A similarity solution for the unsteady flat plate boundary layer equations

[摘要] The unsteady two-dimensional boundary layer equations are solved through the use of proper similarity variables and asymptotic techniques. The equations lend themselves to the derivation of similarity variables which ultimately transform the equations to a nonlinear partial differential equation (PDE). Asymptotic perturbation techniques reduce the PDE to a set of coupled ordinary differential equations. The zeroth order equation is solved for its behavior close to the plate and far from the plate using a Taylor Expansion and asymptotic analysis respectively. The first order equation is solved at each limit asymptotically. The resulting equations are matched to solve for the constants generated from each solution. Interestingly, comparison of well established numerical results reveals a reasonable degree of accuracy when the constants from the zeroth order equations are modified with the small corrective constants generated from the first order equations.

[发布机构] Rice University