Rev. Cub. Fis. 33, 89 (2016) ART ´ ICULOS ORIGINALES ON THE ONSET OF INSTABILITY OF A VISCOELASTIC FLUID SATURATING A POROUS MEDIUM IN ELECTROHYDRODYNAMICS SOBRE LA APARICI ´ ON DE INESTABILIDAD PARA UN FLUIDO VISCOEL ´ ASTICO QUE SATURA UN MEDIO POROSO EN LA ELECTROHIDRODIN ´ AMICA G. C. Rana a† , R. Chand b ,V.Sharma c a) Department of Mathematics, NSCBM Govt. P. G. College, Hamirpur-177 005, Himachal Pradesh, India; drgcrana15@gmail.com † b) Department of Mathematics, Govt. College Nurpur, District Kangra, Himachal Pradesh, India c) Department of Mathematics and Statistics, Himachal Pradesh University, Shimla – 171 005, Himachal Pradesh, India † corresponding author Recibido 5/7/2016; Aceptado 12/10/2016 In this paper, we study the effect of AC electric field on the onset of electrohydrodynamic instability in a viscoelastic fluid layer saturating a porous medium caused by dielectrophoretic force due to variation in the dielectric constant with temperature. Walters’ (model B’) fluid model is used to describe the behaviour of a viscoelastic dielectric fluid and for porous medium, Darcy model is employed. The fluid layer is induced by the dielectrophoretic force due to the variation of dielectric constant with temperature. We derive the dispersion relation describing the influence of viscoelasticity, Darcy number and AC electric field by applying linear stability theory and normal mode analysis method. It is observed that Walters’ (model B’) fluid behaves like an ordinary Newtonian fluid in the stationary convection whereas Darcy number and AC electric field have destabilizing effect on the stationary convection. The present results are in good agreement with the earlier published results. En este art´ ıculo estudiamos el efecto de un campo el´ ectrico alterno en la aparici´ on de la inestabilidad electrohidrodin ´ amica en una capa de un fluido viscoel ´ astico que satura un medio poroso, causada por la fuerza dielectrofor´ etica debido a la variaci´ on de la constante diel ´ ectrica con la temperatura. Se usa el modelo de Walter (modelo B’) para describir el comportamiento de un fluido diel ´ ectrico viscoel ´ astico y, para el medio poroso, el modelo de Darcy. La capa flu´ ıda es inducida por la fuerza dielectrofor´ etica debida a la variaci ´ on de la constante diel ´ ectrica con la temperatura. Derivamos la relaci ´ on de dispersi ´ on que describe la influencia del n´ umero de Darcy de la viscoelasticidad y el campo el ´ ectrico alterno aplicando la teor´ ıa de estabilidad lineal y el m ´ etodo de an´ alisis de modo normal. Se observa que el fluido que sigue el modelo B’ se comporta como un fluido Newtoniano ordinario en la convecci´ on estacionaria, mientras que el n ´ umero de Darcy y el campo el ´ ectrico alterno tienen un efectos desestabilizante sobre la convecci ´ on estacionaria. Estos resultados est ´ an en concordancia con resultados previamente publicados. PACS: Electrohydrodynamics, 47.65.-d, non-Newtonian, 47.50.-d, fluid dynamics, 47.53.+n, through porous media, 47.56.+r I. INTRODUCTION The study of Newtonian fluid heated from below saturating a porous medium has attracted many researchers for the last few decades as it has various applications in geophysics, food processing, oceanography, soil sciences, ground water hydrology, astrophysics etc. Chandrasekher [1] discussed thermal instability of Newtonian fluid under the various assumptions of hydrodynamics and hydromagnetics. A good account of thermal instability problems in a porous medium is given by Wooding [2], Ingham and Pop [3], Vafai and Hadim [4] and Nield and Bejan [5]. Recently, the study of electrohydrodynamic instability in dielectric fluid attracts many researchers because it has various applications in climatology, oceanography, EHD enhanced thermal transfer, EHD pumps, EHD in microgravity, micromechanic systems, drug delivery, micro-cooling system, nanotechnology etc. Chen et al. [6] discussed the applications of electrohydrodynamics in brief. They said that EHD heat transfer came out as an alternative method to enhance heat transfer, which is known as electrothermohydrodynamics (ETHD). Many researchers have been studied the effect of AC or DC electric field on natural convection in a horizontal dielectric fluid layer by taking different types of fluids. The onset of electrohydodynamic convection in a horizontal layer of dielectric fluid was studied by Landau [7], Robert [8], Castellanos [9], Lin [10], Gross and Porter [11], Turnbull [12], Maekawa et al.[13], Smorodin and Velarde [14], Galal [15], Rudraiah and Gayathri [16] and Chang et al.[17]. Takashima and Ghosh [18] studied the electrohydrodynamic instability in a viscoelastic liquid layer and found that oscillatory modes of instability exist only when the thickness of the liquid layer is smaller than about 0.5 mm and for such a thin layer the force of electrical origin is much more important than buoyancy force while Takashima and Hamabata [19] studied the stability of natural convection in a vertical layer of dielectric fluid in the presence of a horizontal AC electric field. In these fluids, an applied temperature gradient produces non-uniformities in the electrical conductivity and the variation of the electrical conductivity of the fluid with temperature produces free charges in the bulk of the fluid. These free charges interacting with applied or induced REVISTA CUBANA DE F ´ ISICA, Vol 33, No. 2 (2016) 89 ART ´ ICULOS ORIGINALES (Ed. E. Altshuler)