Thermal Gradient-Mediated Instability in a Bilayer Flow Over a Porous Medium

In the current work, we explore the noticeable features of thermal gradient-triggered instability of a bilayer placed over a porous media. A comprehensive Orr-Sommerfield (OS) analysis is used to inspect the instability of a bilayer flow narrowed between a Darcy-Brinkman porous medium and a rigid plate. The OS equations are then numerically solved by implying suitable boundary conditions to get the length and time scales of instability aroused in the system. The parametric analysis gives the critical conditions at which the system becomes unstable and causes one of the layers in the bilayer to rupture, leading to the formation of micro-scale shapes. The predicted length scale at which the interface is highly unstable is in good agreement with the existing works. Interestingly, the length scale of the instability after film ruptures is identical to the most catastrophic wavelength of the system and with the available literature.