Near continuum boundary layer flows at a flat plate

The problem of boundary layer flows at a flat plate surface with velocity-slip and temperature-jump boundary conditions is analyzed. With the velocity slip conditions, there are multiple physical factors lumped together, and the boundary layer solutions significantly change their behaviors. The self-similarity in the solutions degenerates, however, the problem is still an ordinary differential equation which can be solved. Shooting methods are applied to solve the flowfield. The results include velocity and temperature for both the surface and flowfield. Unlike the traditional Blasius flat plate boundary layer solutions which are self-similar through all the plate boundary layer, the new solutions indicate that the front tip is actually a singularity point, especially at locations within one mean free path from the leading edge.