Boundary effects on electrothermal convection in a dielectric fluid layer

• Autorzy: Ravisha M. , Raghunatha K. R. , Mamatha A. L. , Shivakumara I. S.

Identyfikatory

DOI

10.24425/ather.2019.128287

• Języki publikacji: EN

Abstrakty

EN

The instability characteristics of a dielectric fluid layer heated from below under the influence of a uniform vertical alternating current (AC) electric field is analyzed for different types of electric potential (constant electric potential/ electric current), velocity (rigid/free) and temperature boundary conditions (constant temperature/heat flux or a mixed condition at the upper boundary). The resulting eigenvalue problem is solved numerically using the shooting method for various boundary conditions and the solution is also found in a simple closed form when the perturbation heat flux is zero at the boundaries. The possibility of a more precise control of electrothermal convection (ETC) through various boundary conditions is emphasized. The effect of increasing AC electric Rayleigh number is to hasten while that of Biot number is to delay the onset of ETC. The system is more stable for rigid-rigid boundaries when compared to rigid-free and least stable for free-free boundaries. The change of electric potential boundary condition at the upper boundary from constant electric potential to constant electric current is found to instill more stability on the system.

Słowa kluczowe

EN

boundary effect; dielectric fluid; AC electric field; thermal convection

PL

konwekcja termiczna; płyn dielektryczny; warunki brzegowe

• Wydawca: Wydawnictwo Instytutu Maszyn Przepływowych PAN ; Komitet Termodynamiki i Spalania PAN
• Czasopismo: Archives of Thermodynamics
• Rocznik: 2019
• Tom: Vol. 40, no 1
• Strony: 3--19
• Opis fizyczny: Bibliogr. 20 poz., rys., tab., wz.

Twórcy

autor

Ravisha M.

• Department of Mathematics, Dr. G Shankar Government Women’s First Grade College and Post Graduate Study Centre, Ajjarkadu, Udupi – 576101, India

autor

Raghunatha K. R.

• Department of Mathematics, Bangalore University, Bangalore 560 056, India

autor

Mamatha A. L.

• Department of Mathematics, Smt. Rukmini Shedthi Memorial National Government First Grade College, Barkur-576210, India

autor

Shivakumara I. S.

• Department of Mathematics, Bangalore University, Bangalore 560 056, India

Bibliografia

• [1] Castellanos A. (Ed): Electrohydrodynamics. Springer-Verlag, New York 1999.
• [2] Kebarle P.: A brief overview of the present status of the mechanisms involved in electrospray mass spectrometry. J. Mass Spectrom. 35(2000), 7, 804–817.
• [3] Law S.E.: Agricultural electrostatic spray application: a review of significant research and development during the 20th century. J. Electrostat. 51(2001), 1, 25–42.
• [4] Chen X., Cheng J., Yin X.: Advances and applications of electrohydrodynamics. Chinese Sci. Bulletin 48(2003), 11, 1055–1063.
• [5] Lin H.: Electrokinetic instability in microchannel flows: A review. Mech. Res. Commun. 36(2009), 1, 33–38.
• [6] Turnbull R.J.: Electroconvective instability with a stabilizing temperature gradient, I and II: Theory and experimental results. Phys. Fluids 11(1968), 12, 2588–2603.
• [7] Roberts P.H.: Electrohydrodynamic convection. Quart. J. Mech. Appl. Math. 22(1969), 2, 211–220.
• [8] Takashima M., Aldridge K.D.: The stability of a horizontal layer of dielectric fluid under the simultaneous action of a vertical DC electric field and vertical temperature gradient. Quart. J. Mech. Appl. Math. 29(1976), 1, 71–87.
• [9] Martin P.J., Richardson A.T.: Conductivity models of electrothermal convection in a plane layer of dielectric liquid. J. Heat Trans. 106(1984), 1, 131–136.
• [10] Maekawa T., Abe K., Tanasawa I.: Onset of natural convection under an electric field. Int. J. Heat Mass Trans. 35(1992), 3, 613–621.
• [11] Pontiga F., Castellanos A.: Physical mechanisms of instability in a liquid layer subjected to an electric field and a thermal gradient. Phys. Fluids 6(1994), 5, 1684–1701.
• [12] Jones T.B.: Electrohydrodynamically enhanced heat transfer in liquids – A review. In: Advances in heat transfer, Vol. 14, (A79-47255 21-34), Academic Press, Inc., New York 1978, 107–148.
• [13] Saville D.A.: Electrohydrodynamics: The Taylor-Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29(1997), 27–64.
• [14] Shivakumara I.S., Nagashree M.S., Hemalatha K.: Electroconvective instability in a heat generating dielectric fluid layer. Int. Comm. Heat Mass Trans. 34(2007), 9-10, 1041–1047.
• [15] Shivakumara I.S., Rudraiah N., Hemalatha K.: Electrothermoconvection in a dielectric fluid layer in the presence of heat generation. Int. J. Appl. Math. 1(2009), 1, 87–101.
• [16] Shivakumara I.S., Rudraiah N., Jinho Lee, Hemalatha K.: The onset of Darcy–Brinkman electroconvection in a dielectric fluid saturated porous layer. Transp. Porous Med. 90(2011), 2, 509–528.
• [17] Nield D.A.: The thermohaline Rayleigh-Jeffreys problem. J. Fluid Mech. 29(1967), 3, 545–558.
• [18] Nield D.A.: Onset of thermohaline convection in a porous medium. Water Resour. Res. 4(1968), 3, 553–560.
• [19] Sparrow E.M., Goldstein R.J., Jonsson U.K.: Thermal instability in a horizontal fluid layer: Effect of boundary conditions in a horizontal fluid layer: Effect of boundary conditions and non-linear temperature profiles. J. Fluid Mech. 18(1964), 4, 513–528.
• [20] Shivakumara I.S., Jinho Lee, Nanjundappa C.E.: Onset of thermogravitational convection in a ferrofluid layer with temperature dependent viscosity. J. Heat Trans. 134(2011), 1, 012501-1- 012501-7.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).