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The effect of rotation on the onset of electrohydrodynamic instability of an elastico-viscous dielectric fluid layer

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Języki publikacji
EN
Abstrakty
EN
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 fluid stimulated by the dielectrophoretic force due to the variation of dielectric constant with temperature is studied. Walters’ (model B’) fluid model is used to describe rheological behaviour of an elastico-viscous fluid. The onset criterions for stationary and oscillatory convection are derived for the case of free-free boundaries. It is observed that Walters’ (model B’) fluid behaves like an ordinary Newtonian fluid and rotation has stabilizing influence whereas AC electric field has destabilizing influence on the stability of the system. The necessary condition for the occurrence of oscillatory convection is also obtained. The present results are in good agreement with the earlier published results.
Rocznik
Strony
143--149
Opis fizyczny
Bibliogr. 27 poz., wykr.
Twórcy
autor
  • Department of Mathematics, Sidharth Govt. College, Nadaun-177 005, Himachal Pradesh, India
  • Visiting Faculty, Department of Mathematics, Apex Professional University, Pasighat, Arunachal Pradesh, India
autor
  • Visiting Faculty, Department of Mathematics, Apex Professional University, Pasighat, Arunachal Pradesh, India
  • Department of Mathematics, Government College Nurpur, Himachal Pradesh, India
autor
  • Department of Mathematics and Statistics, Himachal Pradesh University, Shimla, India
Bibliografia
  • [1] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover Publication, New York, 1961.
  • [2] L.D. Landau, Electrodynamics of Continuous Media, Oxford, 1960.
  • [3] P.H. Roberts, “Electrohydrodynamic convection”, Q.J. Mechanics and Applied Mathematics 22, 211-220 (1969).
  • [4] A. Castellanos, Electrohydrodynmics, Springer-Verlag, New York, 1998.
  • [5] J.R. Melcher and G.I. Taylor, “Electrohydrodynamics: a review of the role of interfacial shear stresses”, Annu. Rev. Fluid Mech. 1, 11-146 (1969).
  • [6] T.B. Jones, “Electrohydrodynamically enhanced heat transfer in liquids-a review”, in Advances in Heat Transfer, eds. T.F. Irvine Jr. & J.P. Hartnett, pp. 107-144, Academic Press, London, 1978.
  • [7] X. Chen, J. Cheng, and X. Yin, “Advances and applications of electrohydrodynamics”, Chinese Science Bulletin 48, 1055-1063 (2003).
  • [8] M.J. Gross and J.E. Porter, “Electrically induced convection in dielectric liquids”, Nature 212, 1343-1345 (1966).
  • [9] R.J. Turnbull, “Effect of dielectrophoretic forces on the Benard instability”, Phys. Fluids 12, 1809-1815 (1969).
  • [10] T. Maekawa, K. Abe, and I. Tanasawa, “Onset of natural convection under an electric field”, Int. J. Heat Mass Trans. 35, 613-621 (1992).
  • [11] B.L. Smorodin, “Stability of plane flow of a liquid dielectric in a transverse alternating electric field”, Fluid Dynamics 36, 548-555 (2001).
  • [12] M.M. Galal, “Electrohydrodynamic instability if two superposed viscous miscible streaming liquids”, J. Electrostatics 40, 185-190 (1997).
  • [13] N. Rudraiah and M.S. Gayathri, “Effect of thermal modulation on the onset of electrothermoconvection in a dielectric fluid saturated porous medium”, ASME J. Heat Tranfer 131, 101009-101015 (2009).
  • [14] M.H. Chang, A.C. Ruo, and F. Chen, “Electrohydrodynamic instability in a horizontal fluid layer with electrical conductivity gradient subject to a weak shear flow”, J. Fluid Mech. 634, 191-215 (2009).
  • [15] M. Takashima, “The effect of rotation on electrohydrodynamic instability”, Canadian J. Physics 54, 342-347 (1976).
  • [16] M. Takashima and A.K. Ghosh, “Electrohydrodynamic instability in a viscoelastic liquid layer”, J. Phys. Soc. Japan 47, 1717-1722 (1979).
  • [17] M. Takashima and H. Hamabata, “The stability of natural convection in a vertical layer of dielectric fluid in the presence of a horizontal ac electric field”, J. Phys. Soc. Japan 53, 1728-1736 (1984).
  • [18] M.I. Othman, “Electrohydrodynamic instability of a rotating layer of a viscoelastic fluid heated from below”, Zeitschriftf ¨ur Angewandte Mathematik und Physik 55, 468-482 (2004).
  • [19] I.S. Shivakumara, M.S. Nagashree, and K. Hemalatha, “Electroconvective instability in a heat generating dielectric fluid layer”, Int. Communications in Heat and Mass Transfer 34, 1041-1047 (2007).
  • [20] K. Walters’, “The solution of flow problems in the case of materials with memory”, J. Mecanique 1, 469-778 (1962).
  • [21] V. Sharma and G.C. Rana, “Thermal instability of a Walters’ (Model B’) elastico-viscous fluid in the presence of variable gravity field and rotation in porous medium”, J. Non-Equilib. Thermodyn. 26, 31-40 (2001).
  • [22] I.S. Shivakumara, J. Lee, M.S. Malashetty, and S. Sureshkumara, “Effect of thermal modulation on the onset of thermal convection in Walters’ B viscoelastic fluid in a porous medium”, Transport in Porous Media 87, 291-307 (2011).
  • [23] G.C. Rana and H.S. Jamwal, “Effect of rotation on the onset of compressible viscoelastic fluid saturating a darcy-brinkman porous medium”, Engineering Mechanics 19, 445-455 (2012).
  • [24] R. Chand and G.C. Rana, “On the onset of thermal convection in rotating nanofluid layer saturating a Darcy-Brinkman porous medium”, Int. J. Heat Mass Transfer 55, 5417-5424 (2012).
  • [25] G.C. Rana, S.K. Kango, and S. Kumar, “Effect of rotation on the onset of convection in Walters’ (model B’) heated from below in a Brinkman porous medium”, J. Porous Media 15, 1149-1153 (2012).
  • [26] A.C. Ruo, M.H. Chang, and F. Chen, “Effect of rotation on the electrohydrodynamic instability of a fluid layer with an electrical conductivity gradient”, Physics of Fluids 22, 024102-1-024102-11 (2010).
  • [27] I.S. Shivakumara, M. Akkanagamma, and Chiu-on Ng, “Electrohydrodynamic instability of a rotating couple stress dielectric fluid layer”, Int. J. Heat Mass Transfer 62, 761-771 (2013).
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-abed55b1-1ad5-4601-9017-0ad15865ab97
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