Hydrodynamic and hydromagnetic stability

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Buoyancy Effects In Fluids

The onset of nanofluid convection in the presence of an externally applied magnetic field is investigated numerically based on the non-homogeneous Buongiorno’s mathematical model. In this study, we use the latest experimental correlations and powerful analytical models for expressing the thermo-physical properties of some electrically conducting nanofluids, such as copper-water, sliver-water and gold-water nanofluids, in which the Brownian motion and thermophoresis effects on slip flow in nanofluids are taken into account in this model (i.e., two-phase transport model). In this paper, we assume that the nanofluid has Newtonian behavior, confined horizontally between two infinite impermeable boundaries and heated from below, in such a way that the nanoparticles tend to concentrate near the upper wall. Considering the basic state of the nanofluidic system, the linear stability theory has been successfully applied to obtain the principal stability equations, which are solved numerically for an imposed volumetric fraction of nanoparticles and no-slip impermeable conditions at the isothermal walls bounding the nanofluid layer. The linear boundary-value problem obtained in this investigation is converted into a pure initial-value problem, so that we can solve it numerically by the fourth-fifth-order Runge-Kutta-Fehlberg method. The generalized Buongiorno’s mathematical model proposed in this study allows performing a highly accurate computational analysis. In addition, the obtained results show that the stability of the studied nanofluidic system depends on several parameters, namely, the magnetic Chandrasekhar number Q , the reference value for the volumetric fraction of nanoparticles $ \phi_0$
 and the size of nanoparticles $ d_p$
 . In this analysis, the thermo-hydrodynamic stability of the studied nanofluid is controlled through the critical thermal Rayleigh number $ R_{ac}$
 , which characterizes the onset of convection cells, whose size is $ L_c=2\pi/a_c$
 . Furthermore, the effects of various pertinent parameters on the critical stability parameters $ R_{ac}$
 and $ a_c$
 are discussed in more detail through graphical and tabular illustrations, for three types of nanofluids including copper-water, sliver-water, and gold-water.

Influence of a uniform transverse magnetic field on the thermo-hydrodynamic stability in water-based nanofluids with metallic nanoparticles using the generalized Buongiorno’s mathematical model

Thermodynamic modeling and multi-objective optimization of two stage thermoelectric generator in electrically series and parallel configuration

A comprehensive review on convective heat transfer of nanofluids in porous media: Energy-related and thermohydraulic characteristics

Chaotic and oscillatory magneto-convection in a binary viscoelastic fluid under g-jitter

Thermal instability in a horizontal porous medium saturated with temperature-dependant viscous fluid has been considered, and the effect of time-periodic temperature modulation has been investigated. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small and the disturbances are expanded in terms of power series of amplitude of convection. A weak non-linear stability analysis has been performed for the stationary mode of convection, and heat transport in terms of the Nusselt number, which is governed by the non-autonomous Ginzburg–Landau equation, is calculated. The effects of thermo-rheological parameter, amplitude and frequency of modulation, thermo-mechanical anisotropies, and Vadasz number on heat transport have been analyzed and depicted graphically. It is found that an increment in the value of thermo-rheological parameter results in the enhancement of heat transport in the system. Further, the study establishes that the heat transport can be controlled effectively by a mechanism that is external to the system.

Heat Transport in an Anisotropic Porous Medium Saturated with Variable Viscosity Liquid Under Temperature Modulation

Effect of rotational speed modulation on heat transport in a fluid layer with temperature dependent viscosity and internal heat source

Using a complex non-autonomous Ginzburg–Landau equation, we have investigated oscillatory Rayleigh–Benard convection under Gravity modulation, considering a viscoelastic fluid layer. The influence of (stress) relaxation and (strain) retardation times of viscoelastic fluid on heat transfer has been discussed. The study establishes that the heat transport can be controlled effectively by a mechanism that is external to the system. Modulation has a destabilization effect at low frequencies and a stabilization effect at high frequencies, which increases with increasing the amplitude of modulation. Finally, it is found that overstability advances the onset of convection, hence increases heat transfer.

Weak non-linear oscillatory convection in a viscoelastic fluid layer under gravity modulation

A study of thermal instability driven by buoyancy force is carried out in an initially quiescent infinitely extended horizontal porous medium saturated with viscoelastic fluid. Modified Darcy’s law is used to explain characteristics of fluid motion. The time periodic gravity field has been considered, and its effect on the system has been investigated. A weak 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 non-autonomous Ginzburg–Landau equation, is calculated. The influence of relaxation and retardation times of viscoelastic fluid on heat transfer has been discussed. Further, the study establishes that the heat transport can be controlled effectively by a mechanism that is external to the system. Finally, it is found that overstability advances the onset of convection, and hence increases heat transfer.

Palle Kiran

Papers

Chaotic and oscillatory magneto-convection in a binary viscoelastic fluid under g-jitter

Heat Transport in an Anisotropic Porous Medium Saturated with Variable Viscosity Liquid Under Temperature Modulation

Effect of rotational speed modulation on heat transport in a fluid layer with temperature dependent viscosity and internal heat source

Weak non-linear oscillatory convection in a viscoelastic fluid layer under gravity modulation

Weak Nonlinear Oscillatory Convection in a Viscoelastic Fluid-Saturated Porous Medium Under Gravity Modulation