Controlling Rayleigh–Bénard Magnetoconvection in Newtonian Nanoliquids by Rotational, Gravitational and Temperature Modulations: A Comparative Study

The effect of three different types of time periodic modulations on the Rayleigh–Bénard magnetic system involving Newtonian nanoliquids is studied. Multiple-scale analysis (homogenization method) is used to arrive at the Ginzburg–Landau equation. The curiosity in the work is to know the individual effects of (1) rotation, (2) gravity and (3) temperature modulations on Rayleigh–Bénard magnetoconvection in weakly electrically conducting Newtonian nanoliquids. A significant effort in this research is devoted toward linear and nonlinear stability analyses as well as the homogenization method which leads to the Ginzburg–Landau evolution equation. Although several studies have concluded similar results for nanoliquids compared with those of pure base fluids, many fundamental issues like the choice of phenomenological models for the thermo-physical properties and “the” best type of nanoparticles are not well understood. This research focuses on several important issues involving mathematical and computational problems arising in heat transfer analysis in the presence of nanoliquids. Effects of various nanoliquid parameters, frequency and amplitude of modulation on heat transport are analyzed. This investigation focuses on five nanoliquids, with water as a carrier liquid and five nanoparticles, viz. copper, copper oxide, silver, alumina and titania. Enhanced heat transport was observed for rotation, gravity and temperature modulations. In the case of rotation modulation, it is found that increase in the amplitude of modulation results in a decrease in the critical Rayleigh number and thereby to an increase in the mean Nusselt number. The increase in the amplitude of the gravity modulation is shown to enhance the heat transport, whereas increase in frequency is to inhibit the heat transport. Two types of temperature modulations are considered, viz. in-phase (synchronous) and out-of-phase (asynchronous) temperature modulations with the assumption that the boundary temperatures vary sinusoidally with time. The amplitudes of modulation are considered to be very small. In the case of in-phase modulation, there is no significant difference between the heat transports in the presence and in the absence of temperature modulation. On this reason, out-of-phase temperature modulation is used to either enhance or diminish heat transport by suitably adjusting the frequency and phase difference of the modulated temperature. The effect of magnetic field, in all three cases of modulations, is to inhibit the onset of convection and thereby diminish the heat transport.