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Zbl 0904.76006
Yürüsoy, Muhammet; Pakdemirli, Mehmet
Symmetry reductions of unsteady three-dimensional boundary layers of some non-Newtonian fluids. (English)
[J] Int. J. Eng. Sci. 35, No.8, 731-740 (1997). ISSN 0020-7225

Summary: Three-dimensional, unsteady, laminar boundary layer equations of a general model of non-Newtonian fluids are treated. In this model, the shear stresses are considered to be arbitrary functions of velocity gradients. Using Lie group analysis, we calculate the infinitesimal generators accepted by the equations in the arbitrary shear stress case. The extension of Lie algebra, for the case of Newtonian fluids, is also presented. Then we consider a general boundary value problem modeling the flow over a moving surface with suction or injection, and calculate the restrictions imposed by the boundary conditions on the generators. Assuming all flow quantities to be independent of the $z$-direction, the three-independent-variable partial differential system is converted into a two-independent-variable system by using two different subgroups of the general group. Lie group analysis is further applied to the resulting equations, and final reductions to ordinary differential systems are obtained.

MSC 2000:: *76A05 Non-Newtonian fluids
35Q35 Other equations arising in fluid mechanics
35A30 Geometric theory for PDE, transformations

Keywords: shear stresses; Lie group analysis; infinitesimal generators; Lie algebra; Newtonian fluids; boundary value problem; moving surface; suction; injection

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