Heat and Mass Transfer, and Chaotic Convection in Nanofluids

Abstract

The regular and chaotic convection in top-heavy and bottom-heavy Boussinesq nanofluid confined between two horizontal layers heated underneath is investigated. A five-dimensional Lorenz like nonlinear model is obtained using Galerkin technique. This 5-D model possesses two major characteristics viz reflection symmetry and dissipation. The bifurcation diagrams and the phase portraits are used to analyse the characteristics of the dynamical system. The onset of chaos in ordinary fluid, nanofluid bottom-heavy, and nanofluid top-heavy configurations take place at scaled Rayleigh number (R) equals 24.73684211, 26.98908141, and 32.24788322 respectively. The case of ordinary fluids has also been deduced from the five-dimensional model. Weakly nonlinear analysis is also done in order to understand the heat and mass transport inside the system with the variation of scaled Rayleigh number. It is observed that the convection starts earlier in case of top-heavy configuration of nanofluid while gets delayed in bottom-heavy configuration as compared to an ordinary fluid. Moreover onset of chaos gets delayed in case of nanofluids. Another major finding of the study is that the system turns chaotic for higher values of scaled Rayleigh number in the top-heavy case as compared to that of in the bottom-heavy case of nanofluid.