Stability Analysis of Darcy–Bénard Convection Subjected to Time-Dependent Heating Using an LTNE Model

A bounded porous domain saturated with a Newtonian fluid and subjected to time-dependent temperature variation has various practical applications, such as in solar energy storage, nuclear reactors, food processing industry, and agricultural science. In the current work, we study Darcy–Bénard convection in a horizontal fluid-saturated porous layer that is heated from below and confined in all directions. We look into an intricate form of the modulated Darcy–Bénard problem, where the temperatures at the bottom and top boundaries undergo sinusoidal temporal modulation about their mean values. We perform linear stability analysis to understand the onset of convection using a two-phase heat model based on the assumption that the solid and fluid phases of the system are not in local thermal equilibrium. The time-periodic eigenvalue problem obtained here is solved using the Floquet theory to find the onset threshold value of critical Rayleigh number. Our results suggest that the convection through subharmonic modes is preferable for either small (\(\text {H} < 4.3)\) or large (H \(> 175\)) interphase heat transfer coefficient, while for the moderate values of H, convection takes place through harmonic mode only. In the paper, we discuss the results in detail and present a comparison with those from previous studies.