Synchronous and asynchronous boundary temperature modulations of Bénard–Darcy convection

A 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 Bénard–Darcy, Bénard–Rayleigh, Bénard–Brinkman and Bénard–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 importance of local acceleration term is discussed.
► Real and non-autonomous Ginzburg–Landau equation is derived.
► Nusselt number is obtained as a function of amplitude of convection.
► Other modulated-Bénard problems are recovered as limiting cases.
► Asynchronous temperature modulation is shown to regulate heat transfer.