Abstract
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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