Linear Instability of Water–Oil Electrohydrodynamic Nanofluid Layers: Analytical and Numerical Stud

Abstract

The linear instability of two electrically conducting nanofluid layers (Water-Mineral oil) is investigated. Two cases are considered, the first case of the Water Al2O3-Oil CuO with its physical values for the nanofluid parameters. The second case considers Water Al2O3-Oil TiO2 nanofluid layers. The nanofluid model includes both the Brownian motion and thermophoresis effects which are discussed due to the nanoparticels volume fraction percent and the temperature difference at the basic state. All properties of the nanofluids are considered variables. Firstly the stability is discussed analytically by obtaining the solutions of the linearized equations of motion with the equations of heat and nanoparticles volume fraction with employing the normal modes technique. The continuity of the normal stress tensor at the interface is applied to produce an implicit dispersion relation between the growth rate and the wave number. Secondly, the stability analysis is studied numerically depending on the relation of the energy growth function with time. The numerical results support the analytical stability results. The streamlines contours are presented graphically in the two nanofluid layers. The results illustrate that the Water Al2O3-Oil CuO interface is more stable than Water Al2O3-Oil TiO2 nanofluid interface. Also, the increase of the temperature difference destabilizes the interface due to the increase of particles motion. The numerical results illustrate that the greater energy growth function occurs at the Oil TiO2 layer which is the most unstable nanofluid layer.