Exact analytic solutions of nonlinear boundary value problems in fluid mechanics (Blasius equations)

Abstract

In this work it is shown that, by a series of admissible functional transformations, the generalized Blasius equation in fluids can be exactly reduced to a three-term generalized Emden-Fowler equation. Furthermore, the restricted in axisymmetric flows and simplified forms of this equation can be reduced to (i) two-term generalized Emden-Fowler equations; (ii) generalized Emden-Fowler equations; (iii) Emden-Fowler equations of the normal form; and (iv) Abel equations of the second kind. By means of a recently developed mathematical solution methodology (Panayotounakos, Fifth Greek Congress on Mechanics, Xania, Crete, 22-25 June 2004, Hellas, Greece), we provide exact analytic solutions for the simplified as well as for the restricted forms of the above-mentioned Blasius equations. Thus, it is proved that important, unsolvable in exact form problems in nonlinear fluid dynamics now can be analytically solved. (C) 2005 American Institute Of Physics