Linear Instability of Electromagnetic Viscoelastic Nanofluid: Analytical and Numerical Study

Abstract

In this study, the effect of the induced electromagnetic fields on the linear instability of a viscoelastic nanofluid liquid layer is discussed. Two physical cases are considered for the channel flow. The first one is considered for the free–free boundaries and the second for the rigid–rigid boundaries. The instability is investigated analytically due to the normal mode analysis and numerically according to the relation between the energy density function and time. The Routh–Hurwitz criteria are applied. The dispersion relation is obtained as a sixth-degree equation of the growth rate. Also, the stationary, as well as oscillatory states of the thermal Rayleigh number, are obtained. The numerical solution is compared with the exact solution for a special choice of the parameters and the results show higher match between the results. The main important result of the study concludes that the Brownian motion of the nanoparticles destabilizes the nanofluid layer. This means that the pure fluid layer is more stable than the nanofluid layer. Also, the results confirm that the flow between the rigid–rigid boundaries is more stable than the free–free boundaries. Finally, due to the Lorentz force, the induced magnetic field destabilizes the motion due to the temperature rise.