Effect of trigonometric sine, square and triangular wavetype time-periodic gravity-aligned oscillations on Rayleigh–
Be´nard 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–Be´nard 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
