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1
Content available remote Electrohydrodynamic instability of a rotating Walters’ (model B’) fluid in a porous medium: Brinkman model
Rana G. C., Chand R., Sharma Veena
Mechanics and Mechanical Engineering
|
2019
|
Vol. 23, nr 1
138--143
EN
In this study, the instability of Walters’ (model B’) viscoelastic fluid in a Darcy-Brinkman-Boussinesq system heated from below saturating a porous medium in electrohydrodynamics is considered. By applying the linear stability analysis and normal modes, the dispersion relations accounting for the effect of Prandtl number, electric Rayleigh number, Darcy number, Brinkman-Darcy number, Taylor number and kinematic viscoelasticity parameter is derived. The effects of electric Rayleigh number, Darcy number, Brinkman-Darcy number and Taylor number on the onset of stationary convection have been investigated both analytically and graphically.
2
Content available remote Thermal instability analysis of an elastico-viscous nanofluid layer
Chand R., Rana G. C., Puigjaner D.
Engineering Transactions
|
2018
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Vol. 66, iss. 3
301--324
EN
The purpose of this paper is to study the thermal instability analysis of an elastico-viscous nanofluid layer heated from below. The Rivlin-Ericksen type fluid model is used to describe the rheological behavior of an elastico-viscous nanofluid. The linear stability criterion for the onset of both stationary and oscillatory convection is derived by applying the normal model analysis method. The presence of nanoparticles enhances the thermal conductivity of the fluid, and the model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The effect of the physical parameters of the system, namely the concentration Rayleigh number, Prandtl number, capacity ratio, Lewis number, and kinematic visco-elasticity coefficient, on the stability of the system is numerically investigated. In addition, sufficient conditions for the non-existence of oscillatory convection are reported.
3
Content available remote Thermal instability of a Rivlin-Ericksen nanofluid saturated by a Darcy-Brinkman porous medium: a more realistic model
Rana G. C., Chand R., Sharma V.
Engineering Transactions
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2016
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Vol. 64, iss. 3
271--286
EN
In this paper, we study thermal instability in a horizontal layer of Rivlin-Ericksen elasticoviscous nanofluid in porous medium. Brinkman model is used as a porous medium and RivlinEricksen fluid model is used to describe the rheological behavior of nanofluid. In the earlier model (Chand and Rana [18]), we constrained both temperature and nanoparticle volume fractions at the boundaries of Rivlin-Ericksen nanofluid layer. In this paper, we assume that the value of temperature can be constrained on the boundaries, while the nanoparticle flux is zero on the boundaries. The considered boundary condition neutralizes the possibility of oscillatory convection due to the absence of two opposing forces, and only stationary convection occurs, in which Rivlin-Ericksen elastico-viscous nanofluid behaves like an ordinary nanofluid. The effects of Lewis number, medium porosity, modified diffusivity ratio, Darcy-Brinkman number and concentration Rayleigh number in stationary convection are discussed analytically and numerically. The results of this study are in good agreement with the results published earlier.
4
Content available The effect of rotation on the onset of electrohydrodynamic instability of an elastico-viscous dielectric fluid layer
Rana G. C., Chand R., Sharma V.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2016
|
Vol. 64, nr 1
143--149
EN
In this paper the combined effect of uniform rotation and AC electric field on the onset of instability in a horizontal layer of an elastico-viscous fluid stimulated by the dielectrophoretic force due to the variation of dielectric constant with temperature is studied. Walters’ (model B’) fluid model is used to describe rheological behaviour of an elastico-viscous fluid. The onset criterions for stationary and oscillatory convection are derived for the case of free-free boundaries. It is observed that Walters’ (model B’) fluid behaves like an ordinary Newtonian fluid and rotation has stabilizing influence whereas AC electric field has destabilizing influence on the stability of the system. The necessary condition for the occurrence of oscillatory convection is also obtained. The present results are in good agreement with the earlier published results.
5
Content available Rayleigh-Bénard convection in an elastico-viscous Walters’ (model B’) nanofluid layer
Rana G. C., Chand R.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2015
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Vol. 63, nr 1
235--244
EN
In this study, the onset of convection in an elastico-viscous Walters’ (model B’) nanofluid horizontal layer heated from below is considered. The Walters’ (model B’) fluid model is employed to describe the rheological behavior of the nanofluid. By applying the linear stability theory and a normal mode analysis method, the dispersion relation has been derived. For the case of stationary convection, it is observed that the Walters’ (model B’) elastico-viscous nanofluid behaves like an ordinary Newtonian nanofluid. The effects of the various physical parameters of the system, namely, the concentration Rayleigh number, Prandtl number, capacity ratio, Lewis number and kinematics visco-elasticity coefficient on the stability of the system has been numerically investigated. In addition, sufficient conditions for the non-existence of oscillatory convection are also derived.
6
Content available Magneto convection in a layer of nanofluid with soret effect
Chand R., Rana G. C.
Acta Mechanica et Automatica
|
2015
|
Vol. 9, no. 2
63--69
EN
Double diffusive convection in a horizontal layer of nanofluid in the presence of uniform vertical magnetic field with Soret effect is investigated for more realistic boundary conditions. The flux of volume fraction of nanoparticles is taken to be zero on the isothermal boundaries. The normal mode method is used to find linear stability analysis for the fluid layer. Oscillatory convection is ruled out because of the absence of the two opposing buoyancy forces. Graphs have been plotted to find the effects of various parameters on the stationary convection and it is found that magnetic field, solutal Rayleigh number and nanofluid Lewis number stabilizes fluid layer, while Soret effect, Lewis number, modified diffusivity ratio and nanoparticle Rayleigh number destabilize the fluid layer.
7
Content available The onset of thermal convection in couple-stress fluid in hydromagnetics saturating a porous medium
Rana G. C.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2014
|
Vol. 62, nr 2
357--362
EN
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 R ≤4π2/Pl (1 + 2π2F + PlQ/2ε) the result clearly establishes the stabilizing character of couple-stress parameter and magnetic field whereas destabilizing character of medium permeability.
8
Content available Triple-diffusive convection in Walters' (Model B') fluid with varying gravity field saturating a porous medium
Kango S. K., Rana G. C., Chand R.
Studia Geotechnica et Mechanica
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2013
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Vol. 35, nr 3
45--56
EN
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.
9
Content available Hydromagnetic thermal instability of compressible Walters' (Model B') rotating fluid permeated with suspended particles in porous medium
Rana G. C., Jamwal H. S.
Studia Geotechnica et Mechanica
|
2013
|
Vol. 35, nr 4
75--88
EN
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.
10
Content available Variable gravity effects on thermal instability of nanofluid in anisotropic porous medium
Chand R., Rana G. C., Kumar S.
International Journal of Applied Mechanics and Engineering
|
2013
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Vol. 18, no. 3
631--642
EN
In this paper, we study the effects of variable gravity on thermal instability in a horizontal layer of a nanofluid in an anisotropic porous medium. Darcy model been used for the porous medium. Also, it incorporates the effect of Brownian motion along with thermophoresis. The normal mode technique is used to find the confinement between two free boundaries. The expression of the Rayleigh number has been derived, and the effects of variable gravity and anisotropic parameters on the Rayleigh number have been presented graphically.
11
Content available Effect of magnetic field on thermal instability of Oldroydian viscoelastic rotating fluid in porous medium
Thakur R. C., Rana G. C.
International Journal of Applied Mechanics and Engineering
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2013
|
Vol. 18, no. 2
555--569
EN
In this paper, we investigate the effect of a vertical magnetic field on thermal instability of an Oldroydian visco-elastic rotating fluid in a porous medium. By applying the normal mode analysis method, the dispersion relation governing the effects of rotation, magnetic field and medium permeability is derived and solved analytically and numerically. For the case of stationary convection, the Oldroydian viscoelastic fluid behaves like an ordinary Newtonian fluid and it is observed that rotation has a stabilizing effect while the magnetic field and medium permeability have a stabilizing/destabilizing effect under certain conditions on thermal instability of the Oldroydian viscoelastic fluid in a porous medium. The oscillatory modes are introduced due to the presence of rotation, the magnetic field and gravity field. It is also observed that the ‘principle of exchange of stability’ is invalid in the presence of rotation and the magnetic field.
12
Content available remote Stability of incompressible Rivlin-Ericksen elastico-viscous superposed fluid in porous medium
Rana G. C., Sharma V., Kango S. K.
International Journal of Applied Mechanics and Engineering
|
2012
|
Vol. 17, no. 2
471-480
EN
The stability of a Rivlin-Ericksen elastico-viscous superposed fluid in a porous medium is considered. The system is found to be stable/unstable for bottom heavy / top heavy configurations density wise as in a Newtonian viscous fluid. For an exponential varying density, viscosity, viscoelasticity, medium porosity and medium permeability, the system is found to be stable for all wave numbers for becomes stable stratifications and unstable for the unstable stratifications. The behavior of growth with respect to fluid kinematic viscosity, viscoelasticity, medium porosity and medium permeability is examined analytically and graphically.
13
Content available remote Effect of rotation and suspended particles on the stability of an incompressible Walters�f (model B�Ś) fluid hated from below under a variable gravity field in a porous medium
Rana G. C., Kumar S.
Engineering Transactions
|
2012
|
Vol. 60, iss. 1
55-68
EN
The effect of rotation and suspended particles on the stability of an incompressible Walters�f (model B�Ś) fluid heated from below under a variable gravity field in a porous medium is considered. By applying a normal mode analysis method, the dispersion relation has been derived and solved numerically. It is observed that the rotation, gravity field, suspended par- ticles, and viscoelasticity introduce oscillatory modes. For stationary convection, the rotation has a stabilizing effect and suspended particles are found to have a destabilizing effect on the system, whereas the medium permeability has a stabilizing or destabilizing effect on the system under certain conditions. The effect of rotation, suspended particles, and medium permeability has also been shown graphically.
14
Content available remote Thermal instability of Walters' (model B') elastico-viscous compressible fluid in the presence of Hall current
Kumar S., Gupta D., Jaswal R., Rana G. C.
Studia Geotechnica et Mechanica
|
2011
|
Vol. 33, nr 3
61-72
EN
The thermal instability of a compressible elastico-viscous fluid is examined for viscoelastic polymeric solutions in the presence of uniform vertical magnetic field to include the Hall-current. These solutions are known as Walters' (model B') fluids and their rheology is approximated by the Walters' (model B') constitutive relations, proposed by WALTERS [12]. It is found that the stability criterion is independent of the effects of viscosity and viscoelasticity and is dependent on the magnitude of the magnetic field and Hall current. The magnetic field is found to stabilize a certain wave number range of the unstable configuration. The Hall current has destabilizing and stabilizing effects on the system.
15
Content available remote Thermal instability of Rivlin-Ericksen elasto-viscous rotating fluid permeating with suspended particles under variable gravity field in porous medium
Rana G. C., Kumar S.
Studia Geotechnica et Mechanica
|
2010
|
Vol. 32, nr 4
39-54
EN
The problem of thermal instability of the Rivlin-Ericksen elasto-viscous fluid in a porous medium is considered in the presence of uniform rotation, suspended particles and variable gravity field. The rotation, gravity field, suspended particles and viscoelasticity introduce oscillatory modes. It is found that the principle of the exchange of stabilities is valid, provided that some condition is fulfilled. In a stationary convection, suspended particles are found to have destabilizing effect on the system, while rotation has stabilizing effect on the system under certain conditions. The effect of rotation, suspended particles, and medium permeability have also been shown graphically.
16
Content available remote Thermosolutal instability of Walters' (model B') visco-elastic rotating fluid permeated with suspended particles and variable gravity field in porous medium
Sharma V., Rana G. C.
International Journal of Applied Mechanics and Engineering
|
2001
|
Vol. 6, no 4
843-860
EN
The thermosolutal instability of Walters' (model B') elastico-viscous rotating fluid in a porous medium is considered in the presence of a uniform rotation, suspended particles and variable gravity field. the stable solute gradient, rotation, gravity field, suspended particles and viscoelasticity introduce oscillatory modes. For the stationary convection, the stable gradient and rotation have stabilizing effects and suspended particles are found to have destabilizing effect on the system, whereas the medium permeability has destabilizing or stabilizing efect on the system under certain conditions. The effects of stable solute gradient, rotation, suspended particles, medium permeability have also been shown graphically.
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