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Kango, S. K.
- Triple-Diffusive Convection in Rivlin-Ericksen Fluid under varying gravity field in Porous Medium
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Authors
Affiliations
1 Department of Mathematics, Govt. College, Haripur (Manali) Distt. Kullu (HP)-175 136, IN
2 Govt. College, Bassa, Dist. Mandi (HP), IN
3 Jwalaji Degree College, Jwalamukhi, Distt. Kangra (HP), IN
1 Department of Mathematics, Govt. College, Haripur (Manali) Distt. Kullu (HP)-175 136, IN
2 Govt. College, Bassa, Dist. Mandi (HP), IN
3 Jwalaji Degree College, Jwalamukhi, Distt. Kangra (HP), IN
Source
Research Journal of Science and Technology, Vol 5, No 1 (2013), Pagination: 96-103Abstract
The Triple-Diffusive convection in Rivlin-Ericksen 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.Keywords
Triple-Diffusive Convection, Rivlin-Ericksen Fluid, Solute Gradients, Vertical Magnetic Field, Varying Gravity Field, Porous Medium.
References
- A. J. Pearlstein, R. M. Harris and G. Terrones, The onset of convective instability in triply diffusive fluid layer, J. Fluid Mech., 1989, 202, 443-465.
- B. D. Straughan and W. Walker, Multi component diffusion and penetrative Convection, Fluid Dynamics Research, 1997, 19, 77-89.
- C. Oldenberg and K. Pruess, Layered thermohaline convection in hypersaline geothermal systems, Transport in Porous Media, 1998, 33, 29-63.
- D. A. Nield and A.Bejan, Convection in porous medium, New York, Springer, 1992.
- E. A. Spiegel, Convective instability in a compressible atmosphere, Astrophys. J., 1965, 141, 1068.
- G. K. Pradhan, P. C. Samal and U.K.Tripathi, Thermal instability of the fluid layer under variable gravitational field, J. Math., 1989, 20,736.
- G. Veronis, Thermohaline convection in a layer of fluid heated from below, J. Marine Res., 1965, 23, 1-17.
- R.S. Rivlin and J.L Ericksen, Stress-deformation relaxations for isotropic Materials, J. Rational Mech. Anal., 1955, 4, 323-329.
- S. Chand, Triple-Diffusive convection in Walters’ (Model B') fluid in porous medium in hydromagnetics, Research J. Engineering and Tech., 2012, 3(2), 140-145.
- S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover Publication, NewYork, 1981.
- S. K. Kango, Vikram Singh and G. C. Rana, Thermosolutal instability in Walters’ B' fluid in the presence of Hall Currents in porous medium in Hydromagnetics, Journal of Indian Math. Soc., 2011, 78 (1-4), 65-77.
- Veena Sharma and Kamal Kishor, Hall Effect on Thermosolutal Instability of Rivlin-Ericksen Fluid with Varying Gravity Field in Porous Medium, Indian J. Pure. Appl. Math., 2001, 32(11), 1643-1657.
- Veena Sharma et al., The Onset of Thermal Instability in a triply Diffusive Three Dimensional Fluid Layer in Porous Medium, Research J. Engineering and T
- Stability of Two Superposed Rivlin-Ericksen Viscoelastic Fluids in the Presence of Suspended Particles and Variable Magnetic Field in Porous Medium
Abstract Views :205 |
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Authors
S. K. Kango
1,
G. C. Rana
2
Affiliations
1 Department of Mathematics, Government College, Haripur (Manali) – 175 136, IN
2 Department of Mathematics, NSCBM Govt. P. G. College, Hamirpur-177 005, IN
1 Department of Mathematics, Government College, Haripur (Manali) – 175 136, IN
2 Department of Mathematics, NSCBM Govt. P. G. College, Hamirpur-177 005, IN
Source
The Journal of the Indian Mathematical Society, Vol 80, No 3-4 (2013), Pagination: 265-274Abstract
The stability of two superposed Rivlin-Ericksen viscoelastic fluids is considered in the presence of suspended particles and variable magnetic field in porous medium. The system is stable in the potentially stable case and unstable in the potentially unstable case. The effect of a variable horizontal magnetic field is also considered. The presence of magnetic field stabilizes a certain wave number band, whereas the system is unstable for all wave numbers in the absence of the magnetic field for the potentially unstable arrangement.Keywords
Stability, Viscoelasticity, Rivlin-Ericksen Fluid, Suspended Particles, Variable Magnetic Field, Porous Medium.- Thermosolutal Instability in Walters'B' Fluid in the Presence of Hall Currents in Porous Medium in Hydromagnetics
Abstract Views :187 |
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Authors
Affiliations
1 Department of Mathematics, Govt. College, Haripur (Manali)-175136, IN
2 Department of Mathematics, Jwalaji College, Jwalamukhi (Kangra)-176031, IN
3 Department of Mathematics, Govt. College, Hamirpur-177005, IN
1 Department of Mathematics, Govt. College, Haripur (Manali)-175136, IN
2 Department of Mathematics, Jwalaji College, Jwalamukhi (Kangra)-176031, IN
3 Department of Mathematics, Govt. College, Hamirpur-177005, IN
Source
The Journal of the Indian Mathematical Society, Vol 78, No 1-4 (2011), Pagination: 65-77Abstract
The thermosolutal instability of a layer ofWalters' B′ elasticoviscous fluid is considered in the presence of uniform horizontal magnetic field to include the Hall currents in porous medium. For the case of stationary convection, the Hall currents hasten the onset of convection, the magnetic field postpones the onset of convection, medium permeability also postpones the onset of convection in the presence of Hall currents, whereas kinematic viscoelasticity has no effect on the onset of convection. The Hall currents, kinematic viscoelasticity, magnetic field, medium permeability and solute parameter introduce oscillatory modes in the system, which were non-existent in their absence. The case of overstability is also considered wherein the sufficient conditions for the non-existence of overstability are obtained.Keywords
Thermosolutal Instability, Hall Currents, Walters’ B' Fluid, Viscoelasticity.- Megneto-Convection in a Layer of Maxwell Visco-Elastic Fluid in a Porous Medium with Soret Effect
Abstract Views :156 |
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Authors
Affiliations
1 Department of Mathematics, Government College, Nurpur, HP, IN
2 Department of Mathematics, Government College Haripur (Manali), HP, IN
3 Department of Mathematics, Jawalaji Degree College Jawalamukhi, HP, IN
1 Department of Mathematics, Government College, Nurpur, HP, IN
2 Department of Mathematics, Government College Haripur (Manali), HP, IN
3 Department of Mathematics, Jawalaji Degree College Jawalamukhi, HP, IN
Source
Research Journal of Engineering and Technology, Vol 6, No 1 (2015), Pagination: 23-30Abstract
Double Diffusive convection in a horizontal layer of Maxwell visco-elastic fluid in a porous medium in the presence of constant vertical magnetic field and Soret coefficient is investigated. Flow in porous medium is characterized by Darcy model. The normal mode method is used to find linear stability analysis for the fluid layer confined between two free-free boundary surfaces. The stability criterions for stationary and oscillatory convection have been derived. Effects of various parameters on the stationary have been obtained analytically and graphically.Keywords
Maxwell Visco-Elastic Fluid, Chandrasekhar Number, Soret Parameter, Rayleigh-Darcy Number, Magnetic Prandtl Number.- Effect of Suspended Particles on the Stability of Stratified Viscoelastic Rivlin-Ericksen Fluid Saturating a Porous Medium
Abstract Views :217 |
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Authors
S. K. Kango
1,
Vikram Singh
2
Affiliations
1 Department of Mathematics, Govt. College, Haripur (Manali) Himachal Pradesh – 175136, IN
2 Department of Mathematics, Jwalaji Degree College, Jwalamukhi Himachal Pradesh-176032, IN
1 Department of Mathematics, Govt. College, Haripur (Manali) Himachal Pradesh – 175136, IN
2 Department of Mathematics, Jwalaji Degree College, Jwalamukhi Himachal Pradesh-176032, IN
Source
Research Journal of Engineering and Technology, Vol 3, No 2 (2012), Pagination: 51-56Abstract
In this paper, the stability of stratified elastic-viscous Rivlin-Ericksen fluid in the presence of suspended particles and uniform horizontal magnetic field in porous medium is considered. In contrast to the Newtonian fluids, the system is found to be unstable at stable stratification for low values of permeability o0r high values of kinematic viscoelasticity. The uniform horizontal magnetic field stabilizes the system for certain wave number range. It has been found that the growth rate increases with the increase in kinematic viscosity and permeability, whereas it decreases with the increase in kinematic viscoelasticity.Keywords
Rivlin-Ericksen Fluid, Viscoelasticity, Permeability, Suspended Particles, Porous Medium.- Hydrodynamic and Hydromagnetic Stability of Stratified Elastico-Viscous Walters' (Model B') Fluid in the Presence of Suspended Particles in Porous Medium
Abstract Views :162 |
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Authors
Affiliations
1 Department of Mathematics, Govt. College, Haripur (Manali) Himachal Pradesh – 175136, IN
1 Department of Mathematics, Govt. College, Haripur (Manali) Himachal Pradesh – 175136, IN
Source
Research Journal of Engineering and Technology, Vol 3, No 2 (2012), Pagination: 146-151Abstract
In this paper, the stability of stratified elastico-viscous Walters' (model B') elastico-viscous fluid in the presence of suspended particles and uniform horizontal magnetic field in porous medium is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved numerically. The system is found to be unstable for stable stratifications and unstable for unstable stratifications, which is in contrast to the Newtonian fluid where the system is always stable for stable stratifications. The uniform horizontal magnetic field stabilizes the system for certain wave number range. It has been found that the growth rates decrease with the increase in kinematic viscosity, kinematic viscoelasticity, suspended particles number density and magnetic field.Keywords
Walters’ B' Fluid, Viscoelasticity, Permeability, Suspended Particles, Porous Medium, Stratification.- Triple-Diffusive Convection in a Micropolar Rotating Ferrofluid
Abstract Views :202 |
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Authors
Affiliations
1 Government College, Barsar (Hamirpur)-174305, Himachal Pradesh, IN
2 Government College, Darang (Mandi), Himachal Pradesh, IN
3 Government College, Sujanpur (Hamirpur), Himachal Pradesh, IN
1 Government College, Barsar (Hamirpur)-174305, Himachal Pradesh, IN
2 Government College, Darang (Mandi), Himachal Pradesh, IN
3 Government College, Sujanpur (Hamirpur), Himachal Pradesh, IN
Source
International Journal of Technology, Vol 6, No 2 (2016), Pagination: 123-132Abstract
This paper deals with the theoretical investigation of the triple-diffusive convection in a micropolar ferrofluid layer heated and soluted below subjected to a transverse uniform magnetic field in the presence of uniform vertical rotation. For a flat fluid layer contained between two free boundaries, an exact solution is obtained. A linear stability analysis theory and normal mode analysis method have been carried out to study the onset convection. The influence of various parameters like rotation, solute gradients, and micropolar parameters (i.e. coupling parameter, spin diffusion parameter and micropolar heat conduction parameter) has been analyzed on the onset of stationary convection. The critical magnetic thermal Rayleigh number for the onset of instability is also determined numerically for sufficiently large value of buoyancy magnetization parameter M1(ratio of the magnetic to gravitational forces). The principle of exchange of stabilities is found to hold true for the micropolar fluid heated from below in the absence of micropolar viscous effect, microinertia, solute gradient and rotation. The oscillatory modes are introduced due to the presence of the micropolar viscous effect, microinertia, solute gradient and rotation, which were non-existent in their absence.Keywords
Triple-Diffusive Convection, Micropolar Ferrofluid, Solute Gradient, Vertical Magnetic Field, Rotation, Magnetization.- Triple-Diffusive Convection in a Layer of Viscoelastic Nanofluid
Abstract Views :221 |
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Authors
Affiliations
1 Department of Mathematics, NSCBM Govt. College, Hamirpur-177005, Himachal Pradesh, IN
2 Department of Mathematics, Govt. College, Nurpur-177 103, District Kangra, Himachal Pradesh, IN
3 Department of Mathematics, Govt. College, Barsar, District Hamirpur, Himachal Pradesh, IN
1 Department of Mathematics, NSCBM Govt. College, Hamirpur-177005, Himachal Pradesh, IN
2 Department of Mathematics, Govt. College, Nurpur-177 103, District Kangra, Himachal Pradesh, IN
3 Department of Mathematics, Govt. College, Barsar, District Hamirpur, Himachal Pradesh, IN
Source
International Journal of Technology, Vol 6, No 2 (2016), Pagination: 71-80Abstract
Triple-diffusive convection in a horizontal layer of nanofluid heated from below and salted from above and below is considered. The Rivlin-Ericksen type fluid model is used to describe the rheological behavior of viscoelastic nanofluid. The effects of thermophoresis and Brownian diffusion parameters are also introduced through Buongiorno model in the governing equations. By using linear stability analysis and normal modes analysis method, the dispersion relation accounting for the effect of various parameters is derived. The influences of solute-Rayleigh number, analogous solute-Rayleigh number, thermo-nanofluid Lewis number, modified diffusivity ratio and nanoparticle Rayleigh number on the stability of stationary convection are presented analytically and graphically.Keywords
Convection, Triple-Diffusive, Nanofluid, Nanoparticles, Rayleigh Number.- Thermal Instability of Ferromagnetic Fluid in the Presence of Hall Effect and Suspended Particle under Varying Gravity Field
Abstract Views :199 |
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Authors
Affiliations
1 Department of Mathematics, Govt. College, Haripur (Manali) (H,P.) – 175136, IN
2 Department of Mathematics, Jwalaji Degree College, Jwalamukhi (H,P.) – 176031, IN
1 Department of Mathematics, Govt. College, Haripur (Manali) (H,P.) – 175136, IN
2 Department of Mathematics, Jwalaji Degree College, Jwalamukhi (H,P.) – 176031, IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 1-9Abstract
In this paper we consider theoretical investigation of the effect hall current and the suspended particle under varying gravity field on the thermal instability of ferromagnetic fluid heated from below. For a fluid layer between two free boundaries and exact solution is obtained using a linearized stability theory and normal mode analysis. A dispersion relation governing the effect of hall current and the suspended particle is obtained. For the case of stationary convection it is found that the magnetic field has a stabilizing the system when the gravity is increasing upward i.e. (λ>0), where as the hall current and suspended particle are found to have the destabilizing effect on the system when the gravity is increasing upward i.e. (λ>0). The critical Rayleigh numbers and wave numbers of the associated disturbances for the onset of stability as stationary convection are obtained. The principle of exchange of stabilities is not valid for the problem under consideration, whereas in the absence of Hall currents hence magnetic field, it is valid under certain conditions.
Keywords
Hall Currents, Suspended Particles, Ferromagnetic Fluid and Varying Gravity Field.- Effect of Hall Currents on Thermosolutal Instability in Non-Newtonian Fluid in Non-Porous Medium
Abstract Views :169 |
PDF Views:0
Authors
S. K. Kango
1,
Sanjay Sharma
2
Affiliations
1 Jawaharlal Nehru Government College, Haripur (Manali), HP – 175136, IN
2 Vallabh Government PG College, Mandi, Himachal Pradesh, IN
1 Jawaharlal Nehru Government College, Haripur (Manali), HP – 175136, IN
2 Vallabh Government PG College, Mandi, Himachal Pradesh, IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 240-247Abstract
The thermosolutal instability of a layer of Rivlin-Ericksen elastico-viscous fluid (a Non-Newtonian fluid) is considered in the presence of uniform horizontal magnetic field to include the Hall currents in non-porous medium. For the case of stationary convection, the Hall currents hasten the onset of convection, the magnetic field postpones the onset of convection, whereas the kinematic viscoelasticity has no effect on the onset of convection. The Hall currents, kinematic viscoelasticity, magnetic field and the solute parameter introduce oscillatory modes in the system, which were non-existent in their absence. The case of overstability is also considered wherein the sufficient conditions for the non-existence of overstability are obtained. The results are also shown graphically.
Keywords
Thermosolutal Instability, Hall Currents, Rivlin-Ericksen Fluid, Viscoelasticity, Overstability.- Thermal Instability of Rotating Kuvshiniski Viscoelastic Nanofluid in a Porous Medium
Abstract Views :182 |
PDF Views:3
Authors
Affiliations
1 Department of Mathematics, Government College Nurpur, Himachal Pradesh, IN
2 Department of Mathematics, NSCBM Govt. College, Hamirpur-177005, Himachal Pradesh, IN
3 Department of Mathematics, Government College Barsar, Himachal Pradesh, IN
1 Department of Mathematics, Government College Nurpur, Himachal Pradesh, IN
2 Department of Mathematics, NSCBM Govt. College, Hamirpur-177005, Himachal Pradesh, IN
3 Department of Mathematics, Government College Barsar, Himachal Pradesh, IN
Source
Research Journal of Science and Technology, Vol 9, No 1 (2017), Pagination: 1-8Abstract
Thermal instability in a horizontal layer of Kuvshiniski viscoelastic nanofluid for more realistic boundary conditions is studied theoretically within the frame work of linear theory. The flux of volume fraction of nanoparticles is taken to be zero on the isothermal boundaries. For porous medium Brinkman model is taken into consideration and the model used for nanofluid incorporates the effect of Brownian diffusion and thermophoresis. The stability criterion for stationary and oscillatory convection have been derived and graphs have been plotted to study the effects of rotation, the Brinkman-Darcy number, the Lewis number, the modified diffusivity ratio and porosity parameter on the stationary convection.Keywords
Kuvshiniski Viscoelastic Fluid, Rotation, Brownian Motion, Galerkin Technique, Porous Medium.- Thermosolutal Instability in Rivlin-Ericksen Fluid in the Presence of Hall Currents
Abstract Views :140 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, Govt. College, Barsar (HP), IN
1 Department of Mathematics, Govt. College, Barsar (HP), IN
Source
Research Journal of Engineering and Technology, Vol 8, No 3 (2017), Pagination: 237-244Abstract
The thermosolutal instability of a layer of Rivlin-Ericksen elastico-viscous fluid is considered in the presence of uniform horizontal magnetic field to include the Hall currents in non-porous medium. For the case of stationary convection, the Hall currents hasten the onset of convection, the magnetic field postpones the onset of convection, whereas the kinematic viscoelasticity has no effect on the onset of convection. The Hall currents, kinematic viscoelasticity, magnetic field and the solute parameter introduce oscillatory modes in the system, which were non-existent in their absence. The case of overstability is also considered wherein the sufficient conditions for the non-existence of overstability are obtained. The results are also shown graphically.Keywords
Thermosolutal Instability, Hall Currents, Rivlin-Ericksen Fluid, Viscoelasticity, Overstability.References
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- E. A. Spiegel, Convective instability in a compressible atmosphere, Astrophys. J. 141(1965) 068-1090.
- A. K., Aggarwal, Effect of rotation on thermosolutal instability of Walters’ (model B') fluid permeated with suspended particles in porous medium, Adv. Theor. Appl. Mech., 3 (2010) 177-188.