Effect of Electric Field Modulation on The Onset of Electroconvection in a Couple Stress Fluid
Abstract
The problem of a convectional instability in a horizontal dielectric fluid layer with electric field modulation under couple stress fluid is examined. The horizontal dielectric upper boundary fluid layer is cooled, and the lower boundary is subjected to an isothermal boundary condition. The regular perturbation method based on the small magnitude of modulation is used to compute the critical Rayleigh number and the corresponding wavenumber. The solidity of the system is the characterised by a correction Rayleigh number, which is computed as a function of thermal, electric, and couple stress parameters and the frequency of electric field modulation. Some of the known findings are retrieved as specific cases in this study. It is demonstrated that the onset of the convection may be advanced or delayed by the proper regulation of different regulation parameters. The outcomes of this study have potential implications for the control of electroconvection with a time-dependent electric field.
Downloads
References
V.K. Stokes, “Couple stresses in fluids”, Phys. Fluids, 9(9), 1709 (1966). https://doi.org/10.1063/1.1761925
T. Ariman, “Couple Stresses in Fluids”, Phys. Fluids, 10(11), 2497 (1967). https://doi.org/10.1063/1.1762061
V.K. Stokes, “Effects of couple stresses in fluids on the creeping flow past a sphere”, Phys. Fluids, 14(7), 1580 (1971). https://doi.org/10.1063/1.1693645
R.C. Sharma, and S. Sharma, “On couple-stress fluid heated from below in porous medium”, Indian J. Phys. 75(2), 137 (2001).
M.S. Malashetty, S.N. Gaikwad, and M. Swamy, “An analytical study of linear and non-linear double diffusive convection with Soret effect in couple stress liquids”, Int. J. Therm. Sci. 45(9), 897 (2006). https://doi.org/10.1016/j.ijthermalsci.2005.12.005
M.S. Malashetty, I.S. Shivakumara, and S. Kulkarni, “The onset of convection in a couple stress fluid saturated porous layer using a thermal non-equilibrium model”, Phys. Lett. Sect. A Gen. At. Solid State Phys. 373(7), 781 (2009). https://doi.org/10.1016/j.physleta.2008.12.057
S. Saravanan, and D. Premalatha, “Effect of couple stress on the onset of thermovibrational convection in a porous medium”, Int. J. Therm. Sci. 57, 71 (2012). https://doi.org/10.1016/j.ijthermalsci.2012.02.013
M. Taj, S. Maruthamanikandan, and S.K. Akbar, “Effect of Chemical Reaction on Convective Instability in a Horizontal Porous Layer Saturated with a Couple-Stress Fluid”, Int. J. Eng. Res. Appl. 3(2), 1742 (2013). https://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=26C9EE742F44CA86219F8CA53B476180?doi=10.1.1.414.6306&rep=rep1&type=pdf
S. George and M. Thomas, “Effect of Gravity Modulation and Internal Heat Generation on Rayleigh-Bénard Convection in Couple Stress Fluid with Maxwell-Cattaneo Law”, Int. J. Appl. Eng. Res. 13(5), 2688 (2018).
R. Sumithra and S. Venkatraman, “Darcy-Benard Marangoni Convection in a Composite Layer Comprising of Couple Stress Fluid”, Int. J. Appl. Eng. Res. 15(7), 659 (2020). https://www.ripublication.com/ijaer20/ijaerv15n7_07.pdf
M. Takashima, and A. K. Ghosh, “Electrohydrodynamic Instability in a Viscoelastic Liquid Layer”, J. Phys. Soc. Japan, 47(5), 1717 (1979). https://doi.org/10.1143/JPSJ.47.1717
R.C. Sharma, and K.D. Thakur, “On couple stress fluid heated from below in porous medium in hydromagnetics”, Czechoslov. J. Phys. 50(6), 753 (2000). https://doi.org/10.1023/A:1022886903213
S. Maruthamanikandan, “Convective instabilities in Newtonian ferromagnetic, dielectric and other complex liquids”, PhD Thesis, Bangalore University, Bangalore, India, 2005.
N. Rudraiah, B.M. Shankar, and C.O. Ng, “Electrohydrodynamic stability of couple stress fluid flow in a channel occupied by a porous medium”, Spec. Top. Rev. Porous Media: An International Journal, 2(1), 11 (2011). https://doi.org/10.1615/SpecialTopicsRevPorousMedia.v2.i1.20
I.S. Shivakumara, M. Akkanagamma, and C.O. Ng, “Electrohydrodynamic instability of a rotating couple stress dielectric fluid layer”, Int. J. Heat Mass Transf. 62(1), 761 (2013). https://doi.org/10.1016/j.ijheatmasstransfer.2013.03.050
S. Maruthamanikandan, and S.S. Nagouda, “Convective Heat Transfer in Maxwell-Cattaneo Dielectric Fluids”, Int. J. Comput. Eng. Res. 3, 347 (2013). https://cutt.ly/AVrcoGi
S.S. Nagouda, and S. Maruthamanikandan, “Rayleigh-Bénard Convection in a Horizontal Layer of Porous Medium Saturated with a Thermally Radiating Dielectric Fluid”, IOSR J. Math. 11(3), 01 (2015). https://www.iosrjournals.org/iosr-jm/papers/Vol11-issue3/Version-3/A011330110.pdf
O.L. Andreeva, and V.I. Tkachenko, “Analytical Solution and Neutral Curves of the Stationary Linear Rayleigh Problem with Rigid or Mixed Boundary Conditions in Cylindrical Geometry”, East Eur. J. Phys. 2(4), 52 (2015). https://periodicals.karazin.ua/eejp/article/view/5118/4672
O.L. Patochkina, Yu.G. Kazarinov, and V.I. Tkachenko, “Physical model of the dependence of the Nusselt number on the Rayleigh number”, ZhTF, 66(11), 23 (2016). (in Russian).
S. Tarannum, and S. Pranesh, “Effect of Gravity Modulation on the Onset of Rayleigh-Bénard Convection in a Weak Electrically Conducting Couple Stress Fluid with Saturated Porous Layer”, Int. J. Eng. Res. 5(01), 2016. https://cutt.ly/7VrvvJY
B.M. Shankar, J. Kumar, and I.S. Shivakumara, “Stability of natural convection in a vertical dielectric couple stress fluid layer in the presence of a horizontal AC electric field”, Appl. Math. Model. 40(9–10), 5462 (2016). https://doi.org/10.1016/j.apm.2016.01.005
S. Myson, and S.S. Nagouda, “Convective instability analysis of couple-stress dielectric fluid saturated anisotropic porous medium with radiation effect”, Multidiscip. Model. Mater. Struct. 16(5), 1019 (2020). https://doi.org/10.1108/MMMS-08-2019-0149
B.L. Smorodin, G.Z. Gershuni, and M.G. Velarde, “On the parametric excitation of thermoelectric instability in a liquid layer open to air”, Int. J. Heat Mass Transf. 42, 3159 (1999). https://doi.org/10.1016/S0017-9310(98)00351-2
B.L. Smorodin, and M.G. Velarde, “On the parametric excitation of electrothermal instability in a dielectric liquid layer using an alternating electric field”, J. Electrostat. 50, 205 (2001). https://doi.org/10.1016/s0304-3886(00)00036-x
B.L. Smorodin, “The Behaviour of Low Conducting Liquid in Modulated Electric Field”, in: Proc. 14th lntemational Conf. Dielectr. Liq., (IEEE, Graz, Austria, 2002). pp. 425–428, 2002. https://doi.org/10.1109/ICDL.2002.1022783
L. Bozbiei, B. Borts, Y. Kazarinov, A. Kostikov, and V.I. Tkachenko, “Experimental Study of Liquid Movement in Free Elementary Convective Sells”, Energetika, 61(2), 45 (2015). (in Russian)
O.L. Andrieieva, B.V. Borts, A.F. Vanzha, I.M. Korotkova, and V.I. Tkachenko, “Stability of a Viscous Incompressible Conducting Liquid Layer of a Cylindrical Shape in an Inhomogeneous Temperature Field and a Magnetic Field of a Vacuum Arc Current Through It”, PAST. 3, 91 (2021). https://vant.kipt.kharkov.ua/ARTICLE/VANT_2021_3/article_2021_3_91.pdf
C. Rudresha, C. Balaji, V. Vidya Shree, S. Maruthamanikandan, “Effect of Electric Field Modulation on Electroconvection in a Dielectric Fluid-Saturated Porous Medium”, Journal of Mines Metals and Fuels. 70(3A), 35 (2022). https://doi.org/10.18311/jmmf/2022/30665
S. Maruthamanikandan, N.M. Thomas, and S. Mathew, “Bénard-Taylor ferroconvection with time-dependent sinusoidal boundary temperatures”, J. Phys. Conf. Ser. 1850(1), 012061 (2021). https://doi.org/10.1088/1742-6596/1850/1/012061
Copyright (c) 2022 Chandrappa Rudresha, Chandrashekar Balaji, Venkatesh Vidya Shree, Sokalingam Maruthamanikandan
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
