Thermal Instability and Chaos in a Hybrid Nanofluid Flow

Abstract

In this work, the linear and nonlinear dynamics of thermal convection in an incompressible Newtonian (alumina-copper)/water hybrid nanofluid each confined in an infinite rectangular cavity and heated from below via the Cattaneo–Christov heat flux model are studied for volume fractions fixed between 0 and 0.05. Firstly, using the governed flow equations and free boundary conditions, we proceed to the classical theory of stationary and oscillatory convection which help us to find the expressions of critical Rayleigh numbers, Cattaneo numbers and wavenumber of base fluid as a function of mono or hybrid nanofluid thermophysical properties. The results show that when the Cattaneo number increases, the critical Rayleigh number is constant in the case of stationary convection but decreases in the case of oscillatory convection for pure base fluid and hybrid nanofluids. It is noted that beyond the threshold Cattaneo number, the critical Rayleigh number of stationary convection is greater than those of oscillatory convection and the critical wavenumber shifts discontinuously from stationary to oscillatory convection. Secondly, the use of the truncated Galerkin approximation made it possible to find a five low-dimensional system in order to study numerically the transition from natural convection to chaotic behavior of nanofluid. We noticed that the addition of hybrid nanoparticle in the heat fluid transfer increases the domain of stationary convection by delaying the oscillatory convection with increasing normalized Rayleigh number. Also, the bifurcation diagrams show that the use of hybrid nanoparticles allows further control of the chaos in base fluid by expanding the convective flow. Furthermore, in the presence of thermal relaxation time, the chaos in the hybrid nanofluid lasts longer compared to the ordinary fluid.