Compressible boundary layer stability with conjugate heat transfer in ablating materials

The stability and transition characteristics of compressible boundary layers over ablating surfaces is an important component to the design of thermal protection systems. In the present work, linear stability analysis of compressible boundary layers over a conducting flat plate is performed. Previous works have considered the stability of boundary layers with heat transfer between the surface and the fluid in the baseflow, but have used homogeneous Dirichlet boundary conditions on the surface temperature perturbations. This boundary condition does not allow the temperature of the solid to fluctuate in response to fluctuations in the boundary layer solution. In the present work, this restriction is removed by considering the linearization of the coupled fluid-solid system, where the surface temperature perturbation is a solution to the coupled system. In the limit of high-frequency oscillations of the perturbations, the coupled system tends towards the zero temperature fluctuation solutions found in previous works. Relevant to the slow timescales of ablating systems, the boundary layer stability implications in the low-frequency regime are explored. A pathway to performing linear stability analysis of a fully coupled ablating system is presented.