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Rana, G. C.
- Thermal Instability in a Layer of Nanofluid Subjected to Rotation and Suspended Particles
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Authors
Affiliations
1 Department of Mathematics, Government College Dhaliara (Kangra), Himachal Pradesh, IN
2 Department of Mathematics, Sidharth Government College Nadaun (Hamirpur), Himachal Pradesh, IN
3 Department of Mathematics, Government College Nagrota Bagwan (Kangra), Himachal Pradesh, IN
4 Department of Mathematics, DDM College of Science and Technology Banehra (Una), Himachal Pradesh, IN
1 Department of Mathematics, Government College Dhaliara (Kangra), Himachal Pradesh, IN
2 Department of Mathematics, Sidharth Government College Nadaun (Hamirpur), Himachal Pradesh, IN
3 Department of Mathematics, Government College Nagrota Bagwan (Kangra), Himachal Pradesh, IN
4 Department of Mathematics, DDM College of Science and Technology Banehra (Una), Himachal Pradesh, IN
Source
Research Journal of Science and Technology, Vol 5, No 1 (2013), Pagination: 32-40Abstract
The objective of the present work is to investigate theoretically the combined effect of rotation and suspended particles on the thermal instability in a layer of nanofluid. A linear stability theory, perturbation method and normal mode technique is used to find the solution of fluid layer confined between two free boundaries. For linear theory analysis, critical Rayleigh number has been obtained to study the stability analysis. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The onset criterion for stationary and oscillatory convection is derived analytically and graphically. The effects of various parameters such as suspended particles, rotation, Lewis number and modified diffusivity ratio on the stationary convection are studied.Keywords
Prandtl Number, Taylor Number, Nanofluid, Suspended Particles, Lewis Number.
References
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- Stability of Stratified Rivlin-Ericksen Fluid Permeated with Suspended Particles and Uniform Horizontal Magnetic Field in Porous Medium
Abstract Views :157 |
PDF Views:0
Authors
G. C. Rana
1,
V. Sharma
2
Affiliations
1 Department of Mathematics, NSCBM Govt. P. G. College, Hamirpur-177 005, IN
2 Department of Mathematics, Himachal Pradesh University, Shimla-171005, IN
1 Department of Mathematics, NSCBM Govt. P. G. College, Hamirpur-177 005, IN
2 Department of Mathematics, Himachal Pradesh University, Shimla-171005, IN
Source
The Journal of the Indian Mathematical Society, Vol 80, No 1-2 (2013), Pagination: 173-182Abstract
In this paper, we investigate the stability of stratified Rivlin-Ericksen elastico-viscous fluid permeated with suspended particles (fine dust) and uniform horizontal magnetic field in porous medium. By applying normal mode analysis method, the dispersion relation is derived and solved numerically. The system is found to be stable for stable stratifications and unstable for unstable stratifications as in the case of Newtonian fluid. The uniform horizontal magnetic field stabilizes the system for certain wave number range. The growth rates decrease with the increase of kinematic viscosity, kinematic viscoelasticity, suspended particle number density and magnetic field.Keywords
Rivlin-Ericksen Elastico-Viscous Fluid, Magnetic Field, SusPended Particles, Porous Medium.- Stability of Two Superposed Rivlin-Ericksen Viscoelastic Fluids in the Presence of Suspended Particles and Variable Magnetic Field in Porous Medium
Abstract Views :206 |
PDF Views:0
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 :188 |
PDF Views:0
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.- Stability of Stratified Rivlin-Ericksen Fluid in the Presence of Horizontal Magnetic Field and Uniform Horizontal Rotation in Porous Medium
Abstract Views :167 |
PDF Views:2
Authors
Affiliations
1 Department of Mathematics, Govt. College, Joginder Nagar, Distt. Mandi, (H.P.), IN
2 Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla, IN
3 Department of Mathematics, Govt. Senior Secondary School, Sunder Nagar, IN
4 Department of Mathematics, Govt. College, Naduan, Distt. Hamirpur (H.P.), IN
1 Department of Mathematics, Govt. College, Joginder Nagar, Distt. Mandi, (H.P.), IN
2 Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla, IN
3 Department of Mathematics, Govt. Senior Secondary School, Sunder Nagar, IN
4 Department of Mathematics, Govt. College, Naduan, Distt. Hamirpur (H.P.), IN
Source
Research Journal of Engineering and Technology, Vol 6, No 1 (2015), Pagination: 63-71Abstract
The influence of viscosity, viscoelasticity and medium permeability on the stability of stratified Rivlin-Ericksen viscoelastic fluid is examined for viscoelastic polymeric solutions in the simultaneous presence of a uniform horizontal magnetic field ⃗H (H, 0, 0) and uniform horizontal rotation Ω(Ω, 0, 0). These solutions are known as Rivlin-Ericksen fluids and their rheology is approximated by the Rivlin-Ericksen constitutive relations, proposed by Rivlin and Ericksen [13]. The effects of Coriolis forces on the stability is chosen along the direction of the magnetic field and transverse to that of the gravitational field g (o,o,-g). The system is found to be stable for all wave numbers for stable stratifications and unstable for unstable stratifications for the stratifications in density, viscosity, viscoelasticity, medium permeability and medium porosity. The system can be completely stabilized by large enough magnetic field, which was unstable in the absence of magnetic field; provided the initial configuration is top-heavy density wise. The kinematic viscosity and kinematic viscoelasticity have damping effects on the growth rates with the increase in kinematic viscosity and kinematic viscoelasticity, respectively, for a fixed wave number. The medium permeability has enhancing effects on the growth rates with its increase for a fixed wave number. The above results have also been shown graphically.Keywords
Rivlin-Ericksen Fluid, Magnetic Field, Rotation, Viscosity, Viscoelasticity, Porous Medium, AMS Classification Number:76A10.- On the Onset of Electrohydrodynamic Instability of Rivlin-Ericksen Viscoelastic Dielectric Fluid Layer
Abstract Views :189 |
PDF Views:1
Authors
Affiliations
1 Department of Mathematics, Sidharth Govt. College, Nadaun-177 005, Himachal Pradesh, IN
2 Department of Physics, Sidharth Govt. College, Nadaun-177 005, Himachal Pradesh, IN
3 Department of Mathematics, Govt. College Dharampur, District Mandi, Himachal Pradesh, IN
1 Department of Mathematics, Sidharth Govt. College, Nadaun-177 005, Himachal Pradesh, IN
2 Department of Physics, Sidharth Govt. College, Nadaun-177 005, Himachal Pradesh, IN
3 Department of Mathematics, Govt. College Dharampur, District Mandi, Himachal Pradesh, IN
Source
Research Journal of Engineering and Technology, Vol 6, No 1 (2015), Pagination: 13-18Abstract
In this paper we investigate the effect of AC electric field on the onset of instability of an elastico-viscous Rivlin-Ericksen dielectric fluid layer stimulated by the dielectrophoretic force due to the variation of dielectric constant with temperature. By applying linear stability theory and normal mode analysis method, we derive the dispersion relation describing the influence of viscelasticity and AC electric field. For the case of stationary convection, it is observed that Rivlin-Ericksen fluid behaves like an ordinary Newtonian fluid whereas AC electric field hastens the stationary convection. The present results are in good agreement with the earlier published results.Keywords
Walter’ (Model B') Fluid, AC Electric Field, Electrohydrodynamic, Viscosity, Viscoelasticity.- Electrohydrodynamic Instability of an Elastico-Viscous Dielectric Fluid Layer under Rotation
Abstract Views :174 |
PDF Views:1
Authors
Affiliations
1 Department of Mathematics, Sidharth Govt. College, Nadaun-177 005, Himachal Pradesh, IN
2 Department of Mathematics, Apex Professional University, Pasighat, Arunachal Pradesh, IN
3 Department of Mathematics, NSCBM Govt. P. G. College Hamirpur, Himachal Pradesh, IN
1 Department of Mathematics, Sidharth Govt. College, Nadaun-177 005, Himachal Pradesh, IN
2 Department of Mathematics, Apex Professional University, Pasighat, Arunachal Pradesh, IN
3 Department of Mathematics, NSCBM Govt. P. G. College Hamirpur, Himachal Pradesh, IN
Source
Research Journal of Engineering and Technology, Vol 6, No 1 (2015), Pagination: 50-57Abstract
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 dielectric fluid layer is examined both analytically and graphically. Rivlin-Ericksen fluid model is used to describe rheological behaviour of an elastico-viscous fluid. The stability criteria for stationary and oscillatory convection are derived for the case of free-free boundaries. It is observed that Rivlin-Ericksen fluid behaves like an ordinary Newtonian fluid in the case of stationary convection and rotation has stabilizing effect whereas AC electric field has destabilizing influence on the stability of the system. The necessary condition for the existence of oscillatory convection is also obtained. The effect of rotation and AC electric field has also been shown graphically. The present results are in agreement with the earlier published results.Keywords
Rivlin-Ericksen Fluid, Rotation, AC Electric Field, Electrohydrodynamic, Viscosity, Viscoelasticity.- Effect of Rotation on the Onset of Compressible Rivlin-Ericksen Fluid Heated from Below Saturating a Darcy-Brinkman Porous Medium
Abstract Views :158 |
PDF Views:0
Authors
G. C. Rana
1,
Ramesh Chand
2
Affiliations
1 Department of Mathematics, NSCBM Govt. P. G. College, Hamirpur-177 005, Himachal Pradesh, IN
2 Department of Mathematics, Govt. P. G. College, Dhaliara-177 103, Himachal Pradesh, IN
1 Department of Mathematics, NSCBM Govt. P. G. College, Hamirpur-177 005, Himachal Pradesh, IN
2 Department of Mathematics, Govt. P. G. College, Dhaliara-177 103, Himachal Pradesh, IN
Source
Research Journal of Engineering and Technology, Vol 3, No 2 (2012), Pagination: 76-81Abstract
The effect of rotation on the onset of convection in compressible Rivlin-Ericksen elastico-viscous fluid heated from below saturating a porous medium is considered. For the porous medium, the Brinkman model is employed. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the medium permeability, compressibility, gravity field and viscoelasticity introduce oscillatory modes. For stationary convection, the rotation has stabilizing effect whereas Darcy number and medium permeability have destabilizing/stabilizing effect on the system under certain conditions. The effects of rotation, Darcy number and medium permeability have also been shown graphically.Keywords
Rivlin-Ericksen Fluid, Thermal Convection, Viscoelasticity, Rotation, Brinkman-Porous Medium.- Triple-Diffusive Convection in a Layer of Viscoelastic Nanofluid
Abstract Views :222 |
PDF Views:0
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 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