Abstract
Investigation of the natural convection in a dielectric fluid confined inside a vertical slot subject to a constant horizontal temperature gradient and a high-frequency electric field was revisited. The thermoelectric coupling produces a dielectrophoretic force which contains a term called electric buoyancy associated with an electric gravity. Similar to the Archimedean buoyancy, this force can induce thermo-electro-convective instability in a stable fluid flow. Including the feedback effect of the electric field on the flow, a three-dimensional linear stability analysis is performed to characterize the instability induced by this force. Different critical modes are found depending on the intensity of the electric field: stationary hydrodynamic modes, oscillatory thermal modes and stationary electric modes. The threshold of the electric modes is independent of the Prandtl number in contrast with the threshold of the hydrodynamic and thermal modes. The obtained results are compared with those of previous studies.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bahloul, A., Mutabazi, I., Ambari, A.: Codimension 2 points in the flow inside a cylindrical annulus with a radial temperature gradient. Eur. Phys. J. AP. 9, 253–264 (2000). https://doi.org/10.1051/epjap:2000112
Baïri, A., Zarco-Pernia, E., García de María, J.-M.: A review on natural convection in enclosures for engineering applications. The particular case of the parallelogrammic diode cavity. Appl. Therm. Eng. 63, 304–322 (2014). https://doi.org/10.1016/j.applthermaleng.2013.10.065
Drazin, P.G.: Introduction to Hydrodynamic Stability. Cambridge University Press (2002)
Fung, L., Hwang, Y.: Linear instability of tilted parallel shear flow in a strongly stratified and viscous medium. JMST Adv. 2(2), 37–51 (2020). https://doi.org/10.1007/s42791-020-00030-8
Gershuni G.Z., Zhukhovitskii, E.M.: Convective Stability of Incompressible Fluids, Israel Program for Scientific Translations. Keter Publishing House, Jerusalem (1976)
Gross, M.J., Porter, J.E.: Electrically induced convection in dielectric liquids. Nature. 212, 1343–1345 (1966). https://doi.org/10.1038/2121343a0
Jones, T.B.: Electrohydrodynamically enhanced heat transfer in liquids – a review. Adv. Heat Transfer. 14, 107–148 (1979). https://doi.org/10.1016/S0065-2717(08)70086-8
Kang, C., Mutabazi, I.: Dielectrophoretic buoyancy and heat transfer in a dielectric liquid contained in a cylindrical annular cavity. J. Appl. Phys. 125, 184902 (2019). https://doi.org/10.1063/1.5086980
Kang, C., Meyer, A., Yoshikawa, H.N., Mutabazi, I.: Thermoelctric convection in a dielectric liquid inside a cylindrical annulus with a solid-body rotation. Phys. Rev. Fluids. 4, 093502 (2019). https://doi.org/10.1103/PhysRevFluids.4.093502
Karmali, F., Shehamer, M.: The dynamics of parabolic flight: flight characteristics and passenger percepts. Acta Astronaut. 63(5–6), 594–602 (2008). https://doi.org/10.1016/j.actaastro.2008.04.009
Landau L.D., Lifshitz E.M.: Electrodynamics of Continuous Media, 2nd ed., Landau and Lifshitz Course of Theoretical Physics, Vol. 8, Elsevier Butterworth-Heinemann, Burlington (1984)
Laohalertdecha, S., Naphon, P., Wongwises, S.: A review of electrohydrodynamic enhancement of heat transfer. Renew Sust Energy Rev. 11, 858–876 (2007). https://doi.org/10.1016/j.rser.2005.07.002
Lee, Y., Korpela, S.A.: Multicellular natural convection in a vertical slot. J. Fluid Mech. 126, 91–121 (1983). https://doi.org/10.1017/S0022112083000063
Meyer, A., Jongmanns, M., Meier, M., Egbers, C., Mutabazi, I.: Thermal convection in a cylindrical annulus under a combined effect of the radial and vertical gravity. C. R. Mecanique. 345, 11–20 (2017). https://doi.org/10.1016/j.crme.2016.10.003
Meyer, A., Crumeyrolle, O., Mutabazi, I., Meier, M., Jongmanns, M., Renoult, M.-C., Seelig, T., Egbers, E.: Flow patterns and heat transfer in a cylindrical annulus under 1g and low-g conditions: theory and simulation. Microgravity Sci. Technol. 30(5), 653–662 (2018). https://doi.org/10.1007/s12217-018-9636-3
Meyer, A., Meier, M., Jongmanns, M., Seelig, T., Egbers, C., Mutabazi, I.: Effect of the initial conditions on the growth of thermoelectric instabilities during parabolic flights. Microgravity Sci. Technol. 31(5), 715–721 (2019). https://doi.org/10.1007/s12217-019-09755-1
Miroshnichenko, I.V., Sheremet, M.A.: Turbulent natural convection heat transfer in rectangular enclosures using experimental and numerical approaches: a review. Renew. Sust. Energ. Rev. 82, 40–59 (2018). https://doi.org/10.1016/j.rser.2017.09.005
Mutabazi, I., Yoshikawa, H.N., Tadie Fogaing, M., Travnikov, V., Crumeyrolle, O., Futterer, B., Egbers, C.: Thermo-electro-hydrodynamic convection under microgravity: a review. Fluid Dyn. Res. 48, 061413 (2016). https://doi.org/10.1088/0169-5983/48/6/061413
Roberts, P.H.: Electrohydrodynamic convection. Q. J. Mech. Appl. Math. 22, 211–220 (1969). https://doi.org/10.1093/qjmam/22.2.211
Shankar, B.M., Kumar, J., Shivakumar, I.S.: Effect of horizontal AC electric field on the stability of natural convection in a vertical dielectric fluid layer. J. Appl. Fluid Mech. 9, 3073–3086 (2016). https://doi.org/10.29252/jafm.09.06.26051
Smorodin, B.L.G., Velarde, M.: On the parametric excitation of electrothermal instability in a dielectric liquid layer using an alternating electric field. J. Electrost. 50, 205–226 (2001). https://doi.org/10.1016/S0304-3886(00)00036-X
Stiles, P.J.: Electro-thermal convection in dielectric liquids. Chem. Phys. Lett. 179, 311–315 (1991). https://doi.org/10.1016/0009-2614(91)87043-B
Tadie Fogaing M.: Instabilités thermoconvectives dans un fluid diélectrique, Ph.D. thesis, Université du Havre, Le Havre, France (2013)
Tadie Fogaing, M., Yoshikawa, H., Crumeyrolle, O., Mutabazi, I.: Heat transfer in the thermo-electro-hydrodynamic convection under microgravity conditions. Eur. Phys. J. E. 37, 9987 (2014). https://doi.org/10.1140/epje/i2014-14035-0
Takashima, M., Hamabata, H.: The stability of natural convection in a vertical layer of dielectric fluid in the presence of a horizontal ac electric field. J. Phys. Soc. Jpn. 53, 1728–1736 (1984). https://doi.org/10.1143/JPSJ.53.1728
Travnikov, V., Crumeyrolle, O., Mutabazi, I.: Numerical investigation of the heat transfer in cylindrical annulus with a dielectric fluid under microgravity. Phys. Fluids. 27, 054103 (2015). https://doi.org/10.1063/1.4921156
Turnbull, R.J.: Effect of dielectrophoretic forces on the Bénard instability. Phys. Fluids. 12, 1809–1815 (1969). https://doi.org/10.1063/1.1692745
Turnbull, R.J., Melcher, J.R.: Electrohydrodynamic Rayleigh-Taylor bulk instability. Phys. Fluids. 12, 1160–1166 (1969). https://doi.org/10.1063/1.1692646
Yoshikawa, H.N., Tadie Fogaing, M., Crumeyrolle, O., Mutabazi, I.: Dielectrophoretic Rayleigh-Bénard convection under microgravity conditions. Phys. Rev. E. 87, 043003 (2013). https://doi.org/10.1103/PhysRevE.87.043003
Acknowledgements
The present work has benefited from the financial support from the CNES (French Space Agency) and the French National Research Agency (ANR) through the program “Investissements d’Avenir (Grant N°ANR-10 LABX-09-01”. The doctoral thesis of E.B.B. is co-funded by CNES and Region Normandie.
Author information
Authors and Affiliations
Corresponding author
Additional information
This article belongs to the Topical Collection: The Effect of Gravity on Physical and Biological Phenomena
Guest Editor: Valentina Shevtsova
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Barry, E.B., Yoshikawa, H.N., Fogaing, M.T. et al. Critical Modes of Thermoelectric Convection Instabilities in a Vertical Slot. Microgravity Sci. Technol. 33, 16 (2021). https://doi.org/10.1007/s12217-020-09856-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12217-020-09856-2