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Thermal instability of Walters' (model B') elastico-viscous compressible fluid in the presence of Hall current

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EN
Abstrakty
EN
The thermal instability of a compressible elastico-viscous fluid is examined for viscoelastic polymeric solutions in the presence of uniform vertical magnetic field to include the Hall-current. These solutions are known as Walters' (model B') fluids and their rheology is approximated by the Walters' (model B') constitutive relations, proposed by WALTERS [12]. It is found that the stability criterion is independent of the effects of viscosity and viscoelasticity and is dependent on the magnitude of the magnetic field and Hall current. The magnetic field is found to stabilize a certain wave number range of the unstable configuration. The Hall current has destabilizing and stabilizing effects on the system.
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Rocznik
Strony
61--72
Opis fizyczny
Bibliogr. 20 poz.
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Bibliografia
  • [1] CHANDRASEKHAR S., Hydrodynamic and Hydromagnetic Stability, Dover Publications, New York, 1981.
  • [2] GUPTA A.S., Hall effects on thermal instability, Rev. Roumaine Math. Pures Appl., 1967, 12, 665–677.
  • [3] SPIEGEL E.A., VERONIS G., On the Boussinesq approximation for a compressible fluid, Astrophys. J., 1960, 131, 442–447.
  • [4] KENT A., Instability of laminar flow of a magnetofluid, Phys. Fluids, 1966, 9, 1286–1289.
  • [5] REINER M., A mathematical theory of dilatancy, American J. Math., 1945, 67, 350–362.
  • [6] RIVLIN R.S., The hydrodynamics of non-Newtonian fluids. I, Proc. Roy. Soc., London, 1948, A193, 260–281.
  • [7] ERICKSEN J.L., Characterstic surfaces of equations of motion of non-Newtonian fluids, ZAMP, 1953, 4, 260–267.
  • [8] TRUESDELL C., NOLL W, The non linear field theories of mechanics, (Handbuch der Physik III/3), Berlin–Heidelberg–New York, Springer, 1965.
  • [9] FREDRICKSEN A.G., Principles and Applications of Rheology, Prentice–Hall Inc., New Jersey, 1964.
  • [10] JOSEPH D.D., Stability of fluid motion II, Springer-Verlag, New York, 1976.
  • [11] WALTERS K., The motion of an elastico-viscous liquid contained between concentric spheres, Quart. J. Mech. Applied Math., 1960, 13, 325–333.
  • [12] WALTERS K., Non-Newtonian effects in some elastico-viscous liquids whose behaviour at small rates of shear is characterized by a general linear equation of state, Quart. J. Mech. Applied. Math., 1962, 15, 63–76.
  • [13] SHARMA R.C., KANGO S.K., Stability of two superposed Walters’ (model B′) viscoelastic fluids in the presence of suspended particles and variable magnetic field in porous medium, Appl. Mech. Engng., 1999, 4(2), 255–269.
  • [14] SHARMA V., KUMAR S., Rayleigh–Taylor instability of stratified Walters’ (model B′) fluid in the presence of a variable horizontal magnetic field and suspended particles, Journal of Indian Math. Soc., 2001, 68, 209–219.
  • [15] SHARMA V., KUMAR S., Magnetogravitational instability of a thermally conducting rotating Walters’ (model B′) fluid with Hall current, Proc. Nat. Acad. Sci. India, 2000, 70(A)I, 87–97.
  • [16] SHARMA R. C., AGGARWAL A. K., Effect of compressibility and suspended particles on thermal convection in a Walters’ B′ elastico-viscous fluid in hydromagnetics, Int. J. of Appl. Mech. Eng., 2006, 2, 391–399.
  • [17] KUMAR S., SHARMA V., Effect of suspended particles on thermal convection in a viscoelastic Walters’ (model B′) fluid in hydromagnetics, Shekher (New Series) Int. J. Maths., 2009, 1, 1–11.
  • [18] KUMAR S., GUPTA D., JASWAL R., The instability of streaming Walters’ (model B′) fluid in porous medium, Int. J. Math. Sci. & Engg. Appls., 2010, 4, 355–367.
  • [19] RANA G.C., KUMAR S., Thermal instability of Rivlin–Ericksen elastico-viscous rotating fluid permeating with suspended particles under variable gravity field in porous medium, Studia Geotechnica et Mechanica, 2010, XXXII, No. 4, 39–54.
  • [20] VERONIS G., Convective instability in a compressible atmosphere. I, Astrophys. J., 1965, 141, 1068–1090.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPW8-0020-0015
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