Instability analysis of the flow between two parallel plates where the bottom one coated with porous media

This study investigates the instability of pure Newtonian fluid flow between two parallel plates where the bottom one coated with various porous media with permeability, K and porosity, ε. We have applied normal modes to perturb the coupled flow system. Specifically, the effects of some dimensionless parameters such as depth ratio, permeability parameter, and the porosity of the porous medium on the instability have been examined. We found these parameters play a critical role in the instability. Depending on these parameters, instability is initiated and dominated either by the fluid or by the porous region. In particular, we found that there are ranges of the depth ratio and the permeability parameter for each value of the porous media porosity that affect the instability of this coupled flow. We have also determined a new parameter which specifies the potential dominance and the stability margin of each mode. To validate our calculations, we have also compared our results with the Orr-Sommerfeld equation. In addition, we have examined three special extreme conditions to study the coupled flow system in more detail.