Effect of Initial Temperature Profile on Recovery Factor Computations

In many aeronautical applications the interaction between fluid flow and a high-speed vehicle is of crucial practical relevance, in view of vehicle performance as well as mechanical and thermal loading of the structure. Viscous flow effects, such as frictional drag and thermodynamic heating, usually play a dominant role in high-speed flight. Surface heating due to frictional effects becomes a design concern for flight Mach numbers of two and above. The elevated temperature that is reached under thermal equilibrium conditions (adiabatic wall temperature $Taw$⁠) is described by the recovery factor $r$⁠, as (1,2,3)where $ue$ and $Te$ are the velocity and temperature outside the boundary layer and with the specific heat $cp$ constant. In the context of the incompressible flat plate boundary layer...