Thermal Convective Instabilities and Chaos in a Rotating Hybrid Nanofluid Layer with Cattaneo–Christov Heat Flux Model

Abstract

The linear and nonlinear dynamics of thermal convection of a rotating hybrid nanofluid layer heated from below with the Cattaneo–Christov heat flux model are studied in this paper. Starting from the flow equations of a hybrid nanofluid and exploiting the free boundary conditions, the analytical expressions of the stationary and oscillatory Rayleigh numbers of the base fluid are determined as a function of the dimensionless parameters of the heat transfer fluid and the thermophysical properties of the hybrid nanofluid. The effects of hybrid nanoparticles and Taylor number on the onset of stationary convection in the base fluid are investigated graphically. Then, a numerical study of the transition from natural convection to chaotic behaviour of the hybrid nanofluid is made using the truncated Galerkin approximation. This approximation allowed us to find a novel six-dimensional nonlinear system depending on the parameters of the base fluid and the thermophysical properties of the hybrid nanofluid that can be reduced to five, four, or three dimensions when we tend some parameters to zero. The different results showed that the addition of hybrid nanoparticles (alumina-copper) to a thermal fluid (water) subjected to the rotation force in the presence or absence of the thermal relaxation time allows control of the chaotic convection in the base fluid. On the other hand, the increase of the rescaled Taylor number and the Cattaneo number widens the domain of chaos in the hybrid nanofluid with the increase of the rescaled Rayleigh number of the base fluid.