The effect of time-periodic temperature/gravity modulation on thermal instability in a fluid-saturated rotating porous layer has been investigated by performing a weakly nonlinear stability analysis. The disturbances are expanded in terms of power series of amplitude of convection. The Ginzburg-Landau equation for the stationary mode of convection is obtained and consequently the individual effect of temperature/gravity modulation on heat transport has been investigated. Further, the effect of various parameters on heat transport has been analyzed and depicted graphically.

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.

a b s t r a c tA theoretical analysis of thermo-convective instability in a densely packed porous medium is carried out when the boundary temperatures vary with time in a sinusoidal manner. By performing a weakly non-linear stability analysis, the Nusselt number is obtained as a function of amplitude of convection which is governed by a non-autonomous Ginzburg-Landau equation derived for the stationary mode of convection. The paper succeeds in unifying the modulated Bé nard-Darcy, Bé nard-Rayleigh, Bé nardBrinkman and Bé nard-Chandrasekhar convection problems and hence precludes the study of these individual problems in isolation. A new result that shows that asynchronous temperature modulation may be effectively used to either enhance or reduce heat transport by suitably adjusting the frequency and phase-difference of the modulated temperature is presented.

The criterion for the onset of Darcy–Bénard convection is analyzed when the fluid and porous medium are out of thermal equilibrium and the temperatures of the boundaries vary sinusoidally with time in either a synchronous or an asynchronous manner. A stability analysis of the linearized governing equations is performed by using the matrix differential operator theory. The shift in the critical Darcy–Rayleigh number is evaluated in terms of system parameters, and the effect of those on the shift is depicted graphically to realize the significant effect of temperature modulation on the onset, especially when the thermal non-equilibrium effects are prominent.

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