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It is proved analytically that the complex growth rate n = nr + ini (nr and ni are the real and imaginary parts of n , respectively) of an arbitrary neutral or unstable oscillatory disturbance of growing amplitude in rotatory electrothermoconvection in a dielectric fluid layer saturating a sparsely distributed porous medium heated from below, for the case of free boundaries, is located inside a semicircle in the right half of the nrni − plane, whose centre is at the origin and radius = max T a P r 2 , R ea P r A , where Ta is the modified Taylor's number, Pr is the modified Prandtl number, Rea is electric Rayleigh number and A is the ratio of heat capacities. The upper limits for the case of rigid boundaries are derived separately. Furthermore, similar results are also derived for the same configuration when heated from above. [ABSTRACT FROM AUTHOR]

The onset of convective instability in an internally heated dielectric fluid‐saturated porous layer under the influence of a uniform AC electric field for different types of boundary conditions is investigated. The flow in the porous medium is described by the Brinkman model with fluid viscosity different from effective viscosity. The lower adiabatic and the top with finite heat transfer coefficient to the external environment boundaries are considered to be either rigid or stress‐free. The presence of a uniform volumetric heat source alters the conduction profile of the temperature field from linear to quadratic in the vertical coordinate. A modal linear stability analysis of the basic motionless state is carried out and the general regime of linear instability is investigated by solving the stability eigenvalue problem numerically using the Galerkin method of weighted residual technique. The neutral stability condition as well as the critical value of the thermal Rayleigh number is computed for rigid–rigid, free–free, and rigid–free boundaries for various values of governing parameters. It is seen that the nature of boundaries affect the stability of the system only quantitatively, though not qualitatively. The rigid–rigid boundaries offer a more stabilizing effect against convection in comparison with rigid–free and free–free boundaries. The study found that the effect of increasing thermal electric Rayleigh number and the Darcy number is to hasten the onset of instability, while the opposite trend is perceived with an increase in the ratio of viscosities and Biot number. The outcomes of this investigation are found to be in good agreement with past studies under the limiting cases. [ABSTRACT FROM AUTHOR]

The 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. [ABSTRACT FROM AUTHOR]

The effect of time-periodic electric field modulation on electroconvection in a compactly packed dielectric liquid-permeable layer is investigated using the small perturbation method coupled with the regular perturbation method. The dielectric constant is assumed to be a linear function of temperature. For small amplitude electric field modulation, the critical correction Rayleigh number is determinedusing the regular perturbation method. The critical Rayleigh number is obtained in terms of the electrical Rayleigh number, Vadasz number, normalized porosity, and the modulation frequency to determine the stability of the system. It is found that electric field modulation at low frequencies can create subcritical convective motion. The impact of Vadasz number is shown to be akin to that of the dielectrophoretic force. The stabilizing influence of normalized porosity is more pronounced when the frequency of electric field modulation is modest and large. The study reveals that time-varying electric fields and a densely packed porous layer may have implications for the control of electroconvection in heat transfer applications involving dielectric fluids as working media. [ABSTRACT FROM AUTHOR]

The stability of a horizontal sparsely packed porous layer of a dielectric fluid heated from below is examined when the fluid layer is subjected to time-dependent electric field modulation. The dielectric constant is assumed to be a linear function of temperature. The regular perturbation method is used to find the critical Rayleigh number and the corresponding wavenumber for small amplitude electric field modulation. The stability of the system characterized by a correction Rayleigh number is computed as a function of thermal, electric, and porous parameters, and the frequency of electric field modulation. It is found that the onset of electro-convection can be delayed or advanced by the presence of these parameters. The effect of various parameters is found to be significant for moderate values of the frequency of electric field modulation. Some of the known results are recovered as special cases of the present study. The findings of the present study have possible implications in the control of electro-convection with a time-varying electric field. [ABSTRACT FROM AUTHOR]

Purpose: The study of instability due to the effects of Maxwell–Cattaneo law and internal heat source/sink on Casson dielectric fluid horizontal layer is an open question. Therefore, in this paper, the impact of internal heat generation/absorption on Rayleigh–Bénard convection in a non-Newtonian dielectric fluid with Maxwell–Cattaneo heat flux is investigated. The horizontal layer of the fluid is cooled from the upper boundary, while an isothermal boundary condition is utilized at the lower boundary. Design/methodology/approach: The Casson fluid model is utilized to characterize the non-Newtonian fluid behavior. The horizontal layer of the fluid is cooled from the upper boundary, while an isothermal boundary condition is utilized at the lower boundary. The governing equations are non-dimensionalized using appropriate dimensionless variables and the subsequent equations are solved for the critical Rayleigh number using the normal mode technique (NMT). Findings: Results are presented for two different cases namely dielectric Newtonian fluid (DNF) and dielectric non-Newtonian Casson fluid (DNCF). The effects of Cattaneo number, Casson fluid parameter, heat source/sink parameter on critical Rayleigh number and wavenumber are analyzed in detail. It is found that the value Rayleigh number for non-Newtonian fluid is higher than that of Newtonian fluid; also the heat source aspect decreases the magnitude of the Rayleigh number. Originality/value: The effect of Maxwell–Cattaneo heat flux and internal heat source/sink on Rayleigh-Bénard convection in Casson dielectric fluid is investigated for the first time. [ABSTRACT FROM AUTHOR]

The instability characteristics of a dielectric fluid layer heated from below under the influence of a uniform vertical alternating current (AC) electric field is analyzed for different types of electric potential (constant electric potential/ electric current), velocity (rigid/free) and temperature boundary conditions (constant temperature/heat flux or a mixed condition at the upper boundary). The resulting eigenvalue problem is solved numerically using the shooting method for various boundary conditions and the solution is also found in a simple closed form when the perturbation heat flux is zero at the boundaries. The possibility of a more precise control of electrothermal convection (ETC) through various boundary conditions is emphasized. The effect of increasing AC electric Rayleigh number is to hasten while that of Biot number is to delay the onset of ETC. The system is more stable for rigid-rigid boundaries when compared to rigid-free and least stable for free-free boundaries. The change of electric potential boundary condition at the upper boundary from constant electric potential to constant electric current is found to instill more stability on the system. Besides, increase in the AC electric Rayleigh number and the Biot number is to reduce the size of convection cells. [ABSTRACT FROM AUTHOR]

The onset of instability in a layer of dielectric micropolar fluid under the simultaneous action of an AC electric field and temperature gradient has been investigated. The dispersion relation has been derived and various critical values of non-dimensional Rayleigh number in the fluid layer have been determined. The influence of micropolar viscosity and electric Rayleigh number on the onset of convection has been analyzed. Thermal Rayleigh number has been computed for various values of electric Rayleigh number for the onset of instability. The stabilizing and destabilizing effects of electric Rayleigh number, micropolar viscosity and Prandtl number have been discussed. [ABSTRACT FROM AUTHOR]

Abstract: The simultaneous effect of a vertical AC electric field and rotation on the onset of thermal convective instability in a horizontal rotating dielectric fluid layer is studied by performing linear stability analysis. The lower and upper boundaries of the fluid layer are considered to be either rigid or free and either isothermal or insulated to temperature perturbations. The resulting eigenvalue problem is solved exactly for free–free isothermal boundaries. It is observed that the oscillatory convection is not a preferred mode of instability for dielectric fluids and the necessary conditions for its occurrence are independent of applied vertical AC electric field. For the other combinations of velocity and temperature boundary conditions, the problem is solved numerically using the Galerkin method. The similarities and differences between the results of isothermal and insulated boundaries are highlighted. It is noted that the effect of increasing AC electric Rayleigh number is to increase the transfer of heat more effectively and hence to hasten the onset of convection. To the contrary, the effect of rotation is to delay the electrothermal convection for a fixed type of boundary conditions. Although the rigid–rigid boundaries enhance the stability when compared to rigid–free and free–free boundaries up to moderate values of Taylor number, the situation is reversed at high Taylor number domain. This trend depends on the temperature boundary conditions as well. [Copyright &y& Elsevier]

Abstract: The combined effects of vertical d.c. electric field and uniform internal heat generation on the onset of convection in a horizontal poorly conducting dielectric fluid layer heated uniformly from below are investigated. The Galerkin method is used to solve the resulting eigenvalue problem. Parametric study is conducted to know the effects of varying electric Rayleigh number, R e and dimensionless heat source strength, N s . It is found that these two parameters exhibit a dual effect on the onset of natural convection; a result noticed in contrast to their effects when they are acting in isolation. [Copyright &y& Elsevier]

Research on the improvement of the heat transfer performance by forming a voltage difference in the dielectric fluid has been actively conducted in the recent years. This study investigates the electro-thermo-convective flow in a two-dimensional (2D) square cavity composed of cold right and hot left walls. We introduce herein the results of the heat transfer enhancement when positive and grounded electrodes are alternately arranged on each vertical wall instead of installing the same kind of electrode (positive or grounded electrode) on the entire surface of a vertical wall. The case of alternately arranged electrodes demonstrates that the heat transfer coefficient increases more than twice compared to that of the single kind of electrode. The heat transfer enhancement by the electric field is maximized in the low Rayleigh condition. In the Ra = 2000 and T = 1000 condition, the alternately placed electrodes accomplished a 10 times higher heat transfer coefficient when compared to the pure natural convection. The heat transfer results of using a silicon oil have been summarized for the Rayleigh number range of 2000 to 106 and electrical Rayleigh number of 0 to 1000. [ABSTRACT FROM AUTHOR]