On the Oscillatory Convective Instability in Nanofluid Layer with Temperature Dependent Viscosity

Abstract

In the present paper, the problem of thermal convection in nanofluid layer heated from below with temperature dependent viscosity is studied mathematically for general boundary conditions, when the instability sets in as oscillatory convection. The expressions for Rayleigh numbers for exponential temperature dependent viscosity variation are derived using Galerkin method from the eigenvalue problem for each combination of rigid (the surfaces with non-slip condition) and dynamically free (the surfaces with stress free condition) boundaries. The effects of viscosity variation parameter, Lewis number, concentration Rayleigh number, modified diffusivity ratio and Prandtl number on the onset of oscillatory convection for each case of boundary conditions are investigated numerically. It is observed that the exponential variation of temperature dependent viscosity has stabilizing effect on the onset of oscillatory convection in nanofluid layer for each case of boundary conditions. However, the Lewis number and the concentration Rayleigh number have destabilizing effect on the onset of oscillatory convection.