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Nanofluid has emerged as a remarkable heat and mass transfer fluid due to its thermal characteristics. Despite this, continuing research is required to address problems in real applications and offer a solution for controlling transfer analysis. Therefore, in this study, the authors intend to model (Ginzburg–Landau equation) and analyze the two-dimensional nanofluid convection with gravity modulation. The perturbed analysis is adapted to convert the leading equations into Ginzburg–Landau equation. Lower amplitude (δ\delta values from 0 to 0.5) values are taken since they influence transfer analysis. The values of Pr are considered as 0 to 2 to retain the local acceleration term in the system of equations. A lower amount of frequency of modulation (Ω\Omega values from 0 to 70) is sufficient to enhance the heat and mass transfer rates. It is found that g-jitter and concentration Rayleigh numbers control the stability of the system. The Prandtl number and the amplitude of modulation enhance nano-heat and nano-mass transfer. This shows a destabilizing effect of modulation on nano-convection. Also the nano-Rayleigh number Rn has a dual nature on the kinetic energy transfer for positive and negative signs. A comparison is made between modulated and unmodulated systems, and it is found that the modulated systems influences the stability problem than the unmodulated systems. Finally, it is found that g-jitter influences effectively to regulate the transport process in the layer.

The present study investigates the gyrotactic microorganism flow in a rotating porous medium containing Newtonian fluid. Using gravity modulation, Darcy–Brinkman biothermal convection is examined. Linear theory describes the stationary convective mode which derives the expression for critical Rayleigh number. This indicates the onset of bioconvection. The system's marginal stability is demonstrated by graphical and tabular representation which has a good agreement with each other. The Ginzburg–Landau equation governs the Nusselt number, which is used to further explore heat transfer. The study provides an explanation and graphical representation of the effects of the following factors on heat transfer: cell eccentricity, modified Vadasz number and bioconvective Rayleigh–Darcy number, modulation frequency, and amplitude along with Taylor number. The mean Nusselt number has been plotted in the current study. The effect of rotating porous media and gravity modulation is explained in this work. Additionally, a comparison graph is plotted to examine the effects of gravity, both modulated and unmodulated, on the Nusselt number. This demonstrates how well gravity modulation on rotating porous media controls the system's heat transfer. A comparison between numerical and analytical results for unmodulated cases is also explained graphically. [ABSTRACT FROM AUTHOR]

The effect of gravity-field modulation is investigated in a nano liquid-confined Hele-Shaw cell. This study aims to finish the work described in (S. N. Rai, B. S. Bhadauria, K. Anish, and B. K. Singh, "Thermal instability in nanoliquid under four types of magnetic-field modulation within Hele-Shaw cell," Int. J. Heat Mass Transfer, vol. 145, no. 7, p. 072501, 2023) for oscillatory convection. The existence of the complex Ginzburg-Landau equation (CGLE) model is constrained by the requirement ω2 > 0. The magnetic fluxes in the Hele-shaw cell are governed by CGLE with g-jitter. The quantity of heat-mass transfer is examined in the presence of a g-jitter. In addition, the findings of our research on transport analysis indicate that oscillatory mode is preferable to stationary mode. It is also found that the gravity-driven Hele-Shaw layer has lower transport properties. Further, the transport analysis is compared to previous research and shown to have improved results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The stability of nonlinear nanofluid convection is examined using the complex matrix differential operator theory. With the help of finite amplitude analysis, nonlinear convection in a porous medium is investigated that has been saturated with nanofluid and subjected to thermal modulation. The complex Ginzburg-Landau equation (CGLE) is used to determine the finite amplitude convection in order to evaluate heat and mass transfer. The small amplitude of convection is considered to determine heat and mass transfer through the porous medium. Thermal modulation of the system is predicted to change sinusoidally over time, as shown at the boundary. Three distinct modulations IPM, OPM, and LBMOhave been investigated and found that OPM and LBMO cases are used to regulate heat and mass transfer. Further, it is found that modulation frequency (ωf varying from 2 to 70) reduces heat and mass transfer while modulation amplitude (δ1varying from 0.1 to 0.5) enhances both. [ABSTRACT FROM AUTHOR]

This paper deals with a mathematical model of controlling heat transfer in nanofluids. The time-periodic vertical vibrations of the system are considered to effect an external control of heat transport along with internal heating effects. A weakly non-linear stability analysis is based on the five-mode Lorenz model using which the Nusselt number is obtained as a function of the thermal Rayleigh number, nano-particle concentration based Rayleigh number, Prandtl number, Lewis number, modified diffusivity ratio, amplitude and frequency of modulation. It is shown that modulation can be effectively used to control convection and thereby heat transport. Further, it is found that the effect of internal Rayleigh number is to enhance the heat and nano-particles transport.

The effect of throughflow and temperature modulation on rotating porous medium is in- vestigated. Weakly nonlinear flow model is considered to study heat transfer with oscillatory mode of convection. Heat transfer is measured in terms of the Nusselt number, which is governed by the non--autonomous complex Ginzburg--Landau equation. Both concepts of rotation and throughflow are used as an external mechanism to regulate heat transfer. The amplitude and frequency of modula- tion show significant effect on heat transport. Throughflow has duel effect on heat transfer depending its direction. The outflow enhances and inflow diminishes the heat transfer. Similarly high rotation rates promotes heat transfer and low rotation rates diminish heat transfer. Further, the effect of mod- ulation on mean Nusselt number is discussed. The results computed numerically using Runge-Kutta- Fehlberg Method. [ABSTRACT FROM AUTHOR]

A study of thermal instability driven by buoyancy force is carried out in an initially quiescent infinitely extended horizontal rotating fluid layer. The temperature at the boundaries has been taken to be time-periodic, governed by the sinusoidal function. A weakly nonlinear stability analysis has been performed for the oscillatory mode of convection, and heat transport in terms of the Nusselt number, which is governed by the complex form of Ginzburg-Landau equation (CGLE), is calculated. The influence of external controlling parameters such as amplitude and frequency of modulation on heat transfer has been investigated. The dual effect of rotation on the system for the oscillatory mode of convection is found either to stabilize or destabilize the system. The study establishes that heat transport can be controlled effectively by a mechanism that is external to the system. Further, the bifurcation analysis also presented and established that CGLE possesses the supercritical bifurcation. [ABSTRACT FROM AUTHOR]

Weak nonlinear hydrodynamic thermal instability analysis has been performed for double diffusive oscillatory mode of convection in a horizontal layer of viscoelastic fluid, heated from below. Employing complex non-autonomous Ginzburg–Landau equation, effects of various viscoelastic parameters on thermal instability have been investigated. The weak nonlinear analysis reveals that values of viscoelastic parameters have significant effect on the instability. The present study is to investigate the effect of time-periodic temperature modulation on heat and mass transfer, where controlling convection external to the system is important. Sinusoidal profile is taken to modulate the temperature of the boundaries. It is found that the variation of Nusselt number and Sherwood number with respect to the slow time scale becomes rapid as either increasing Rs , Pr , λ , δ or decreasing Γ , ε , Ω . Further, it is found that in-phase temperature modulation has negligible effect, while out of phase temperature modulation and only lower plate temperature modulation have oscillatory effects on heat and mass transport. [ABSTRACT FROM AUTHOR]