Effect of couple stress on the onset of thermovibrational convection in a porous medium

Thermovibrational convection in a porous layer permeated by a fluid exhibiting antisymmetric stress due to the presence of couple stress is considered. The criteria for the onset of convection are found when the layer is heated either from the bottom or from the top. Low amplitude vibrations are considered. A linear stability analysis based on the method of small perturbations is performed using normal mode assumption. The critical values of the parameters are found with the help of the Mathieu functions. The instability limits for both synchronous and subharmonic responses and the transition in between them are predicted.

► Vibrating frequency always augments the onset of convection in top heating.
► Couple stress parameter always stabilizes the diffusive equilibrium state.
► It restricts the synchronous mode to lower frequencies in bottom heating.
► It extends the synchronous mode to higher frequencies in top heating.