Rayleigh-Bénard Convection of Water-Copper and Water-Alumina Nanofluids Based on Minimal- and Higher-Mode Lorenz Models

Linear and nonlinear stability analyses of Rayleigh–Bénard convection in water-copper and water-alumina nanofluids are studied in the paper by considering a minimal as well as an extended truncated Fourier representation. These representations respectively result in a third-order classical Lorenz model and a five-dimensional extended Lorenz model. The marginal stability plots reveal that the influence of added dilute concentration of nanoparticles in water is to destabilize the system. The rate of destabilization depends on the nanoparticles’ thermophysical properties and their volume fraction. Influence of adding an additional mode in the horizontal direction is to modify the cell size. This can be observed through the marginal curves as well as the stream line plots. Further, from the Nusselt number plots it is evident that the presence of dilute concentration of nanoparticles in water is to enhance heat transport in the system significantly. The dynamical behavior of the minimal and the extended Lorenz models is investigated using the bifurcation diagram. From the study an important finding that emerges is that the Fourier truncated solution is predicted to have different effects in lower-order and higher-order models. The extended penta-modal Lorenz system predicts advanced onset of chaos compared to that predicted by the classical third-order Lorenz model. The individual influence of both nanoparticles in water is to advance the onset of convection as well as to advance the onset of chaos.