Thermal instability in an electrically conducting fluid saturated porous medium, confined between two horizontal walls, has been investigated in the presence of an applied vertical magnetic field and rotation, using the Brinkman model. The temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent oscillatory part. Only infinitesimal disturbances are considered. The combined effect of permeability, rotation, vertical magnetic field, and temperature modulation has been investigated using Galerkin’s method and Floquet theory. The value of the critical Rayleigh number is calculated as function of amplitude and frequency of modulation, Chandrasekhar number, Taylor number, porous parameter, Prandtl number, and magnetic Prandtl number. It is found that rotation, magnetic field, and porous medium all have a stabilizing influence on the onset of thermal instability. Further, it is also found that it is possible to advance or delay the onset of convection by proper tuning of the frequency of modulation of the walls’ temperature. In addition the results corresponding to the Brinkman model and Darcy model have been compared for neutral instability.
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