SYMMETRY CLASSIFICATION OF NEWTONIAN INCOMPRESSIBLE FLUID'S EQUATIONS FLOW IN TURBULENT BOUNDARY LAYERS

Abstract

Lie-group method is applicable to both linear and nonlinear partial dierential equations, which leads to nd new solutions for partial dierential equations. Lie symmetry group method is applied to study Newtonian incompressible uid’s equations ow in turbulent boundary layers. (Flow and heat transfer of an incompressible viscous uid over a stretching sheet appear in several manufacturing processes of industry such as the extrusion of polymers, the cooling of metallic plates, the aerodynamic extrusion of plastic sheets, etc. In the glass industry, blowing, oating or spinning of bres are processes, which involve the ow due to a stretching surface.) The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained [9, 10]. Finally the structure of the Lie algebra such as Levi decomposition, radical subalgebra, solvability and simplicity of symmetries is given.