A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate. (English) Zbl 0931.76017
Summary: We apply a new analytic technique, namely the homotopy analysis method, to give an explicit, analytic, uniformly valid solution of the equation governing the two-dimensional laminar viscous flow over a semi-infinite flat plate, , under the boundary conditions , . This analytic solution is uniformly valid in the whole region . For Blasius’ (1908) flow (, ), this solution converges to Howarth’s (1938) numerical result and gives analytic value . For the Falkner-Skan (1931) flow (), it gives the same family of solutions as Hartree’s (1937) numerical results, and provides a related analytic formula for when . Additionally, this analytic solution allows to prove that for , the Hartree’s (1937) family of solutions possesses the property that exponentially as .
|76D10||Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids)|
|76M45||Asymptotic methods, singular perturbations (fluid mechanics)|