Research Journal of Engineering and Technology

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Characterization of Rotatory Thermal Convection in Rivlin-Ericksen Viscoelastic Fluid


Affiliations
1 Department of Mathematics, Govt. College Nadaun (Hamirpur), (HP) INDIA 177033, India
     

   Subscribe/Renew Journal


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.
Subscription Login to verify subscription
User
Notifications
Font Size


  • Banerjee, M.B., Katoch, D.C., Dube,G.S. and Banerjee, K., Bounds for growth rate of perturbation in thermohaline convection. Proc. R. Soc. A, 1981,378, 301-304

  • 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.


Abstract Views: 737

PDF Views: 0




  • Characterization of Rotatory Thermal Convection in Rivlin-Ericksen Viscoelastic Fluid

Abstract Views: 737  |  PDF Views: 0

Authors

Ajaib S. Banyal
Department of Mathematics, Govt. College Nadaun (Hamirpur), (HP) INDIA 177033, India

Abstract


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