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We have investigated the study of double diffusive stationary convection in the presence of applied magnetic field and internal heating. A weakly nonlinear stability analysis has been performed using the finite amplitude Ginzburg-Landau model. This finite amplitude of convection is obtained at third order of the system. It is assumed that the buoyancy term has two parts, steady and oscillatory parts. The second part is varying sinusoidally with time and vibrates the system with finite amplitude δ1 and frequency ω. The effects of δ1 and on heat/mass transports have been analysed and depicted graphically. The studies are established that the heat/mass transports can be controlled effectively by gravity modulation. Further, it is found that internal Rayleigh number Ri is to enhance heat transfer and reduces the mass transfer in the system.

Weakly nonlinear stability analysis has been performed using the finite amplitude Ginzburg-Landau model. The layer is oscillating vertically in sinusoidal manner. Using the finite amplitude analysis heat mass/transfer is quantified in the system. The disturbances of the flow are expanded in power series of small parameter. In addition to the modulation, the effect of throughflow is discussed on heat/mass transfer in the system. The values of viscoelastic parameters are considered in this paper are λ1 > λ2 and Γ < 1 to validate the problem. The time relaxation parameter λ1 has destabilizing effect, while the time retardation parameter λ2 has stabilizing effect on the system. The effects of amplitude and frequency of modulation on heat/mass transports have been analyzed and depicted graphically. The studies establish that the heat/mass transports can be controlled effectively by g-jitter and throughflow. Further, it is found that better results may obtain for an oscillatory mode of convection.

This communication explores the significance of suction/injection for gravity modulation mixed convection in micropolar fluid flow due to an inclined sheet in the presence of magnetic field and thermal radiation. In recent years, very extensive modern technological applications have rise the interest in mixed convection controlled by g-jitter forces associated with microgravity. The novelty of the present study is effects of g-jitter on dynamics of micropolar fluid adjustable inclination to the sheet taken into account. Mathematical formulation based on usual laws of conservation is non dimensionalized with emerging parameters through implementation of similarity transform to yield a corresponding set of partial differential equations. In the face of convective non linearity combined with coupling due to mixed convection and micropolarity, a finite element discretization is harnessed to be coded and run on Matlab platform. The credibility of numerical procedure is assured for its acceptable adoption with the established results. The growing strength of amplitude of modulation is showing proportional decrease and increase in the fluctuation of heat transfer and skin friction coefficients, and the fluctuation of reduced skin friction factor, couple stress, and Nusselt number improves with larger inputs of amplitude. These findings would be helpful to experts dealing with upper space heat transportation, performance of materials such as crystals and effectiveness of chemical catalytic reactors.

This paper investigates the effect of gravity modulation on Rayleigh–Bénard convection using the rigid isothermal boundary conditions. We calculate heat transfer results using the Nusselt and mean Nusselt numbers through the finite-amplitude of convection, which we got from the Ginzburg–Landau equation (GLE). The Ginzburg–Landau equation is derived analytically from the Fredholm solvability condition at third order. The finite amplitude equation (GLE) is a function of system parameters and solved numerically. The gravity modulation considered in terms of steady and sinusoidal parts. The sinusoidal part defines gravity modulation in terms of amplitude and frequency. Our study shows that gravity modulation controls the heat transfer results. The amplitude of modulation enhances heat transfer for low frequencies and diminishes for high frequencies. Further, we found that rigid isothermal boundary conditions are diminishing heat transfer than free and isothermal boundaries. Finally, we concluded that rigid isothermal boundary conditions and gravity modulation controls heat transfer results.

We explore the modifications brought about by gravity modulation in self-aligned two-dimensional (2D) stationary rolls and higher-order convective instabilities with horizontal magnetic field. The Chandrasekhar number plays no role in determining critical values of the forcing parameters for convection to begin. The onset is in the form of 2D rolls with periodically varying intensity. The external magnetic field is solely responsible for aligning the rolls while the induced magnetic field comes into play after three-dimensional convection sets in. Gravity modulation destabilizes the system and results in chaotic flow much earlier above onset.

The present article aims at investigating the effect of gravity modulation on chaotic convection of a viscoelastic fluid in porous media. For this, the problem is reduced into Lorenz system (non-autonomous) by employing the truncated Galerkin expansion method. The system shows transitions from periodic to chaotic behavior on increasing the scaled Rayleigh number R. The amplitude of modulation advances the chaotic nature in the system while the frequency of modulation has a tendency to delay the chaotic behavior which is in good agreement with the results due to [1]. The behavior of the scaled relaxation and retardation parameter on the system is also studied. The phase portrait and time domain diagrams of the Lorenz system for suitable parameter values have been used to analyze the system.

Thermovibrational flow can be seen as a variant of standard thermogravitational convection where steady gravity is replaced by a time-periodic acceleration. As in the parent phenomena, this type of thermal flow is extremely sensitive to the relative directions of the acceleration and the prevailing temperature gradient. Starting from the realization that the overwhelming majority of research has focused on circumstances where the directions of vibrations and of the imposed temperature difference are perpendicular, we concentrate on the companion case in which they are parallel. The increased complexity of this situation essentially stems from the properties that are inherited from the corresponding case with steady gravity, i.e., the standard Rayleigh&ndash, B&eacute, nard convection. The need to overcome a threshold to induce convection from an initial quiescent state, together with the opposite tendency of acceleration to damp fluid motion when its sign is reversed, causes a variety of possible solutions that can display synchronous, non-synchronous, time-periodic, and multi-frequency responses. Assuming a square cavity as a reference case and a fluid with Pr = 15, we tackle the problem in a numerical framework based on the solution of the governing time-dependent and non-linear equations considering different amplitudes and frequencies of the applied vibrations. The corresponding vibrational Rayleigh number spans the interval from Ra&omega, = 104 to Ra&omega, = 106. It is shown that a kaleidoscope of possible variants exist whose nature and variety calls for the simultaneous analysis of their temporal and spatial behavior, thermofluid-dynamic (TFD) distortions, and the Nusselt number, in synergy with existing theories on the effect of periodic accelerations on fluid systems.

In the present paper, we deal with the effect of G-jitter (time periodic gravity modulation) on the stability of double diffusive convection in couple stress liquid by method of non-linear analysis. The infinitesimal disturbances are expanded in terms of power series of amplitude of modulation. Couple stress term has been employed in momentum equation. For the stationary convection, the Ginzburg–Landau equation has been used to investigate the effect of modulation on heat and mass transfer. The effect of Prandtl number, couple stress parameter, Lewis number and solute Rayleigh number has also been investigated. Keywords: Rayleigh–Benard convection, Couple stress liquid, Gravity modulation, Ginzburg–Landau equation

In this research article, we investigated the weakly non-linear effect of gravity modulation for the temperature dependent viscous fluid in a horizontal porous layer in the presence of internal heat source. We use power series expansion in terms of the amplitude of gravity modulation, which is considered to be small for double-diffusive convection in porous media. We graphically show the effect of internal heat source, solute Rayleigh number, Lewis number, Vadász number, thermo-rheological parameter, the amplitude of gravity modulation, the frequency of modulation on the heat and mass transfer using Ginzburg-Landau equation. The effect of gravity modulation is found significant and is more effective for the low values of frequency of modulation.

On the basis of Darcy-Brinkman model, the chaotic convection in a couple stress fluid saturated porous media under gravity modulation is investigated using the nonlinear stability analyses. The transition from steady convection to chaos is analysed with the effect of Darcy-Brinkman couple stress parameter and the gravity modulation. The results show that the chaotic behavior is connected with the critical value of Rayleigh number which is dependent upon the oscillation frequency and the Darcy-Brinkman couple stress parameter. If the oscillation frequency Ω is not zero, the Rayleigh number value R of the chaotic behavior increases with the increase of the Darcy-Brinkman couple stress parameter. The Darcy-Brinkman couple stress parameter and the gravity modulation decrease the rate of heat transfer. Keywords: Darcy-Brinkman model, Gravity modulation, Nonlinear stability, Chaotic convection

In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.

This paper carried out a nonlinear thermal convection in a porous medium saturated with viscoelastic nanofluid under vibrations. The Darcy model has been used for the porous medium, while the nanofluid layer incorporates the effect of Brownian motion along with thermophoresis. An Oldroyd-B type constitutive equation was used to describe the rheological behavior of viscoelastic nanofluids. The non-uniform vertical vibrations of the system, which can be realized by oscillating the system vertically, is considered to vary sinusoidally with time. In order to find the heat and mass transports for unsteady state, a nonlinear analysis, using a minimal representation of the truncated Fourier series of two terms, has been performed. Effect of various parameters has been investigated on heat and mass transport and then presented graphically. It is found that gravity modulation can be used effectively to regulate either heat or mass transports in the system.

The effect of vertical throughflow and time-periodic gravity field has been investigated on Darcy convection. The amplitude of gravity modulation is considered to be very small and the disturbances are expanded in terms of power series of amplitude of convection. A weak nonlinear stability analysis has been performed for the stationary mode of convection. As a consequence heat transport evaluated in terms of the Nusselt number, which is governed by the non-autonomous Ginzburg-Landau equation. Throughflow can stabilize or destabilize the system for stress free and isothermal boundary conditions. The amplitude and frequency of modulation, Prandtl Darcy number on heat transport have been analyzed and depicted graphically. Further, the study establishes that the heat transport can be controlled effectively by a mechanism that is external to the system. Finally flow patterns are presented in terms of streamlines and isotherms.

The effect of vertical throughflow and internal heating effects on fluid saturated porous medium under gravity modulation is investigated. The amplitude of modulation is considered to be very small and the disturbances are expanded in terms of power series of amplitude of convection. A weakly nonlinear stability analysis is proposed to study stationary convection. The Nusselt number is obtained numerically to present the results of heat transfer while using Ginzburg–Landau equation. The vertical throughflow has dual effect either to destabilize or to stabilize the system for downward or upward directions. The effect of internal heat source ( R i > 0 ) enhances or sink ( R i 0 ) diminishes heat transfer in the system. The amplitude and frequency of modulation have the effects of increasing or diminishing heat transport. For linear model Venezian approach suggested that throughflow and internal heating have both destabilizing and stabilizing effects for suitable ranges of Ω . Further, the study establishes that heat transport can be controlled effectively by a mechanism that is external to the system throughflow and gravity modulation.

This study examines the effects of asymmetric gravity modulation in a horizontal layer and a closed cavity heated from below, and the effects of asymmetric rotational oscillations of a closed cavity heated from below. The critical modulation amplitude is obtained as a function of the asymmetry parameter for microgravity, and the limiting flow characteristics as a function of the asymmetry parameter. It is shown that the asymmetry of rotational oscillations of the closed cavity influences the critical amplitude and the bifurcation diagram.

The outset of convection in a thin layer of couple stress fluid is analyzed using the linear stability analysis when the fluid is heated from below. In order to assimilate the inertial effects Maxwell-Cattaneo law is used in lieu of the classical Fourier's heat conduction law. The normal mode analysis is used to arrive at the eigenvalues of the perturbed state and a regular perturbation method to find the analytical solutions. The effect of Cattaneo number, couple stress parameter and Prandtl number is discussed and it is concluded that gravity modulation can delay or advance the onset of convection.

The effect of gravity modulation on the onset of convection in a horizontal layer of viscoelastic Oldroyd fluid heated from below is considered. The analytical solution of the problem has been obtained for the case of stress-free boundaries and rectangular modulation. It has been shown that depending on the parameter values, the modulation can produce either stabilizing or destabilizing effects. The deformation retardation always exerts a stabilizing effect, which is most pronounced in the shortwave range. The numerical results obtained by the solution of full nonlinear problems agree well with the results of linear stability analysis.

The characteristics of natural convection in a rectangular cavity with simultaneous thermocapillary and gravity modulation effects have been studied numerically. Because of the practical applications, the simulation focuses on low-Prandtl-n umber and zero-gravity situations. The two-dimensional, time-dependent NavierStokes and energy equations are numerically integrated by a semi-implicit time-splitting method. For a specific Rayleigh number, Prandtl number, and Marangoni number, the problem is investigated for different modulation frequencies and directions. From the results, it can be concluded that thermocapillarity seriously affected the flowfield, especially in high-frequency cases.

The stability of a horizontal layer of fluid heated from above or below is examined for the case of a time-dependent buoyancy force which is generated by shaking the fluid layer, thus causing a sinusoidal modulation of the gravitational field. A linearized stability analysis is performed to show that gravity modulation can significantly affect the stability limits of the system. In this analysis, much emphasis is placed on qualitative results obtained by an approximate solution, which permits a rather complete stability analysis. A useful mechanical analogy is developed by considering the effects of gravity modulation on a simple pendulum. Finally, some effects of finite amplitude flows are considered and discussed.