cores.

Magnetic source effect on EG-CuO nanofluid in a semi-annulus using RBFs

In this study, numerical simulation of hydrothermal behaviour of ethylene glycol based CuO nanofluid in a semi-annulus with a magnetic source is investigated. The non-dimensional governing equations are discretized by radial basis functions in spatial derivatives, and by backward-Euler in temporal derivatives. The effects of dimensionless parameters Hartmann number, Rayleigh number, magnetic number, Eckert number and solid volume fraction are presented both in terms of streamlines, isotherms and vorticity contours, and average Nusselt number through the heated wall. The results show that augmentation in magnetic number accelerates the convective heat transfer at a small Rayleigh number, and at a larger heated inner circle. Convective heat transfer is inhibited with the rise of Hartmann number, and with the increase in Eckert number while it is enhanced with the increase in concentration of nanoparticles and Rayleigh number.

A solid-liquid local thermal non-equilibrium lattice Boltzmann model for heat transfer in nanofluids. Part II: Natural convection of nanofluids in a square enclosure

The novel solid-liquid local thermal non-equilibrium lattice Boltzmann model, developed in Part I of this paper series [1], is applied to the classical problem of natural convection of nanofluids in a square enclosure with vertical walls at differential temperatures. Effects of Rayleigh numbers, nanoparticles random motion, nanoparticles volume fraction and nanoparticles non-uniform distribution in natural convection of nanofluids are studied. Because random motions of nanoparticles are intensified with temperature, vertical velocity and temperature profiles in the nanofluid are asymmetric with respect to the hot and cold vertical walls. Distribution of nanoparticles in the nanofluid inside the enclosure is affected by both the Rayleigh number and random motion of nanoparticles, and nanoparticles’ distribution become relatively non-uniform at relatively high Rayleigh numbers. The non-uniform distribution of nanoparticles also affect local vertical velocity distribution, local temperature distribution, and the average Nusselt numbers. The effect of random motion of nanoparticles is shown to be responsible for enhanced convection at small Rayleigh numbers, the increasing viscosity of nanofluids is shown to be responsible for the deteriorating effects on heat transfer at intermediate Rayleigh numbers and non-uniform distribution of nanoparticles is shown to be responsible for ascending trend of Nusselt numbers at high Rayleigh numbers. The non-monotonous variation of the Nusselt number with respect to the Rayleigh number are in qualitative agreement with existing experimental data.

Natural convection in a horizontal cylindrical enclosure filled with a magnetic nanofluid: Influence of the uniform outer magnetic field

An analytical and numerical study of laminar convection in a horizontal cylindrical enclosure heated from below is performed. It is found analytically that uniform outer magnetic field can cause instability of the equilibrium state of magnetic nanofluid or influence gravity convection. Particular attention is paid to the steady convection, structure transients and the onset of unsteadiness. The Prandtl number from 0.7 to 700, different Rayleigh numbers (up to 106) and magnetic Rayleigh number are considered. For a nonmagnetic fluid, we studied the influence of the Prandtl number on the Rayleigh number values for which the equilibrium state becomes unstable, convective flow becomes bi-cellular, or becomes nonstationary. The effect of the magnetic Rayleigh number and the thermal conductivity of the solid block surrounding the enclosure on the onset of the convection is investigated. It is found that the magnetic permeability of the magnetic fluid filling the enclosure is an important factor. Four modes of fluid flow are studied analytically and then two of them are demonstrated during numerical simulation. It is shown that the outer uniform magnetic field turns to nonuniform in the magnetic fluid heated from below with not only the vertical, but also with the horizontal components of the gradient. So, there is a weak no-threshold convective flow even for very small magnetic Rayleigh numbers. The influence of the convective flow on magnetic field structure in the volume of a non-conducting magnetic fluid is found. Critical temperature difference for the experiment is predicted.

Thermoconvective instabilities of a non-uniform Joule-heated liquid enclosed in a rectangular cavity

Natural convection produced by a non-uniform internal heat source is studied numerically. Our investigation is limited to a two-dimensional enclosure with an aspect ratio equal to two. The energy source is Joule dissipation produced by an electric potential applied through two electrodes corresponding to a fraction of the vertical walls. The system of conservative equations of mass, momentum, energy and electric potential is solved assuming the Boussinesq approximation with a discontinuous Galerkin finite element method integrated over time. Three parameters are involved in the problem: the Rayleigh number $Ra$, the Prandtl number $Pr$ and the electrode length $L_{e}$ normalized by the enclosure height. The numerical method has been validated in a case where electrodes have the same length as the vertical walls, leading to a uniform source term. The threshold of convection is established above a critical Rayleigh number, $Ra_{cr}=1702$. Due to asymmetric boundary conditions on thermal field, the onset of convection is characterized by a transcritical bifurcation. Reduction of the size of the electrodes (from bottom up) leads to disappearance of the convection threshold. As soon as the electrode length is smaller than the cavity height, convection occurs even for small Rayleigh numbers below the critical value determined previously. At moderate Rayleigh number, the flow structure is mainly composed of a left clockwise rotation cell and a right anticlockwise rotation cell symmetrically spreading around the vertical middle axis of the enclosure. Numerical simulations have been performed for a specific $L_{e}=2/3$ with $Ra\in [1;10^{5}]$ and $Pr\in [1;10^{3}]$. Four kinds of flow solutions are established, characterized by a two-cell symmetric steady-state structure with down-flow in the middle of the cavity for the first one. A first instability occurs for which a critical Rayleigh number depends strongly on the Prandtl number when $Pr&lt;3$. The flow structure becomes asymmetric with only one steady-state cell. A second instability occurs above a second critical Rayleigh number that is quasiconstant when $Pr&gt;10$. The flow above the second critical Rayleigh number becomes periodic in time, showing that the onset of unsteadiness is similar to the Hopf bifurcation. When $Pr&lt;3$, a fourth steady-state solution is established when the Rayleigh number is larger than the second critical value, characterized by a steady-state structure with up-flow in the middle of the cavity.

Numerical investigation of ferrofluid convection with Kelvin forces and non-Darcy effects

In this study, natural convection in a porous, ferrofluid-filled cavity is numerically investigated utilizing the multiquadric (MQ) radial basis function (RBF) based pseudo spectral (PS) method. The influence of Kelvin forces, Brinkman and Forchheimer terms and a magnetic source is also taken into account. Results reveal that convective heat transfer is inhibited with the rise of Hartmann number, and with the decrease in Darcy number while it is enhanced with the increase in porosity of the porous medium, solid volume fraction and Rayleigh number. At a small Rayleigh number, the average Nusselt number enhances with the augmentation of magnetic number.

Natural convection under sub-critical conditions in the presence of heating non-uniformities

When the heating intensity is below the critical threshold required for the onset of Rayleigh-Bénard (RB) convection, heat transport across a horizontal fluid layer uniformly heated from below is driven by conduction, placing a limit on its magnitude. A methodology to increase the heat flow through the use of spatial heating non-uniformities is proposed. The non-uniformities create convection whose pattern is dictated by the pattern of the heating, and this convection supplements the conductive heat transport. It has been shown that the effectiveness of this convection, the primary convection, is a strong function of the heating wave number and it may increase the heat flux by up to ten times when compared with the conductive state if the most effective heating wave number is used. The primary convection is subject to transitions to various secondary states and the critical conditions for these transitions have been determined using linear stability theory. Three modes of secondary convection have been identified giving rise either to rolls parallel to the primary rolls, to rolls orthogonal to the primary rolls, or to oblique rolls. Conditions leading to their onset define the limits on the heat transfer predictions based on the analysis of the primary convection. In general, transition to secondary convection occurs at smaller Rayleigh numbers in the presence of heating non-uniformities than those required for the onset of RB convection, however, under certain conditions these non-uniformities increase the critical Rayleigh number.

Study on the Instability of Two-Phase Flow in the Heat-Absorbing Tube of Trough Solar Collector

The Marangoni effect and Rayleigh-Benard effect in the two-phase region of solar trough heat-absorbing tube are simulated by FTM (front tracking method). Considering the Marangoni effect alone, although surface tension gradient and surface tension affect the interface wave, the two effects have different characteristics. The surface tension gradient caused by the temperature gradient is one of the factors that swing the interface. The amplitude attenuation of the interface wave decreases with the increase of the Marangoni number (Ma). In general, the surface tension gradient enhances the convection opposite to the temperature gradient. Under the gravity field, the Rayleigh-Benard effect influences the development of the vortex structure in the flow field, which in turn affects the velocity gradient near the interface to influence the evolution of the interface fluctuation. In a small Rayleigh number (Ra), the buoyancy convection reduces the velocity gradient, thus suppressing the evolution of the interfacial wave. In the range of Ra &lt; 4.0E4, the larger the Ra, the stronger the inhibitory effect. However, when the Ra number is large (Ra &gt; 4.0E4), the situation is just the opposite. The larger the Ra is, the stronger the promoting effect is.