Nonlinear Thermal Instability in a Rotating Viscous Fluid Layer Under Temperature/Gravity Modulation

Abstract

In the present paper, the effect of time-periodic temperature/gravity modulation on the thermal instability in a rotating viscous fluid layer has been investigated by performing a weakly nonlinear stability analysis. The disturbances are expanded in terms of power series of amplitude of modulation, which has been assumed to be small. The amplitude equation, viz., the Ginzburg–Landau equation, for the stationary mode of convection is obtained and using the same, the effect of temperature/gravity modulation on heat transport has been investigated. The stability of the system is studied and the stream lines are plotted at different slow times as a function of the amplitude of modulation, Rossby number, and Prandtl number. It is found that the temperature/gravity modulation can be used as an external means to augment/diminish heat transport in a rotating system. Further, it is shown that rotation can be effectively used in regulating heat transport.

Effect of internal-heating on weakly non-linear stability analysis of Rayleigh–Bénard convection under g-jitter

“…3) as heat transport increases on increasing the value of Pr. This is compatible with the result of Bhadauria et al [23] obtained for rotating fluid layer. However, as the value of τ increases the effect of Prandtl number on thermal instability diminishes.…”

“…The effect of internal-heating is found to hasten the convection, thus increasing the heat transport. Further, the effect of Pr in the present case, for lower values of τ, is found to be compatible with the result of Bhadauria et al [23], obtained for rotating fluid layer. However, there is a disagreement at large values of τ, as the effect of Pr on thermal instability diminishes in the present case, which may be due to the internal-heating of the system.…”

“…Also we found that heat transport increases on increasing the amplitude of gravity modulation. In the present case, the effect of increasing the frequency of modulation is found to decrease the magnitude of Nu, while it is not so in non-internal-heating case of Bhadauria et al [23]. Further heat transport is more due to the presence of internal heat source than in the absence of internal heating.…”

“…They showed that gravity modulation can be used to enhance/diminish the heat transport in stationary magneto-convection. Bhadauria et al [23] studied thermally/gravity modulated non-linear stability problem in a rotating viscous fluid layer, using Ginzburg-Landau equation for stationary mode of convection.…”

Study of heat transport in a temperature-dependent viscous liquid under temperature modulation

“…At present there are very few studies available in the literature in which nonlinear analysis has been done under temperature modulation. These are due to Siddheshwar et al [18], who studied stationary magneto-convection in a Newtonian liquid under temperature or gravity modulation using Ginzburg-Landau model, Bhadauria et al [19], investigated a non-linear thermal instability in a rotating viscous fluid layer under temperature/gravity modulation, and calculated heat transfer across the fluid layer, Bhadauria et. al, [20] studied weak nonlinear of time-periodic thermal boundary conditions and internal heating on heat transport in a porous medium.…”