A comparative study of individual influences of suspended multiwalled carbon nanotubes and alumina nanoparticles on Rayleigh-Bénard convection in water

Abstract

The generalized Lorenz model for studying the Rayleigh-Bénard convection in water-multiwalled carbon nanotubes and water-alumina in the presence of heat source/sink is derived using a tri-modal, Fourier series representation under the assumption of the Boussinesq approximation and small-scale convective motion. On the premise that the multiwalled carbon nanotubes/alumina nanoparticles undergo all motions which water particles undergo the single-phase description of the Khanafer-Vafai-Lightstone model can be adopted. The thermophysical properties of the two nanoliquids are calculated using the phenomenological laws and traditional mixture theory. The transition of the dynamical Lorenz system from stability to chaos followed by periodic motion in a window of periodicity and then a sequence of such motions are explained in detail by calculating the maximum Lyapunov exponent. Specifically, the individual effect of multiwalled carbon nanotubes and alumina nanoparticles on the stability of the dynamical system is investigated from a new perspective of time series solution and attractors of the Lorenz model. We then study the individual influence of multiwalled carbon nanotubes and alumina nanoparticles on the onset of convection and heat transport. The findings of a feasibility study indicate that less expensive spherical alumina nanoparticles are preferable in heat transfer applications over the more expensive multiwalled carbon nanotubes, in spite of the latter having a larger surface area and higher thermal conductivity. It is found that exactly the same amount of heat transfer obtained by using multiwalled carbon nanotubes can be achieved by replacing them with a slightly higher volume fraction of the much cheaper alumina nanoparticles.