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Onset of electroconvective instability of Oldroydian viscoelastic liquid layer in Brinkman porous medium. (English) Zbl 1168.76322
Summary: The problem of the onset of electrohydrodynamic instability in a horizontal layer of Oldroydian viscoelastic dielectric liquid through Brinkman porous medium under the simultaneous action of a certical ac electric field and a vertical temperature gradient is analyzed. Applying linear stability theory, we derive an equation of eight order. Under somewhat suitable boundary conditions, this equation can be solved exactly to yield the required eigenvalue relationship from which various critical values are determined in detail. Both the cases of stationary and oscillatory instabilities are discussed if the liquid layer is heated from below or above. The effects of the porosity of porous medium, the medium permeability, the Prandtl number, the ratio of retardation time to relaxation time, the elastic number, in the presence or absence of Rayleigh number are shown graphically for both cases. Some of the known results are derived as special cases. The electrical force has been shown to be the sole agency causing instability of the considered system since it is much more important than the buoyancy force even if the medium is porous.

MSC:
76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76E06 Convection in hydrodynamic stability
76A10 Viscoelastic fluids
76S05 Flows in porous media; filtration; seepage
80A20 Heat and mass transfer, heat flow (MSC2010)
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