scholarly journals The onset of thermal convection in couple-stress fluid in hydromagnetics saturating a porous medium

2014 ◽  
Vol 62 (2) ◽  
pp. 357-362
Author(s):  
Gian C. Rana

Abstract In this paper, the effect of magnetic field on thermal convection in couple-stress fluid saturating a porous medium is considered. By applying linear stability theory and the normal mode analysis method, a mathematical theorem is derived which states that the viscoelastic thermal convection at marginal state, cannot manifest as stationary convection if the thermal Rayleigh number R, the medium permeability parameter Pι the couple-stress parameter F and the Chandrasekher number Q, satisfy the inequality the result clearly establishes the stabilizing character of couple-stress parameter and magnetic field whereas destabilizing character of medium permeability.

2011 ◽  
Vol 66 (5) ◽  
pp. 304-310 ◽  
Author(s):  
Pardeep Kumar ◽  
Hari Mohan

The double-diffusive convection in a compressible couple-stress fluid layer heated and soluted from below through porous medium is considered in the presence of a uniform vertical magnetic field. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the compressibility, stable solute gradient, magnetic field, and couple-stress postpone the onset of convection whereas medium permeability hastens the onset of convection. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient and magnetic field introduce oscillatory modes in the system, which were non-existent in their absence. A condition for the system to be stable is obtained by using the Rayleigh-Ritz inequality. The sufficient conditions for the non-existence of overstability are also obtained.


2016 ◽  
Vol 21 (1) ◽  
pp. 83-93 ◽  
Author(s):  
C.B. Mehta ◽  
M. Singh ◽  
S. Kumar

Abstract An investigation is made on the effect of Hall currents on thermal instability of a compressible couple-stress fluid in the presence of a horizontal magnetic field saturated in a porous medium. The analysis is carried out within the framework of the linear stability theory and normal mode technique. A dispersion relation governing the effects of viscoelasticity, Hall currents, compressibility, magnetic field and porous medium is derived. For the stationary convection a couple-stress fluid behaves like an ordinary Newtonian fluid due to the vanishing of the viscoelastic parameter. Compressibility, the magnetic filed and couple-stress parameter have stabilizing effects on the system whereas Hall currents and medium permeability have a destabilizing effect on the system, but in the absence of Hall current couple-stress has a destabilizing effect on the system. It has been observed that oscillatory modes are introduced due to the presence of viscoelasticity, magnetic field porous medium and Hall currents which were non-existent in their absence.


2021 ◽  
Vol 16 ◽  
pp. 68-78
Author(s):  
Pardeep Kumar ◽  
Gursharn Jit Singh

The thermal convection of a plasma in porous medium is investigated to include simultaneously the effect of rotation and the finiteness of the ion Larmor radius (FLR) in the presence of a vertical magnetic field. Following linear stability theory and normal mode analysis method, the dispersion relation is obtained. It is found that the presence of a uniform rotation, finite Larmor radius and magnetic field introduces oscillatory modes in the system which were, otherwise, non-existent in their absence. When the instability sets in as stationary convection, finite Larmor radius, rotation, medium permeability and magnetic field are found to have stabilizing (or destabilizing) effects under certain conditions. In the absence of rotation, finite Larmor radius has stabilizing effect on the thermal instability of the system whereas the medium permeability and the magnetic field may have stabilizing or destabilizing effect under certain conditions. The conditions κ<[ε+(1-ε) (ρ_S C_S)/(ρ_0 C)]η and κ<(ε^2 [ε+(1-ε) (ρ_S C_S)/(ρ_0 C)]ν)/(P^2 [εP{√U (x-2)+√(T_(A_1 ) )}^2-2Q_1 ] ) are the sufficient conditions for non-existence of overstability, the violation of which does not necessary involve an occurrence of overstability.


2016 ◽  
Vol 38 (1) ◽  
pp. 55-63
Author(s):  
Chander Bhan Mehta

Abstract The study is aimed at analysing thermal convection in a compressible couple stress fluid in a porous medium in the presence of rotation and magnetic field. After linearizing the relevant equations, the perturbation equations are analysed in terms of normal modes. A dispersion relation governing the effects of rotation, magnetic field, couple stress parameter and medium permeability have been examined. For a stationary convection, the rotation postpones the onset of convection in a couple stress fluid heated from below in a porous medium in the presence of a magnetic field. Whereas, the magnetic field and couple stress postpones and hastens the onset of convection in the presence of rotation and the medium permeability hastens and postpones the onset of convection with conditions on Taylor number. Further the oscillatory modes are introduced due to the presence of rotation and the magnetic field which were non-existent in their absence, and hence the principle of exchange stands valid. The sufficient conditions for nonexistence of over stability are also obtained.


2013 ◽  
Vol 35 (3) ◽  
pp. 45-56 ◽  
Author(s):  
S.K. Kango ◽  
G.C. Rana ◽  
Ramesh Chand

Abstract The Triple-Diffusive convection in Walters’ (Model B') fluid with varying gravity field is considered in the presence of uniform vertical magnetic field in porous medium. For the case of stationary convection, the magnetic field, varying gravity field and the stable solute gradients have stabilizing effects whereas the medium permeability has destabilizing (or stabilizing) effect on the system under certain conditions. A linear stability analysis theory and normal mode analysis method have been carried out to study the onset convection. The kinematic viscoelasticity has no effect on the stationary convection. The solute gradients, magnetic field, varying gravity field, porosity and kinematic viscoelasticity introduce oscillatory modes in the system, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained. The results are also shown graphically.


2014 ◽  
Vol 18 (suppl.2) ◽  
pp. 539-550 ◽  
Author(s):  
Kumar Aggarwal ◽  
Anushri Verma

The purpose of this paper is to study the effects of compressibility, rotation, magnetic field and suspended particles on thermal stability of a layer of visco-elastic Walters? (model) fluid in porous medium. Using linearized theory and normal mode analysis, dispersion relation has been obtained. In case of stationary convection, it is found that the rotation has stabilizing effect on the system. The magnetic field may have destabilizing effect on the system in the presence of rotation while in the absence of rotation it always has stabilizing effect. The medium permeability has destabilizing effect on the system in the absence of rotation while in the presence of rotation it may have stabilizing effect. The suspended particles and compressibility always have destabilizing effect. Due to vanishing of visco-elastic parameter, the compressible visco-elastic fluid behaves like Newtonian fluid. Graphs have also been plotted to depict the stability characteristics. The viscoelasticity, magnetic field and rotation are found to introduce oscillatory modes into the system which were non-existent in their absence.


2013 ◽  
Vol 18 (3) ◽  
pp. 871-886
Author(s):  
M. Singh ◽  
R.K. Gupta

Abstract The effect of Hall currents and suspended dusty particles on the hydromagnetic stability of a compressible, electrically conducting Rivlin-Ericksen elastico viscous fluid in a porous medium is considered. Following the linearized stability theory and normal mode analysis the dispersion relation is obtained. For the case of stationary convection, Hall currents and suspended particles are found to have destabilizing effects whereas compressibility and magnetic field have stabilizing effects on the system. The medium permeability, however, has stabilizing and destabilizing effects on thermal instability in contrast to its destabilizing effect in the absence of the magnetic field. The critical Rayleigh numbers and the wave numbers 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 are depicted graphically. The magnetic field, Hall currents and viscoelasticity parameter are found to introduce oscillatory modes in the systems, which did not exist in the absence of these parameters


2013 ◽  
Vol 35 (4) ◽  
pp. 75-88
Author(s):  
G.C. Rana ◽  
H.S. Jamwal

Abstract In this paper, the thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles (fine dust) in porous medium in hydromagnetics is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, magnetic field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection, Walters’ (Model B′) elastico-viscous fluid behaves like an ordinary Newtonian fluid and it is observed that rotation has stabilizing effect, suspended particles are found to have destabilizing effect on the system, whereas the medium permeability has stabilizing or destabilizing effect on the system under certain conditions. The magnetic field has destabilizing effect in the absence of rotation, whereas in the presence of rotation, magnetic field has stabilizing or destabilizing effect under certain conditions


2018 ◽  
Vol 15 (1) ◽  
pp. 148-155
Author(s):  
W. Stanly ◽  
R. Vasanthakumari

Purpose The purpose of this paper is used to study the combined effect of solute gradient and magnetic field on dusty couple-stress fluid in the presence of rotation through a porous medium. Design/methodology/approach The perturbation technique (experimental method) is applied in this study. Findings For the case of stationary convection, solute gradient and rotation have stabilizing effect, whereas destabilizing effect is found in dust particles in the system. Couple stress and medium permeability both have dual character to its stabilizing effect in the absence of magnetic field and rotation. Magnetic field succeeded in establishing a stabilizing effect in the absence of rotation. Originality/value The results are discussed by allowing one variable to vary and keeping other variables constant, as well as by drawing graphs.


2014 ◽  
Vol 6 (1) ◽  
pp. 24-45
Author(s):  
G. C. Rana

AbstractThe thermosolutal instability of Rivlin-Ericksen elasticoviscous rotating fluid permeated with suspended particles (fine dust) and variable gravity field in porous medium in hydromagnetics is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, magnetic field, gravity field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection, the rotation and stable solute gradient has stabilizing effects and suspended particles are found to have destabilizing effect on the system whereas the medium permeability has stabilizing or destabilizing effect on the system under certain conditions. The magnetic field has destabilizing effect in the absence of rotation whereas in the presence of rotation, magnetic field has stabilizing or destabilizing effect under certain conditions. The effect of rotation, suspended particles, magnetic field, stable solute gradient and medium permeability has also been shown graphically.


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