A revised model for the effect of nanoparticle mass flux on the thermal instability of a nanofluid layer

Abstract

Abstract A revised model of the nanoparticle mass flux is introduced and used to study the thermal instability of the Rayleigh-Benard problem for a horizontal layer of nanofluid heated from below. The motion of nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. The nanofluid layer is confined between two rigid boundaries. Both boundaries are assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition. The material properties of the nanofluid are allowed to depend on the local volume fraction of nanoparticles and are modelled by non-constant constitutive expressions developed by Kanafer and Vafai based on experimental data. The results show that the profile of the nanoparticle volume fraction is of exponential type in the steady-state solution. The resulting equations of the problem constitute an eigenvalue problem which is solved using the Chebyshev tau method. The critical values of the thermal Rayleigh number are calculated for several values of the parameters of the problem. Moreover, the critical eigenvalues obtained were real-valued, which indicates that the mode of instability is via a stationary mode.