Self-Similar Analysis of Start-Up Fluid Flow over Flat Plate

Based on the Lie group method (symmetry transformation groups), an analysis of an unsteady (start-up) flow over a flat surface was performed. This approach enabled reducing the number of independent arguments, which significantly simplifies the process of numerical modeling. An unsteady solution was obtained for the velocity profile in the boundary layer. This enabled estimating the dynamics of the velocity profile transformation and its transition to a steady-state mode. It was shown that in the limit of infinite time of the process, the velocity profile tends to the classical steady-state Blasius profile in the boundary layer. The dynamics of the friction coefficient variation over time were elucidated too.