Temperature modulation effect on the linear stability analysis of Darcy–Bénard convection setup with feedback control and Robin boundary condition on temperature is investigated. The upper and lower plates are assumed to be impermeable. The combination of the Galerkin method, the Maclaurin series expansion, and the Newton–Raphson method for multiple variables is employed to calculate the stationary Rayleigh number. The differential operator method is employed to investigate the effect of temperature modulation on stability of the system. The observations from the study confirm that the effect of feedback control on the system in the presence of temperature modulation is to stabilize the motion. An increase in the Biot number signifies a transition of the thermal boundary condition from an insulating surface to an isothermal surface. This enhanced thermal coupling at the boundary promotes more efficient heat exchange, which suppresses thermal disturbances and thereby stabilizes the system.
Revankar et al. (2026) studied this question.