Porous coatings are an effective strategy for delaying the transition from laminar to turbulent flow in high speed boundary layers. This study uses the harmonic linearized Navier-Stokes approach, which has been shown to achieve sufficient accuracy compared to direct numerical simulations. By analyzing the energy budget analysis of each term in the linear stability equations, we identified key physical sources across a wide range of wall temperature ratios. Wall cooling stabilizes the oblique first mode by causing the Reynolds thermal stress and expansion fluctuations to become out of source with the internal energy fluctuations. It destabilizes the Mack mode by creating a significant wall-normal internal energy transfer region. In contrast, the porous coating destabilizes the oblique first mode by significantly enhancing average shear production, while stabilizing the Mack mode through wall heat transfer. The overall effect of the finite-length porous coating on unstable perturbations shows a critical threshold that separates unstable frequency bands from stable ones. Additionally, a decrease in wall temperature enhances the scattering effect on the Mack mode and shifts the critical frequency to higher frequencies.
 

Energy analysis, Porous coating, High speed