Abstract
The simplest equation method is employed to construct some new exact closed-form solutions of the general Prandtl's boundary layer equation for two-dimensional flow with vanishing or uniform mainstream velocity. We obtain solutions for the case when the simplest equation is the Bernoulli equation or the Riccati equation. Prandtl's boundary layer equation arises in the study of various physical models of fluid dynamics. Thus finding the exact solutions of this equation is of great importance and interest.
Highlights
Many scientific and engineering problems and phenomena are modeled by nonlinear differential equations
Considerable attention has been devoted to the construction of exact solutions of nonlinear equations because of their important role in the study of nonlinear physical models
The exact solutions of the nonlinear differential equations are of great interest and physically more important
Summary
Many scientific and engineering problems and phenomena are modeled by nonlinear differential equations. The equations of the boundary layer theory have been the subject of considerable interest, since they represent an important simplification of the original Navier-Stokes equations These equations arise in the study of steady flows produced by wall jets, free jets, and liquid jets, the flow past a stretching plate/surface, flow induced due to a shrinking sheet, and so on. These boundary layer equations are usually solved subject to certain boundary conditions depending upon the specific physical model considered. The purpose of the present work is to find the exact closed-form solutions of Prandtl’s boundary layer equation for two-dimensional flow with constant or uniform main stream velocity by the use of simplest equation method.
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