scholarly journals Double-Diffusive Convection in Presence of Compressible Rivlin-Ericksen Fluid with Fine Dust

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Mahinder Singh ◽  
Rajesh Kumar Gupta
Keyword(s):  
Normal Modes ◽  
Suspended Particles ◽  
Double Diffusive Convection ◽  
Fine Dust ◽  
Stationary Convection ◽  
Viscoelastic Parameter ◽  
Diffusive Convection ◽  
Rayleigh Numbers ◽  
Solute Gradient ◽  
Double Diffusive

An investigation is made on the effect of suspended particles (fine dust) on double-diffusive convection of a compressible Rivlin-Ericksen elastico-viscous fluid. The perturbation equations are analyzed in terms of normal modes after linearizing the relevant set of equations. A dispersion relation governing the effects of viscoelasticity, compressibility, stable solute gradient, and suspended particles is derived. For stationary convection, Rivlin-Ericksen fluid behaves like an ordinary Newtonian fluid due to the vanishing of the viscoelastic parameter. The stable solute gradient compressibility has a stabilizing effect on the system whereas suspended particles hasten the onset of thermosolutal instability. The Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behaviour of various parameters on Rayleigh numbers has been depicted graphically. It has been observed that oscillatory modes are introduced due to the presence of viscoelasticity, suspended particles, and stable solute gradient which were not existing in the absence of these parameters.

scholarly journals Thermal convection of dusty compressible Rivlin-Ericksen viscoelastic fluid with hall currents

2012 ◽  
Vol 16 (1) ◽  
pp. 177-192 ◽  
Author(s):  
Urvashi Gupta ◽  
Parul Aggarwal ◽  
Kumar Wanchoo
Keyword(s):  
Magnetic Field ◽  
Thermal Instability ◽  
Normal Modes ◽  
Suspended Particles ◽  
Stationary Convection ◽  
Viscoelastic Parameter ◽  
Electrically Conducting ◽  
Stabilizing Effect ◽  
The Stability ◽  
Rayleigh Numbers

An investigation is made on the effect of Hall currents and suspended particles on the hydromagnetic stability of a compressible, electrically conducting Rivlin-Ericksen elastico-viscous fluid. The perturbation equations are analyzed in terms of normal modes after linearizing the relevant set of hydromagnetic equations. A dispersion relation governing the effects of viscoelasticity, magnetic field, Hall currents, compressibility and suspended particles is derived. For the stationary convection Rivlin-Ericksen fluid behaves like an ordinary Newtonian fluid due to the vanishing of the viscoelastic parameter. Compressibility and magnetic field are found to have a stabilizing effect on the system whereas Hall currents and suspended particles hasten the onset of thermal instability. These analytic results are confirmed numerically and the effects of various parameters on the stability parameter are depicted graphically. The critical Rayleigh numbers and the wavenumbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behavior of various parameters on critical thermal Rayleigh numbers has been depicted graphically. It has been observed that oscillatory modes are introduced due to the presence of viscoelasticity, suspended particles and Hall currents which were not existing in the absence of these parameters.

scholarly journals On thermosolutal convection in presence of compressible fluid with fine dust

2014 ◽  
Vol 19 (1) ◽  
pp. 133-143
Author(s):  
M. Singh ◽  
R.K. Gupta
Keyword(s):  
Viscous Fluid ◽  
Compressible Fluid ◽  
Suspended Particles ◽  
Thermosolutal Convection ◽  
Fine Dust ◽  
Stationary Convection ◽  
Onset Of Convection ◽  
Stabilizing Effect ◽  
Dust Effect ◽  
Solute Gradient

Abstract A layer of a Rivlin-Ericksen elastico-viscous fluid heated and soluted from below in the presence of compressibility and suspended particles (fine dust) effect is considered. For stationary convection, the Rivlin- Ericksen, elastico-viscous fluid behaves like a Newtonian fluid. The oscillatory modes are introduced due to the presence of a stable solute gradient, suspended particles destabilize the system whereas the stable solute gradient has a stabilizing effect on the system and the effect of compressibility is to postpone the onset of thermosolutal convection. The stable solute gradient and compressibility postpone the onset of convection, whereas the suspended particles hasten the onset of convection. The stable solute gradient introduces oscillatory modes in the systems which were non-existent in its absence

scholarly journals Thermal instability of compressible Walters’ (Model B′) fluid in the presence of Hall currents and suspended particles

2011 ◽  
Vol 15 (2) ◽  
pp. 487-500 ◽  
Author(s):  
Urvashi Gupta ◽  
Parul Aggarwal
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Thermal Instability ◽  
Normal Modes ◽  
Suspended Particles ◽  
Elastic Parameter ◽  
Stationary Convection ◽  
Electrically Conducting ◽  
Permissible Range ◽  
Rayleigh Numbers

Effect of Hall currents and suspended particles is considered on the hydromagnetic stability of a compressible, electrically conducting Walters? (Model B?) elastico-viscous fluid. After linearizing the relevant hydromagnetic equations, the perturbation equations are analyzed in terms of normal modes. A dispersion relation governing the effects of visco-elasticity, magnetic field, Hall currents and suspended particles is derived. It has been found that for stationary convection, the Walters? (Model B?) fluid behaves like an ordinary Newtonian fluid due to the vanishing of the visco-elastic parameter. The compressibility and magnetic field have a stabilizing effect on the system, as such their effect is to postpone the onset of thermal instability whereas Hall currents and suspended particles are found to hasten the onset of thermal instability for permissible range of values of various parameters. Also, the dispersion relation is analyzed numerically and the results shown graphically. The critical Rayleigh numbers and the wavenumbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behavior of various parameters on critical thermal Rayleigh numbers has been depicted graphically. The visco-elasticity, suspended particles and Hall currents (hence magnetic field) introduce oscillatory modes in the system which were non-existent in their absence.

Double-Diffusive Convection

2013 ◽  
Author(s):  
Gary A. Glatzmaier
Keyword(s):  
Oscillation Amplitude ◽  
Marginal Stability ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Nonlinear Simulations ◽  
Fingering Instability ◽  
Zero Growth ◽  
Salt Fingering ◽  
Rayleigh Numbers ◽  
Double Diffusive

This chapter discusses double-diffusive convection, with a particular focus on the initial instability and eventual nonlinear evolution. It first considers the “salt-fingering” instability and then the “semiconvection” instability before discussing the possibility that the onsets of these instabilities at marginal stability have an amplitude that oscillates in time. The goal is to find the conditions that would result in a zero growth rate of the oscillation amplitude in order to determine the marginal stability constraint on the Rayleigh numbers for the onset of an oscillating instability. The chapter also shows how, after evolving beyond the onset of the instability, thermal diffusion between the moving parcel and the surroundings can alter the initial linear vertical profile of the horizontal-mean temperature into a “staircase” profile. This evolution of the temperature profile is investigated via nonlinear simulations.

scholarly journals THE ONSET OF DOUBLE-DIFFUSIVE CONVECTION IN A LAYER OF NANOFLUID UNDER ROTATION

2016 ◽  
Vol 15 (1) ◽  
pp. 88
Author(s):  
G. C. Rana ◽  
R. C. Thakur
Keyword(s):  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Lewis Number ◽  
Linear Stability Theory ◽  
Mode Analysis ◽  
Brownian Diffusion ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Solute Gradient ◽  
Double Diffusive

Double-diffusive convection in a horizontal layer of nanofluid under rotation heated from below is studied. The nanofluid describes the effects of thermophoresis and Brownian diffusion. Based upon perturbations and linear stability theory, the normal mode analysis method is applied to obtain the dispersion relation characterizing the effect of different parameters when both the boundaries are free. Due to thermal expansion, the nanofluid at the bottom will be lighter than the fluid at the top. Thus, this is a top heavy arrangement which is potentially unstable. In this paper we discuss the influences of various non-dimensional parameters such as rotation, solute gradient, thermo- nanofluid Lewis number, thermo-solutal Lewis number, Soret and Dufour parameter on the stability of stationary convection for the case of free-free boundaries. It is observed that rotation and solute gradient have stabilizing influence on the system. Rotation and solute gradient play important role in the thermal convection of fluid layer and has applications in rotating machineries such as nuclear reactors, petroleum industry, biomechanics etc. and solute gradient finds applications in geophysics, food processing, soil sciences, oil reservoir modeling, oceanography etc. A very good agreement is found between the present paper and earlier published results.

scholarly journals On the Onset of Double-diffusive Convection in a Couple Stress Nanofluid in a Porous Medium

2018 ◽  
Vol 62 (3) ◽  
pp. 233-240
Author(s):  
Gian C. Rana ◽  
Ramesh Chand
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Couple Stress ◽  
Lewis Number ◽  
Double Diffusive Convection ◽  
Stationary Convection ◽  
Stress Parameter ◽  
Diffusive Convection ◽  
Double Diffusive ◽  
Solutal Rayleigh Number

Double-diffusive convection in a horizontal layer of nanofluid in a porous medium is studied. The couple-stress fluid model is considered to describe the rheological behavior of the nanofluid and for porous medium Darcy model is employed. The model applied for couple stress nanofluid incorporates the effect of Brownian motion and thermophoresis. We have assumed that the nanoparticle concentration flux is zero on the boundaries which neutralizes the possibility of oscillatory convection and only stationary convection occurs. The dispersion relation describing the effect of various parameters is derived by applying perturbation theory, normal mode analysis method and linear stability theory. The impact of various physical parameters, like the couple stress parameter, medium porosity, solutal Rayleigh Number, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have been examined on the stationary convection. It is observed that the couple stress parameter, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have stabilizing effects on the stationary convection whereas the solutal Rayleigh number and Dufour parameter have very small effect on the system.

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