Search

This paper examines the effect of rotation on thermal instability under Hele-Shaw cell saturated by Casson nanofluid using both linear and nonlinear ways. The nanofluid model incorporates Brownian and thermophoresis diffusion. While conducting an analysis of nonlinear stability numerically using the truncated Fourier series method, analysis of linear stability is performed analytically using the normal mode methodology. The outcomes are all displayed graphically. The results demonstrate that the rotation has dual effect on Hele-Shaw parameter as well as Casson parameter, for higher value of rotation it has destabilizing effect and it stabilizing  the system for lower values of rotation. Lewis number and concentration Rayleigh number promote the onset of convective motion within the system. On the other hand, rotation stabilize the system. Understanding the behavior of heat and mass transportation, the concentration of nanoparticles and fluid phase, utilize the Nusselt number when Nusselt numbers are assessed as a function of time, it is found that the variation of the rotation, Hele-Shaw and Casson parameter has a major influence on the heat and mass transfer. Both steady and unsteady weakly nonlinear analyses are performed to understand the heat transport in the system. It is concluded that the Casson nanofluid parameter has both stabilizing and destabilizing impact depending upon the rate of rotation and therefore this work can be possibly utilized in both places, where heat removal and heat conservation are required. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The purpose of this article is to analyze, theoretically, the effect of modulation on rotating Brinkman-Lapwood convection, i.e., buoyancy-driven convection in a sparse porous medium subjected to rotation. Darcy-Brinkman momentum equation with Coriolis term has been used to describe the flow. The system is considered rotating about an axis with non-uniform rotation speed. In particular, we assume that the rotation speed is varying sinusoidally with time. A linear stability analysis has been performed to find the critical Rayleigh number in modulated case. The effect of modulated rotation speed is found to have a stabilizing effect on the onset of convection for different values of modulation frequency and the other physical parameters involved. [ABSTRACT FROM AUTHOR]

The effect of temperature modulation on the onset of thermal convection in an electrically conducting fluid-saturated-porous medium, heated from below, has been studied using linear stability analysis. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small. The porous medium is confined between two horizontal walls and subjected to a vertical magnetic field; flow in porous medium is characterized by Brinkman-Darcy model. Considering only infinitesimal disturbances, and using perturbation procedure, the combined effect of temperature modulation and vertical magnetic field on thermal instability has been studied. The correction in the critical Rayleigh number is calculated as a function of frequency of modulation, Darcy number, Darcy Chandrasekhar number, magnetic Prandtl number, and the nondimensional group number χ. The influence of the magnetic field is found to be stabilizing. Furthermore, it is also found that the onset of convection can be advanced or delayed by proper tuning of the frequency of modulation. The results of the present model have been compared with that of Darcy model. [ABSTRACT FROM AUTHOR]

Thermal instability in an electrically conducting fluid saturated porous medium, confined between two horizontal walls, has been investigated in the presence of an applied vertical magnetic field and rotation, using the Brinkman model. The temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent oscillatory part. Only infinitesimal disturbances are considered. The combined effect of permeability, rotation, vertical magnetic field, and temperature modulation has been investigated using Galerkin's method and Floquet theory. The value of the critical Rayleigh number is calculated as function of amplitude and frequency of modulation, Chandrasekhar number, Taylor number, porous parameter, Prandtl number, and magnetic Prandtl number. It is found that rotation, magnetic field, and porous medium all have a stabilizing influence on the onset of thermal instability. Further, it is also found that it is possible to advance or delay the onset of convection by proper tuning of the frequency of modulation of the walls' temperature. In addition the results corresponding to the Brinkman model and Darcy model have been compared for neutral instability. [ABSTRACT FROM AUTHOR]

This paper studies the effect of local thermal nonequilibrium (LTNE) on the thermal instability in a horizontal layer of a Newtonian nanofluid. The nanofluid layer incorporates the effect of Brownian motion along with thermophoresis. A two temperature model has been used for the effect of LTNE among the particle and fluid phases. The boundary condition involved assumes that the nano-concentration flux is zero thereat, including the effect of thermophoresis. The linear stability is based on normal mode technique and for nonlinear analysis, a minimal representation of the truncated Fourier series analysis involving only two terms has been used. The effect of various parameters on Rayleigh number has been presented graphically. A weak nonlinear theory based on the truncated representation of Fourier series me thod has been used to obtain the thermal Nusselt number, whose variation with respect to various parameters has been depicted graphically. [ABSTRACT FROM AUTHOR]