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Mehta, Chander Bhan
- Rayleigh Taylor Instability of Two Rotating Maxwellian Superposed Fluid with Variable Magnetic Field in Porous Medium
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Authors
Affiliations
1 Department of Mathematics, Centre of Excellence, Sanjauli Shimla (H.P)-171006, IN
2 Department of Mathematics, St. Bede’s College, Shimla (H.P)171002, IN
1 Department of Mathematics, Centre of Excellence, Sanjauli Shimla (H.P)-171006, IN
2 Department of Mathematics, St. Bede’s College, Shimla (H.P)171002, IN
Source
Research Journal of Science and Technology, Vol 5, No 1 (2013), Pagination: 65-71Abstract
The instability of the plane interface between two viscoelastic (Maxwellian) superposed fluids in porous medium in the presence of uniform rotation and variable magnetic field is considered. The magnetic field, the viscosity and the density are assumed to be exponentially varying. For stable density stratification, the system is found to be stable for disturbances of all wave numbers. The magnetic field stabilizes the potentially unstable stratification for small wave-length perturbations which are otherwise unstable. The long wave-length perturbations remain unstable and are not stabilized by magnetic field. Rotation does not affect the stability or instability, as such, of stratification.Keywords
Rayleigh-Taylor Instability, Maxwellian Viscoelastic Fluids, Variable Magnetic Field, Uniform Rotation, Porous Medium.
References
- Bhatia, P.K., Rayleigh-Taylor Instability of Two Viscous Superposed Conducting Fluids, Nuovo Cimento, 19B (1974),161 .
- Bhatia, P.K and Mathur, R. P., Instability of Viscoelastic Superposed Fluids in a Vertical Magnetic Field Through Porous Medium, Ganita Sandesh, 17(2) (2003), 21.
- Bhatia, P.K. and Steiner, J.M., Thermal Instability of a Viscoelastic Fluid Layer in Hydromagnetics, J. Math. Anal. Appl., 41 (1973), 271.
- Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Dover publication, New York, 1981.
- Jukes, I.D., On The Rayleigh-Taylor Problem in Magnetohydrodynamics with Finite Resistivity, J. Fluid Mech., 16 (1963), 177.
- Kent, A., Instability of Laminar Flow of a Magneto Fluid, Phys. Fluid, 9 (1966), 1286.
- Lapwood, E.R., Convection of a Fluid in a Porous Medium, Proc. Camb. Phil. Soc., 44 (1948), 508.
- Sengupta, P.R and Basak, P., Stability of Two Superposed Viscoelastic (Maxwell) Fluids in a Vertical Magnetic Field, Indian J. Pure Appl. Math., 35(7) (2004), 905.
- Sharma, R.C., Instability of the Plane Interface Between Two Viscoelastic SuperposedConducting Fluids, J.Math.Phys.Sci.,12 (1978), 603.
- Vest, C.M. and Arpaci, V.S., Overstability of a Viscoelastic Fluid Layer Heated from Below, J. Fluid Mech., 36 (1969), 613.
- On Uniform Magneto-Rotatory Double-Diffusive Convection in Compressible Couple-Stress Fluid
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Authors
Affiliations
1 Department of Mathematics, Govt Excellence Degree College Sanjauli, Shimla (H.P)-171207, IN
2 Department of Mathematics, Rajiv Gandhi Govt. College, Shimla-4 (H.P),, IN
3 Department of Mathematics, GSSS(G), Port More, Shimla-1 (H.P), IN
1 Department of Mathematics, Govt Excellence Degree College Sanjauli, Shimla (H.P)-171207, IN
2 Department of Mathematics, Rajiv Gandhi Govt. College, Shimla-4 (H.P),, IN
3 Department of Mathematics, GSSS(G), Port More, Shimla-1 (H.P), IN
Source
Research Journal of Engineering and Technology, Vol 6, No 1 (2015), Pagination: 155-163Abstract
The effect of uniform vertical magnetic field and uniform vertical rotation on double-diffusive convection in a layer of an electrically conducting couple-stress fluid heated and soluted from below is considered. For the case of stationary convection, it is clear that stable solute gradient, compressibility, rotation and magnetic field postpone the onset of the convection in compressible couple-stress fluid heated from below in the presence of a magnetic field. Couple-stress parameter has duel character in presence of rotation. While in absence of rotation Couple-Stress parameter has postpones the onset of convection only. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. Further, the solute gradient, magnetic field, rotation is found to introduce oscillatory modes in the systems that were non-existent in their absence. The sufficient conditions for the non-existence of overstability have found, the violation of which does not necessarily imply the occurrence of overstability.Keywords
Double-Diffusive Convection, Couple-Stress Fluid, Uniform Vertical Magnetic Field and Rotation, Mathematical Classification (AMSC2010):76A05, 76A10, 80A20, 76E06, 76E15, 76E19, 76N20.- Thermosolutal Convection in Compressible Couple-Stress Fluid with Fine Dust
Abstract Views :170 |
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Authors
Affiliations
1 Department of Mathematics, Centre of Excellence, Sanjauli, Shimla, IN
2 Department of Mathematics, St. Bede’s College, Shimla, IN
3 Department of Mathematics, Govt Boys Sr. Sec. School, Kotkhai, Shimla, IN
1 Department of Mathematics, Centre of Excellence, Sanjauli, Shimla, IN
2 Department of Mathematics, St. Bede’s College, Shimla, IN
3 Department of Mathematics, Govt Boys Sr. Sec. School, Kotkhai, Shimla, IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 1-5Abstract
A layer of compressible, couple-stress fluid permeated with suspended particles (fine dust), heated and soluted from below is considered. For the case of stationary convection; the compressibility, couple-stress and stable solute gradient postpone the set of convection where as the suspended particles hasten the onset of convection. The graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient is found to introduce the overstability modes in the system, which ware non-existing, in its absence. The case of overstability is also considered wherein the sufficient conditions for non-existence of overstability are obtained.