Oscillatory Modes on the Onset of Electrohydrodynamic Instability in Oldroydian Nanofluid Saturated Anisotropic Porous Layer

Abstract

This work deals with an analytical study on the initiation of oscillatory convection in a rheological nanofluid saturating anisotropic porous layer with inclusion of vertical AC electric field using modified boundary conditions with negligible flux of volume fraction of nanoparticles. The rheological properties of the nanofluid are described using Oldroyd model. The Darcy model extended by Brinkman model is deployed to characterize the solid matrix behavior. The used model for nanofluid with inclusion of electric field integrates the additional effect of electrophoresis with that of thermophoresis and Brownian motion in the conservation equations of motion. The partial differential equations are simplified to non-dimensional linear equations 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. The oscillatory modes are found to occur for both the cases of top-/bottom-heavy nanoparticles distributions. The electric Rayleigh number, thermal Prandtl number and stress relaxation parameter advances whereas the Brinkman-Darcy number are found to delay initiation of both stationary and oscillatory convection.