Lie-Group Analysis of Boundary-Layer Equations of Non-Newtonian Fluids

Authors: Muhammed YÜRÜSOY, Mehmet PAKDEMİRLİ

Abstract: Two-dimensional unsteady boundary-layer equations of a general model of non-Newtonian fluids were investigated in this study. In this model, the shear stress is taken as an arbitrary function of the velocity gradient. The infinitesimal generators accepted by the equations were calculated using Lie Group analysis for three cases: 1) Arbitrary shear-stress function, 2) Newtonian fluids 3) Power-Law fluids. Three different boundary-value problems with initial conditions were considered and the restrictions they impose on the intinitesimal generators of the arbitrary shear-stress case were calculated. The problems investigated were flow over a surface, flow due to sheet-stretching and flow with suction or injection. Using scaling symmetry, the equations and boundary conditons were transformed into a partial differential system with two variables. Lie Groups were further applied to these equations. It is shown that the equations do not possess any further symmetry and, hence, the three boundary-value problems can oniy be solved numerically. A numerical treatment of the two-independent-variable partial-differential system would be easier than the original three-independent-variable partial-differential system.

Keywords: Lie Groups, boundary layers, non-Newtonian fluids