The unsteady compressible boundary layer over a semi-infinite flat plate caused by a moving shock

The Lam-Crocco problem is reexamined for arbitrary shock strength and Prandtl number, and its complete numerical solution is provided. Instead of following the Crocco formulation, the present approach introduces an unsteady stream function and a Howarth transformation for the distance normal to the plate. For a linear viscosity-temperature dependence, the equations for momentum and energy are obtained, which are decoupled from each other and identical to those for an incompressible fluid. In contrast to the Crocco form, the solution to these equations requires less cumbersome handling for the boundary conditions. Some of the details of the computation are discussed, and typical results of the velocity and temperature profiles, as well as the Nusselt number variation along the plate, are presented. In order to show the behavior of the thermal boundary layer in more general circumstances, cases where the Prandtl number is large have been included.