ELECTROHYDRODYNAMICS CONVECTION IN DIELECTRIC OLDROYDIAN NANOFLUID LAYER IN POROUS MEDIUM

The onset of thermal convection in an electrically conducting rheological nanofluid to include an external vertical AC electric field saturated by a homogeneous porous medium has been studied using linear stability theory by employing an Oldroydian model which incorporates the effects of the electric field, Brownian motion, thermophoresis, and rheological parameters for bottom heavy distribution of nano- particles. The rheology of the nanofluid is described by the Oldroydian model for calculating the shear stresses from velocity gradients. Exact solutions of the eigenvalue problem for stress-free bounding surface are obtained analytically using Galerkin method and the Darcy Rayleigh number for onset of both stationary and oscillatory convection, obtained for bottom-heavy distribution of nanoparticles. It is found that the Deborah number has a stabilizing effect on the system, while strain retardation time parameter has a destabilizing effect on the oscillatory convection of the system. The effect of the Lewis number tends to stabilize the stationary convection and destabilizes oscillatory convection. The concentration Rayleigh number has a destabilizing effect on stationary convection and a stabilizing effect on the oscillatory convection. Medium porosity has a stabilizing effect on oscillatory convection and is destabilizing on stationary convection. The effect of Vadasz number on oscillatory convection is destabilizing. AC electric field has a destabilizing effect on both the stationary and oscillatory convection.