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Banyal, Ajaib S.
- Characterization of Rotatory Thermal Convection in Rivlin-Ericksen Viscoelastic Fluid
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1 Department of Mathematics, Govt. College Nadaun (Hamirpur), (HP) INDIA 177033, IN
1 Department of Mathematics, Govt. College Nadaun (Hamirpur), (HP) INDIA 177033, IN
Source
Research Journal of Engineering and Technology, Vol 4, No 1 (2013), Pagination: 19-25Abstract
A layer of Rivlin-Ericksen viscoelastic fluid heated from below is considered in the presence of uniform vertical rotation. Following the linearized stability theory and normal mode analysis, the paper mathematically established the condition for characterizing the oscillatory motions which may be neutral or unstable, for rigid boundaries at the top and bottom of the fluid. It is established that all non-decaying slow motions starting from rest, in a Rivlin-Ericksen viscoelastic fluid of infinite horizontal extension and finite vertical depth, which is acted upon by uniform vertical rotation, opposite to gravity and a constant vertical adverse temperature gradient, are necessarily non-oscillatory, in the regime, where the Taylor number and F is is the viscoelasticity parameter. The result is important since it hold for all wave numbers and for horizontal rigid boundaries of infinite extension at the top and bottom of the fluid, and the exact solutions of the problem investigated in closed form, is not obtainable.Keywords
Thermal Convection, Rivlin-Ericksen Fluid, Rotation, PES, Rayleigh Number, Taylor number. MSC 2000 No.: 76A05, 76E06, 76E15, 76E07.
References
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- Banerjee, M. B., and Banerjee, B., A characterization of nonoscillatory motions in magnetohydronamics. Ind. J. Pure and Appl Maths., 1984, 15(4): 377-382
- Banerjee, M.B., Gupta, J.R. and Prakash, J., On thermohaline convection of Veronis type, J. Math. Anal. Appl., Vol.179 (1992), pp. 327-334.
- Banyal, A.S, The necessary condition for the onset of stationary convection in couple-stress fluid, Int. J. of Fluid Mech. Research, Vol. 38, No.5, 2011, pp. 450-457.
- Bénard, H., Les tourbillions cellulaires dans une nappe liquid, Revue Genérale des Sciences Pures et Appliquees 11 (1900), 1261-1271, 1309-1328.
- Bhatia, P.K. and Steiner, J.M., Convective instability in a rotating viscoelastic fluid layer, Zeitschrift fur Angewandte Mathematik and Mechanik 52 (1972), 321-327.
- Bhatia, P.K. and Steiner, J.M., Thermal Instability in a viscoelastic fluid layer in hydromagnetics, Journal of Mathematical Analysis and Applications 41 (1973), no. 2,271- 283.
- Chandrasekhar, S. Hydrodynamic and Hydromagnetic Stability, 1981, Dover Publication, New York
- Rivlin, R.S. and Ericksen, J.L., Stress deformation relations for isotropic materials, J. Rat. Mech. Anal. 4 (1955), 323-429
- Gupta, J.R., Sood, S.K., and Bhardwaj, U.D., On the characterization of nonoscillatory motions in rotatory hydromagnetic thermohaline convection, Indian J. pure appl.Math. 1986,17(1), pp 100-107.
- Jeffreys, H., The stability of a fluid layer heated from below, Philosophical Magazine 2 (1926), 833-844.
- Kumar, P., Mohan, H. and Lal, R., Effect of magnetic field on thermal instability of a rotating Rivlin-Ericksen viscoelastic fluid, Int. J. of Maths. Math. Scs., vol.2006, 1-10.
- Oldroyd, J.G., Non-Newtonian effects in steady motion of some idealized elastic-viscous liquids, Proceedings of the Royal Society of London A245 (1958), 278-297.
- Pellow, A., and Southwell, R.V., On the maintained convective motion in a fluid heated from below, Proc. Roy. Soc. London A, 1940, 176, 312-43.
- Rayleigh, L., On convective currents in a horizontal layer of fluid when the higher temperature is on the underside, Philosophical Magazine 32 (1916),529-546.
- Schultz, M.H. (1973). Spline Analysis, Prentice Hall, Englewood Cliffs, New Jersy.
- Sharma, R.C., Effect of rotation on thermal instability of a viscoelastic fluid, Acta Physica Hungarica 40 (1976), 11-17.
- Sharma, R.C., Thermal instability in a viscoelastic fluid in hydromagnetics, Acta Physica Hungarica 38 (1975), 293-298.
- Sharma, R.C. and Kumar, P., Effect of rotation on thermal instability in Rivlin-Ericksen elastic-viscous fluid, Zeitschrift fur Naturforschung 51a (1996), 821-824.Rivlin, R.S. and.
- Effect of Wave Number on the Onset of Instability in Couple-Stress Fluid and its Characterization in the Presence of Magnetic Field
Abstract Views :167 |
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Authors
Affiliations
1 Department of Mathematics, Govt. College, Indora, Dist. Kangra, (HP), IN
2 Department of Mathematics, Govt. College, Nadaun, Dist. Hamirpur, (HP) - 177033, IN
1 Department of Mathematics, Govt. College, Indora, Dist. Kangra, (HP), IN
2 Department of Mathematics, Govt. College, Nadaun, Dist. Hamirpur, (HP) - 177033, IN
Source
Research Journal of Engineering and Technology, Vol 6, No 1 (2015), Pagination: 119-128Abstract
Thermal instability of couple-stress fluid in the presence of uniform vertical magnetic field is considered. Following the linearized stability theory and normal mode analysis, the paper established the regime for all oscillatory and non-decaying slow motions starting from rest, in a couple-stress fluid of infinite horizontal extension and finite vertical depth in the presence of uniform vertical magnetic field, the necessary condition for the existence of ‘overstability’ and the sufficient condition for the validity of the ‘exchange principle’ is derived. The result is important since it hold for all wave numbers and for any arbitrary combination of free and rigid boundaries at the top and bottom of the fluid. Further, the stationary convection at marginal state with free horizontal boundaries is analyzed numerically and graphically, showing that the couple-stress parameter and magnetic field has stabilizing effect on the system. However, for the constant magnitude of couple-stress parameter and magnetic field, the wave number has a destabilizing effect for a value less than a critical value, which varies with the magnitude of the couple-stress parameter and magnetic field and for higher value than the critical value of the wave number; it has a stabilizing effect on the system.Keywords
Thermal Convection,; Couple-Stress Fluid, PES, Magnetic Field, Chandrasekhar Number, MSC 2000 No.:76A05, 76E06, 76E15, 76U05.- Upper Limit to the Growth Rate of Perturbation in Rotatory Convection in Couple-Stress Fluid in the Presence of Magnetic Field
Abstract Views :152 |
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Authors
Affiliations
1 Department of Mathematics, Govt. College, Amb, Dist. Una, (HP), IN
2 Department of Mathematics, Govt. College, Nadaun, Dist. Hamirpur, (HP) 177033, IN
1 Department of Mathematics, Govt. College, Amb, Dist. Una, (HP), IN
2 Department of Mathematics, Govt. College, Nadaun, Dist. Hamirpur, (HP) 177033, IN
Source
Research Journal of Engineering and Technology, Vol 6, No 1 (2015), Pagination: 129-135Abstract
The thermal instability of a couple-stress fluid acted upon by uniform vertical magnetic field and rotation heated from below is investigated. Following the linearized stability theory and normal mode analysis, the paper through mathematical analysis of the governing equations of couple-stress fluid convection with a uniform vertical magnetic field and rotation, for the case of rigid boundaries shows that the complex growth rate of oscillatory perturbations, neutral or unstable for all wave numbers, must lie inside a semi-circle, in the right half of a complex -plane, where Q is the Chandrasekhar number, is the Taylor number, and F is the couple-stress parameter, which prescribes the upper limits to the complex growth rate of arbitrary oscillatory motions of growing amplitude in a rotatory couple-stress fluid in porous medium heated from below, which provided significant improvement to the result of Khanna and Banyal.Keywords
Thermal Convection, Couple-Stress Fluid, Rotation, Magnetic Field, PES, Chandrasekhar Number, Taylor Number.- Effect of Wave Number on Thermal Convection in Couple-Stress Fluid in The Presence of Rotation and Magnetic Field
Abstract Views :168 |
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Authors
Affiliations
1 Department of Maths, Singhania University, Pacheri Bari, Jhunjhunu- 333515 (Raj.), IN
2 Department of Mathematics, Govt. College Nadaun, Dist. Hamirpur, (HP)-177033, IN
1 Department of Maths, Singhania University, Pacheri Bari, Jhunjhunu- 333515 (Raj.), IN
2 Department of Mathematics, Govt. College Nadaun, Dist. Hamirpur, (HP)-177033, IN
Source
Research Journal of Engineering and Technology, Vol 5, No 4 (2014), Pagination: 169-177Abstract
The effect of wave number and rotation on the thermal convection in couple-stress fluid heated from below in the presence of uniform magnetic field is investigated. The paper established the regime for all non-oscillatory and nondecaying slow motions starting from rest; the necessary condition for the existence of 'overstability' and the sufficient condition for the validity of the 'exchange principle' is also derived, when both the bounding planes are rigid. Further, the stationary convection at marginal state with free horizontal boundaries is analyzed numerically and graphically, showing that the rotation has a stabilizing effect on the system. In the presence of rotation; the magnetic field and couple-stress parameter has stabilizing (or destabilizing) effect on the system depending upon conditions satisfied. In the absence of rotation, both magnetic field and couple-stress parameter has stabilizing effect. However, for the constant magnitude of any of the couple-stress parameter, magnetic field and rotation, the wave number has a destabilizing effect for a value less than the critical value, which varies with the magnitude of the couple-stress parameter, magnetic field and rotation; and for higher values than the critical value of the wave number; it has a stabilizing effect on the system.Keywords
Thermal Convection, Couple-Stress Fluid, Rotation, Magnetic Field, PES, Chandrasekhar Number.- A Characterization of Thermosolutal Convection in Rivlin-Ericksen Fluid in the Presence of Magnetic Field in a Porous Medium
Abstract Views :294 |
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Authors
Affiliations
1 Department of Mathematics, Govt. College Nadaun (Hamirpur), (HP) 177033, IN
1 Department of Mathematics, Govt. College Nadaun (Hamirpur), (HP) 177033, IN
Source
Research Journal of Engineering and Technology, Vol 3, No 4 (2012), Pagination: 270-280Abstract
Thermosolutal instability of Veronis type in Rivlin-Ericksen viscoelastic fluid in the presence of uniform magnetic field in a porous medium is considered. Following the linearized stability theory and normal mode analysis, the paper mathematically established the condition for characterizing the oscillatory motions which may be neutral or unstable, for any arbitrary combination of free and rigid boundaries at the top and bottom of the fluid. It is established that all nondecaying slow motions starting from rest, magneto-thermosolutal instability of Veronis type in a Rivlin-Ericksen viscoelastic fluid of infinite horizontal extension and finite vertical depth in a porous medium, are necessarily nonoscillatory, in the regime.Keywords
Thermosolutal Convection, Rivlin-Ericksen Fluid, Magnetic Field, PES, Rayleigh Number, Chandrasekhar Number.- Upper Limits to Growth Rate in Magneto-Thermosolutal Convection in Rivlin-Ericksen Viscoelastic Fluid in a Porous Medium
Abstract Views :141 |
PDF Views:1
Authors
Affiliations
1 Department of Mathematics, Govt. College Nadaun (Hamirpur), (HP) 177033, IN
1 Department of Mathematics, Govt. College Nadaun (Hamirpur), (HP) 177033, IN