Linear stability analysis of electro‐convection in dielectric Oldroydian nanofluid

Abstract

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.

Effects of throughflow and internal heating in a composite air‐porous medium

“…A detailed discussion on these topics can be found in books by Nield and Bejan. 1,2 The cooling applications within porous media are discussed by Chand and Rana, 3,4 Sharma and Rana, 5 Krishna and Chamkha, 6,7 Gautam et al, 8 Devi et al, [9][10][11] Sharma et al, 12 and Krishna et al [13][14][15] Nield 16 initiated the investigation on the onset of convection in a fluid-porous configuration. In his study, the initiation of convection in a fluid layer above a layer of the porous bed where the top surface of the fluid layer was a deformable surface.…”