Regulation of heat transfer in Rayleigh–Bénard convection in Newtonian liquids and Newtonian nanoliquids using gravity, boundary temperature and rotational modulations

Abstract

The individual effect of time-periodic gravity modulation, in-phase and out-of-phase temperature modulations and rotational modulation on Rayleigh–Benard convection in twenty-eight nanoliquids is studied in the paper using the two-phase description of the generalized Buongiorno model. The generalized Lorenz model for each modulation problem is derived using the truncated Fourier series representation. The method of multiscales is employed to arrive at the Ginzburg–Landau equations from the Lorenz models, and the solution of Ginzburg–Landau equations is used to quantify the heat transport. The modulation amplitude is considered to be small (of order less than unity) and low frequencies of modulation are considered. The coefficient of the linear term of the algebraic part of the Ginzburg–Landau equations is shown to exclusively hold the information on the amplitude and the frequency of modulation. The influence of nanoparticles (nanotubes) on heat transport in the presence/absence of various modulations is explained. The study reveals that the frequency of modulation is a dominant factor in the case of gravity and rotational modulations whereas in the case of boundary temperature modulation in addition to the frequency of modulation, the phase difference plays an important role. Effect of these three modulations is to enhance/diminish heat transport but depends strongly on the choice of values of frequency of modulation and amplitude. For fixed values of frequency ( $$\omega ^*=5$$ ) and amplitude ( $$\delta _2=0.1$$ ) of various modulations, it is shown that the maximum percentage of heat transport enhancement achieved in glycerin due to 5% of $$\hbox {SWCNTs}$$ is 21.86% for gravity modulation, 17.36% for rotational modulation and 15.63% for boundary temperature modulation (out of phase). The reason for highest heat transport in gravity modulation is explained by finding area under the curves of three modulations. The study reveals that the modulation whose area under the curve is maximum transports maximum heat. The results pertaining to the single-phase model are recovered as a limiting case of the present study. The study shows that the single-phase model under-predicts heat transport compared to the two-phase model. The results obtained in the present study are compared with those of previous investigations and qualitatively good agreement is found.