Linear stability analysis of electro‐convection in dielectric Oldroydian nanofluid

This study deals with an analytical and computational study for the initiation of oscillatory convection in a rheological nanofluid permeated with an alternating current electric field using stress‐free boundary conditions. The rheological properties of the nanofluid are described using the Oldroyd model. The used model for nanofluid permeated with electric field integrates the additional effect of electrophoresis, Brownian motion, and thermophoresis in the conservation of momentum equations. The coupled partial differential equations are simplified to a nondimensional ordinary linear differential equation using infinitesimal perturbations, Boussinesq approximation, normal mode technique, and linearized stability theory. The characteristic equation is solved analytically for stress‐free boundary conditions and the expressions for Rayleigh number of non‐oscillatory and oscillatory modes initiation are determined with regard to various nondimensional governing variables. The oscillatory modes are found to occur for both the cases of top‐/bottom‐heavy nanoparticle distributions. The thermal Rayleigh number are presented graphically to investigate the influence of involved variables on the stability of the considered system. The results show that the electric Rayleigh number, Prandtl number, and stress‐relaxation parameter advance whereas the strain‐retardation parameter delays the initiation of both stationary and oscillatory convection.