Prandtl's Boundary Layer Equation for Two-Dimensional Flow: Exact Solutions via the Simplest Equation Method

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.

Lie group symmetries' complete classification for a generalized Chazy equation and its equivalence group

“…The infinitesimal invariance test for the extended system (25) requires the following prolongation of the operator (24), 3) to the extended system (25), we obtain that the invariance condition:…”

“…In [3], [8], [12], [9] it is introduced Prandtl's boundary layer equation for the stream function for an incompressible, steady two-dimensional flow with uniform or vanishing mainstream velocity as…”

“…where g(ω) is a real function and at least C (3) and D = 1 − α (2-dimensional form) or D = 2 − α (radial form), with A = 2 − α in both cases. In [9], the similarity transformation was made explicitly, that is, the author details all the calculations.…”

“…In [3], [12], a rough historical approach in different areas of mathematics and physics is presented for the equation (3).…”

The improved thermal efficiency of Prandtl–Eyring hybrid nanofluid via classical Keller box technique

“…A thickening of the flow occurs at the front or upstream end of these boundaries. In 1904, Prandtl proposed the concept of boundary layers to describe the flow behaviour of viscous fluid near a solid barrier (see Aziz et al 1 ). Using the Navier Stoke equations, Prandtl constructed and inferred boundary layer equations for large Reynolds number flows.…”