Exact Similarity Solutions of Unsteady Laminar Boundary Layer Flows

The studies of laminar unsteady boundary layer flows is crucial for understanding turbulence origins. However, the task of finding its solutions poses a significant challenge. In this paper, we propose a novel approach by introducing a similar transformation to convert the 2D unsteady laminar boundary layer equations into a single partial differential equation with constant coefficients. By applying this transformation, we are able to obtain the exact solution for the velocity field of the 2D unsteady laminar boundary layer equations, specifically for the case of flat plate boundary flow. Notably, this is the first time that such an exact solution has been obtained.