Thermovibrational filtration convection in memory fluids: Bottom and top heating

This paper addresses thermovibrational convection in a thin porous layer permeated by a second grade fluid exhibiting strain history. Necessary conditions for the onset of convection are found when the layer is heated either from the bottom or from the top. A stability analysis based on the method of small perturbations is performed using normal mode assumption. The critical values of the governing parameters are found with the help of the Mathieu functions. The emerging instabilities of synchronous and subharmonic types and the transition between them are examined.