Effect of trigonometric sine, square and triangular wave-type time-periodic gravity-aligned oscillations on Rayleigh–Bénard convection in Newtonian liquids and Newtonian nanoliquids

Abstract

The influence of trigonometric sine, square and triangular wave-types of time-periodic gravity-aligned oscillations on Rayleigh-Bénard convection in Newtonian liquids and in Newtonian nanoliquids is studied in the paper using the generalized Buongiorno two-phase model. The five-mode Lorenz model is derived under the assumptions of Boussinesq approximation, small-scale convective motion and some slip mechanisms. Using the method of multiscales, the Lorenz model is transformed to a Ginzburg-Landau equation the solution of which helps in quantifying the heat transport through the Nusselt number. Enhancement of heat transport in Newtonian liquids due to the presence of nanoparticles/nanotubes is clearly explained. The study reveals that all the three wave types of gravity modulation delay the onset of convection and thereby to a diminishment of heat transport. It is also found that in the case of trigonometric sine type of gravity modulation heat transport is intermediate to that of the cases of triangular and square types. The paper is the first such work that attempts to theoretically explain the effect of three different wave-types of gravity modulation on onset of convection and heat transport in the presence/absence of nanoparticles/nanotubes. Comparing the heat transport by the single-phase and by the generalized two-phase models, the conclusion is that the single-phase model under-predicts heat transport in nanoliquids irrespective of the type of gravity modulation being effected on the system. The results of the present study reiterate the findings of related experimental and numerical studies.The original article has been corrected due to typesetting mistakes made in section 2.2 Mathematical Formulation, Table 1 and in Equation ( 51).

A study of Rayleigh–Bénard convection in hybrid nanoliquids with physically realistic boundaries

“…Further, the Lorenz model ( 27)-( 29) is analytically intractable. To pursue our objective of obtaining an analytical solution we transform the third-order Lorenz model into the first-order Ginzburg-Landau model (see [14,15]). In other words, we project the third-order Lorenz model into the first-order Ginzburg-Landau model.…”

“…The European Physical Journal Special Topics Table 1. Common choice of base liquid and nanoparticles/nanotubes [10]- [15].…”

Onset of synchronous and asynchronous convection in modulated nanofluid filled porous media

“…[21], Shivakumara et al. [22] and Siddheshwar and Kanchana [23]. Despite these and plenty of other works available on the non‐homogeneous model, the advantage of the homogeneous model is well understood even in many state‐of‐art problems.…”

Individual effects of four types of rotation modulation on Rayleigh–Bénard convection in a ferromagnetic fluid with couple stress

“…The effects of sinusoidal and nonsinusoidal time-periodic body force on RBC in a Newtonian fluid and Newtonian nanofluids were first examined by Siddheshwar and Kanchana. 36 They concluded that by fine-tuning the frequency and amplitude of modulation, the onset of convection and heat transport can be controlled. Siddheshwar and Meenakshi 37 compared the effects of trigonometric sine, square, and triangular wave type of gravity modulation on RBC in nanofluids.…”