Electric Rayleigh Number Research Articles

Coulomb Driven Electro-Convection within Two Stacked Layers of Miscible Dielectric Liquids

This article investigates the behavior of two parallel layers of different miscible dielectric liquids enclosed and sandwiched between two electrodes. By applying an electric potential to one electrode while grounding the other, electro-convection occurs when the electric Rayleigh number exceeds a critical value, setting the fluid into motion and resulting in rapid mixing between the two liquids. A numerical model is developed to account for the varying ionic mobility and permittivity of the two liquids, considering their evolution based on the relative concentration field. The simulations confirm that electro-convection significantly enhances the mixing between the two liquids, as expected. Additionally, intriguing ripples are observed near the initial interface during the early stages of electro-convection instability growth. To explain and describe the flow dynamics in terms of stability analysis, a semi-analytical model is presented. This study provides insights into the mixing behavior and flow dynamics of miscible dielectric liquids under the influence of electro-convection. The findings contribute to a better understanding of the underlying mechanisms and can be valuable for applications such as microfluidics, energy conversion, and mixing processes. Further research is encouraged to explore additional parameters and optimize the control of electro-convection for practical applications.

Electric Buoyancy-driven convection in stable and unstable thermal stratifications

Thermo-electro-convective modes induced by a dielectrophoretic force in a differentially heated horizontal rectangular cavity have been investigated using direct numerical simulations in stable and unstable thermal stratifications. The variation of the electric tension applied to the plates of the cavity leads to multiple modes under microgravity as well as under both stable and unstable stratifications in terrestrial conditions. An effective electric Rayleigh number incorporating the effects of both the electric potential and the thermal stratification has been introduced in order to analyze the heat transfer induced by thermoelectric convection, leading to a unique curve of the variation of the Nusselt number with the effective electric Rayleigh number. The results can be used for modeling the heat transfer in microfluidic devices where the Archimedean buoyancy is very weak or to simulate natural convection at any planet using experiments performed on the Earth.

Electrothermosolutal convection in nanofluid

This article employs linear stability theory to investigate the thermosolutal instability phenomenon within a horizontal layer of nanofluid subjected to a vertical alternating current (AC) electric field while being heated from below. The model integrates the impacts of Brownian diffusion, thermophoresis, and electrophoresis into the nanofluid dynamics. Free-free boundary conditions are assumed at the upper and lower boundaries of the fluid layer. Employing the normal mode technique, the set of coupled differential equations is solved analytically for stress-free boundaries. The computed numerical values of the stationary thermal Rayleigh number are illustrated graphically. The conditions for nonexistence of overstability are also derived. The study focuses on stationary convection, examining the analytical and graphical implications of modified diffusivity ratio, AC electric Rayleigh number, solutal Lewis number, nanofluid Lewis number, solutal Rayleigh number, and nanoparticle Rayleigh number on the system dynamics. The analysis demonstrates that the nanofluid Lewis number and modified diffusivity ratio produce a stabilizing effect on the initiation of convection, notably delaying its onset. AC electric field and solutal Rayleigh number exhibit a destabilizing influence, notably accelerating the onset of convection.

Numerical analysis of electrothermoconvection of a dielectric nanofluid in a heated cavity

A numerical analysis of electrohydrodynamic (EHD) flow and heat transfer of nanofluid in a heated rectangular cavity is presented. A two-dimensional (2D) rectangular cavity heated from the bottom is considered. An electric potential difference is applied vertically, with the bottom wall acting as a high-voltage electrode, and the top wall is grounded. TiO2-25 # transformer oil nanofluid with nanoparticle volume fraction ranging from 0–5% is considered. The numerical model for EHD flow and heat transfer of nanofluid is implemented in the finite-volume method (FVM) based numerical framework of OpenFOAM. A single-phase approach based on the effective properties is adopted to model the nanofluids. A two-way coupled EHD flow model is employed to consider mutual interactions of flow and electric field variables. The flow and heat transfer behavior of nanofluids in the presence of an electric field is quantified with reference to the key parameters, electric Rayleigh number (T), and the nanoparticle volume fraction ϕ. The addition of nanoparticles increased the viscosity and marginally reduced the natural convective flow and heat transfer. However, EHD flow induced by the electric field aided in overcoming the weak natural convection flow in nanofluids. Results confirm that nanofluids’ net effective heat transfer rates are notably increased in the presence of the electric field. For the parameters under consideration, combining electric fields with nanofluids led to a significant heat transfer enhancement of up to 32.3%. The present study showcases the feasibility of combining passive heat transfer enhancement using nanoparticles and active heat transfer enhancement using EHD flow.

The electrohydrodynamic enhancement of heat transfer on interdigitated electrodes by a charge injection pump

Electrohydrodynamic pumps, as a representative type of nonmechanical pump, have received significant research attention due to their inherent advantages of having no moving parts and low power consumption. In particular, the planar charge injection pump has exhibited superior fluid driving performance, making it highly promising for applications in microscale flow driving and chip cooling. A sandwich structure pump with multiple pairs of planar interdigitated electrodes is numerically studied in this paper. The interaction of the flow, thermal, and electric fields is analyzed using the lattice Boltzmann method under different pump configurations, governing parameters, and convection mechanisms. The results reveal that the geometric configurations of the planar interdigitated electrodes have direct effects on the pumping performance and heat transfer rate. Specifically, an optimal configuration is achieved when the width of the collector is twice that of the emitter under two-pair electrode simulation conditions. More interestingly, competition between electric and thermal effects is observed, and the optimal threshold for heat transfer is found at an electric Rayleigh number of T = 300 for the considered cases. Finally, the interaction of the electric and thermal fields induces periodic oscillations. The single-vortex mechanism exhibits the longest oscillation period and inhibits heat transfer, while the multi-vortex mechanism has the shortest oscillation period and enhances heat transfer.

Effect of basic Temperature Gradients on Electrothermal Convection in a Rotating Layer of Viscoelastic (Walter’s B) Fluid Saturated Porous Medium Heated from Below

Combined Effect of Thermal Modulation and Rotation on the Onset of Convection in Walter's B Viscoelastic Fluid Saturated Porous Medium has been investigated. The problem is numerically solved using the Galerkin method after applying linear stability analysis and normal modes. It is possible to derive the dispersion relation while accounting for the effects of wave number, electric Rayleigh number, Darcy number, Taylor number, and thermal electric Rayleigh number. Graphically, the effects of the electric Rayleigh number, Darcy number, Wave number, and Taylor number on the onset of stationary convection have been studied. Under the boundary conditions considered, The kinematic viscoelasticity accounting for rheology of the nanofluid has no effect on the stationary convection for Walters’ (model B’) nanofluids and behaves like an ordinary Newtonian nanofluid.

EHD flow and heat transfer of hybrid nanofluid in a free surface cavity fitted with an internal hot obstacle

The objective of this study is to numerically investigate the effects of electrohydrodynamics (EHD) on coupled free convective thermocapillary flow. The study focuses on a free-surface cavity filled with a hybrid nanofluid (MWCTN- Fe3O4-thermal oil) and containing a hot rigid obstacle. An electric field is applied between the obstacle and the lower cavity wall to induce additional instabilities in this region. This technique aims to eliminate the dead zone typically present in traditional natural convection and is expected to greatly improve heat transfer efficiency. To achieve this objective, the equations governing the EHD phenomenon, as well as the equations defining the physicochemical properties of the hybrid nanofluid, are solved using the finite volume method (FVM) coupled with a blocked-off region procedure. A parametric study is conducted, involving the Marangoni number (surface tension), the thermal Rayleigh number (buoyancy force), the electrical Rayleigh number (electrical force), the nanoparticle concentration, the size and the position of the obstacle. It has been demonstrated that applying of an electric field to the convective-thermocapillary flow of the nanofluid (combining two enhancement techniques) significantly enhances heat transfer, resulting in a more than 230 % increase in the Nusselt number.

Thermo-electric convection in a cylindrical annulus during a sounding rocket flight

An experiment on convective flows induced by the dielectrophoretic force was performed under the microgravity condition provided during a sounding rocket flight. The dielectrophoretic force possesses a non-conservative term that can be seen as resulting from an electric gravity. That gravity can be responsible for an electric Rayleigh–Bénard convection between a hot inner cylinder and a cold outer cylinder when an electric field is applied in the radial direction. Four cells with independent temperature and electric field controls allowed the investigation of eight different values of the electric Rayleigh number relatively close to the onset of the thermo-electric instability. A linear stability analysis is performed to predict the stability threshold and the evolution of the growth rate of the instability. The three-dimensional structure of the flow is captured by simultaneous particle image velocimetry and by shadowgraphy. The amplitude of the instability modes and the time evolution of the flow is analysed, and various methods are proposed to extrapolate the experimental critical value of the electric Rayleigh number for the onset of convection. The measured critical electric Rayleigh number is in agreement with the prediction of the linear stability theory. The comparison of the new experimental results with previous ones from parabolic flight campaigns highlights the importance of long-term microgravity for the achievement of thermal convection at low values of the control parameters.

Numerical Investigation of the Electro-Thermo Convection in an Inclined Cavity Filled with a Dielectric Fluid

The present work is a numerical analysis of electro-thermo convection, occurring in a square differentially heated cavity filled with a dielectric fluid. The cavity experiences the combined effects of viscous, electrical, and thermal forces. The equations modelling the physical problem are solved via the finite volume approach. The study focuses on the effect of cavity tilt on the fluid flow structure and thermal performance inside the enclosure under the action of an electric field. A parametric study was performed, where the tilt angle is getting varied between 0° and 90°, as well as the Rayleigh number (5000 ≤ Ra ≤ 250,000) and the electric field (0 ≤ T ≤ 800). Furthermore, the electric charge injection level C, the mobility M and the Prandtl Pr numbers were all adjusted to a value of 10. The obtained results demonstrate that the hydrodynamic and thermal fields are significantly impacted by the cavity inclination. In addition, regardless of the thermal Rayleigh’s number, high electric field values could govern fluid movement through electric forces. Electro-convection typically demonstrates an oscillating flow due to the tilting of the cavity which gives rise to a bicellular regime occupying the entire cavity. A correlation has been established to estimate heat transfer by considering various system parameters such as cavity inclination, electrical Rayleigh number, and thermal Rayleigh number.

Oscillatory Modes on the Onset of Electrohydrodynamic Instability in Oldroydian Nanofluid Saturated Anisotropic Porous Layer

This work deals with an analytical study on the initiation of oscillatory convection in a rheological nanofluid saturating anisotropic porous layer with inclusion of vertical AC electric field using modified boundary conditions with negligible flux of volume fraction of nanoparticles. The rheological properties of the nanofluid are described using Oldroyd model. The Darcy model extended by Brinkman model is deployed to characterize the solid matrix behavior. The used model for nanofluid with inclusion of electric field integrates the additional effect of electrophoresis with that of thermophoresis and Brownian motion in the conservation equations of motion. The partial differential equations are simplified to non-dimensional linear equations using infinitesimal perturbations, Boussinesq approximation, normal mode technique and linearized stability theory. The characteristic equation is solved analytically for stress-free boundary conditions and the expressions for Rayleigh number of non-oscillatory and oscillatory modes initiation are determined. The oscillatory modes are found to occur for both the cases of top-/bottom-heavy nanoparticles distributions. The electric Rayleigh number, thermal Prandtl number and stress relaxation parameter advances whereas the Brinkman-Darcy number are found to delay initiation of both stationary and oscillatory convection.

Three-dimensional electro-convective flows of dielectric liquids between concentric cylinders

This study numerically investigates the flow structures and bifurcations of three-dimensional (3D) electro-convection (EC) between concentric cylinders. The flow motion is driven by the volumetric Coulomb force exerting on the free ions introduced by a strong unipolar injection. Three different sets of cases with periodic or symmetric boundary conditions are carried out. The finite volume method is used to numerically resolve the model problem. The co-effect of 2D roll mode and 3D polygon mode at the initial period of the EC flow is identified. The EC flows are made up of different types of regular or irregular centrally downflowing polygonal cells and are characterized by the central charge density cores surrounded by the charge void regions. The symmetry, periodicity, and staggered distribution characteristics of polygonal cells are identified. The cell patterns of EC flow are strongly influenced by the computational domain and the electric Rayleigh number (T). The subcritical bifurcation of linear instability together with a hysteresis loop is observed. In addition, the stability of the triangular flow pattern is analyzed at a large range of T and found that the annular EC flow is more likely to be unstable in three dimensions than in two dimensions.

Marangoni convection in a dielectric fluid layer with an AC electric field and nonuniform volumetric heat source due to incident radiation

AbstractThe role of a uniform AC electric field and a nonuniform volumetric heat source arising due to an external incident radiation on the onset of Marangoni convection in a horizontal layer of an incompressible dielectric fluid is investigated. The bottom rigid surface is fixed at a constant temperature while the top free surface at which the surface tension acts is considered to be nondeformable and a Robin boundary condition on the perturbation temperature is invoked. The nonuniform internal heating within the fluid layer alters the conduction temperature profile from linear to nonlinear in the vertical coordinate. The linear stability of the quiescent basic solution is studied with respect to normal mode disturbances. The resulting stability eigenvalue problem with variable coefficient is solved numerically using the Galerkin method. The impact of governing parameters on the instability of the system is discussed thoroughly. The forces causing instability reinforce together and are found to be tightly coupled. It is observed that the strength of nonuniform heat source and the electric Rayleigh number is to hasten, while an increase in the Biot number is to delay the onset of Marangoni electroconvection. Finally, the results obtained under the limiting cases are shown to be in good agreement with those published earlier.

Free Electrothermo-Convective Instability in a Dielectric Oldroydian Nanofluid Layer in a Porous Medium

For the last few years, thermal instability of non-Newtonian nanofluids becomes a prominent field of research because it has various applications in automotive industries, energy-saving, nuclear reactors, transportation, electronics etc. and suspensions of nanoparticles are being developed in medical applications including cancer therapy. In this paper, a free electrothermo-convective instability in a dielectric nanofluid layer in a porous medium is studied. An Oldroyd’s constitutive equation is used to describe the behaviour of nanofluid and for porous medium, the Darcy model is employed. The equation of conservation of momentum of fluid is stimulated due to the presence of an AC electric field, stress-relaxation parameter and strain-retardation parameter. The stability of the system is discussed in stationary and oscillatory convections for free–free boundaries. For the case stationary convection, it is found that the Oldroydian Nanofluid behaves like an ordinary nanofluid as the stationary Rayleigh number is independent of the stress-relaxation parameter, the strain-retardation parameter and Vadasz number. The effect of stress-relaxation-time parameter, strain-retardation-time parameter, Vadasz number, nanoparticles Rayleigh number, modified diffusivity ratio, medium porosity, Lewis number and electric Rayleigh number examined numerically and graphs have been plotted to analyse the stability of the system. It is observed that the electrical Rayleigh number has destabilizing influence whereas nanoparticles Rayleigh number, porosity and modified diffusivity ratio have stabilizing effect on the system. The oscillatory convection is possible for the values of the stress-relaxation parameter less than the strain-retardation parameter for both top-heavy/bottom-heavy distributions of nanoparticles.

Study the combined effect of electric field and variable viscosity on the stability of dielectric nanofluid (CuO + water) within a Hele–Shaw cell

In this research article, the combined effect of electric field and variable viscosity on the stability of dielectric nanofluid (CuO + water) within a Hele–Shaw cell is studied. The normal mode technique has been implemented for linear stability analysis and the truncated Fourier series method for nonlinear stability analysis. The effect of the Hele–Shaw number, thermorheological parameter, and alternating current electric Rayleigh number on the onset of convection and heat/mass transfer has been investigated analytically, graphically, and using tables. It is observed that the effect of the thermorheological parameter has a destabilizing effect, and the value of the parameter is always less than [Formula: see text] for this study. We also found that the Hele–Shaw number has stabilizing effect, and it is always greater or equal to [Formula: see text] for this study. The effect of alternating current electric Rayleigh number is destabilized. We observed that in the whole analysis, numerical results are better than analytical results.

Numerical study of electro-convection between annular electrodes based on a dissociation-injection mechanism

In this work, we extend the investigation of the injection-induced electro-convection (EC) between two-dimensional concentric electrodes from perfectly insulating dielectric liquids to dielectric liquids with residual conductivity. A dissociation-injection model of the EC system is implemented by a finite-volume framework of OpenFOAM®. The morphology of hetero-charge layers in a hydrostatic regime is presented. The flow characteristics including the spatial and temporal features of the flow field, electric field, and positive/negative charge density of the EC are analyzed. The subcritical bifurcation phenomenon of EC is observed. The residual conductivity postpones the onset of EC flow and inhibits the flow strength as EC takes place. The difference between onset (Tc) and cessation (Tf) of EC flow decreases as the residual conductivity grows. Gradually increasing the electric Rayleigh number (T), the EC system sequentially evolves via hydrostatic, steady, periodic, and chaotic states with abundant bifurcations. The initialization of the calculation could also strongly influence the instability of the EC system. Furthermore, the effect of residual conductivity on the transition sequences of the EC system is investigated. Four different transition sequences for EC develop from the hydrostatic state to chaos as T increases, and three distinct transition routes from the chaotic state to the motionless state when T reduces are observed and discussed.

Electrohydro dynamics convection in dielectric rotating Oldroydian nanofluid in porous medium

An electrically conducting nanofluid saturated with a uniform porous media has been tested to determine how rotation affects thermal convection. Utilizing the Oldroydian model, which incorporates the specific effects of the electric field, Brownian motion, thermophoresis, and rheological factors for the distribution of nanoparticles that are top- and bottom-heavy, one may use linear stability theory to ensure stability. Analysis and graphical representation of the effects of the AC electric field Rayleigh number, Taylor number, Lewis number, modified diffusivity ratio, concentration Rayleigh number, and medium porosity are provided for both bottom-heavy and top-heavy distribution.

Heat transfer intensification of NEPCM-water suspension filled heat sink cavity with notches cooling tubes by applying the electric field

The effects of an electric field on heat transfer, free convection, and entropy generation of nano-encapsulated phase change material (NEPCM) dissolved in water in a complex inclined chamber are studied. The enclosure consists of a rectangular cavity heated from below and the remaining walls are considered adiabatic. The fluid is cooled by eight cooling tubes, each with four notches. The effects of the electric field, inclination angle (ζ = 45° and ζ = 90°), and Rayleigh number (Ra = 103, 104, and 105) in equal concentration of NEPCM (ϕ = 2 %) are studied using ANSYS Fluent CFD code. The dimensionless form of fluid governing equations, electric potential equation, electric charge density equation, and entropy generation equation are used to set the primitive parameters. Grid verification and validation tests are performed to ensure the reliability of the solution. Calculations show that with increasing Ra, the average Nusselt number (Nuave) decreases from ζ = 45° to 90°, but when an electric field is applied, the results are reversed. As the Rayleigh number increases in conjunction with the electric field, the buoyancy effect becomes more pronounced. Furthermore, owing to its high heat transfer potential and lowest irreversibility, the straight cavity (ζ = 90°) is desirable at Ra = 105.

Finite amplitude electro-thermo convection in a cubic box

Three-dimensional electro-thermo-hydrodynamic (ETHD) flows of dielectric fluids driven by simultaneous Coulomb and buoyancy forces in a cubic box is numerically studied. The set of coupled equations associated with the ETHD phenomena are solved with the finite volume method. The code is first validated by comparing the numerically obtained linear critical values of the pure electro-convection and thermal convection with the previous studies. Then the neutral stability curve of the system is given and the finite amplitude instability thresholds with different Rayleigh numbers () are presented. It is found that along the neutral stability curve, the flow strength becomes weaker with the increase of and the decrease of electric Rayleigh number (T). Besides, the gap between the linear and nonlinear critical values expressed in terms of T decreases with the increase of . Primarily, the distributions of charge density, temperature and velocity fields with different governing parameters near neutral stability curve are presented. The temperature and charge density profiles near the linear and nonlinear critical values are given, showing that higher T results in wider charge void region and shorter distance between the charge void region’s lower boundary and injection electrode. Finally, the symmetries of the flow patterns along the neutral stability curve are also discussed briefly.

Electrohydrodynamic enhancement of phase change material melting in cylindrical annuli under microgravity

Latent heat thermal energy storage has been recommended as an effective technology for the thermal management system of space exploration for its excellent ability to store thermal energy. However, the low thermal conductivity of phase change material seriously weakens the heat charging and discharging rates of the system. This paper introduces electrohydrodynamic, a popular active heat transfer enhancement technology, to enhance the phase change material melting in a shell-tube latent heat storage system under microgravity using the lattice Boltzmann method. Different from some previous works, this work mainly focuses on the combined effects of the electric Rayleigh number T and different gravity conditions on the melting performance. Results indicate that the electrohydrodynamic technique always shows good performance in accelerating the melting process, and especially, it is possible to save up to 90% of the charging time in some cases. In addition, the effect of eccentricity on the charging process is investigated, and it is found that although the concentric annulus is always the optimal configuration under no-gravity conditions, the optimal eccentric position of the internal tube largely depends on the electric Rayleigh number if one takes into account the gravity effects. Moreover, the effect of radius ratio Γ on the heat storage efficiency is also evaluated under no-gravity condition. The present work illustrates that electrohydrodynamic is an effective method for enhancing phase change material melting even under microgravity. • The combined effect of Coulomb force and gravity on PCM melting is studied. • The transient charging process of PCM melting under an electric field is presented. • A maximum of over 90% melting time saving can be observed under an electric field. • The optimal eccentric position relies on the gravity condition.

Full bifurcation scenarios and pattern formation of laminar electroconvection in a cavity

This study numerically investigates the flow structures and bifurcation scenarios of three-dimensional (3D) laminar electroconvection (EC). An efficient parallel lattice Boltzmann model is undertaken to numerically solve the model problem. The results present three steady flow patterns and three pitchfork bifurcations. These three patterns each have one, two, or four charge void cells. The three critical values of electric Rayleigh number Tc are 242, 545, and 665, respectively. There are also two hysteresis loops whose nonlinear criteria Tf are 157 and 435, respectively. An unexpected flow pattern, which has two prism-shaped primary vortex structures, demonstrates the significance of 3D analysis. In addition, we find that the 3D flow in the cavity is more stable by studying the correlation between the 3D and two-dimensional laminar EC. Using dynamic mode decomposition for the flow structures, we reveal that the novel feature is the result of competition between the EC flow structure and the limitation of geometry.