SYMMETRY REDUCTIONS OF UNSTEADY TREE-DIMENSIONAL BOUNDARY-LAYERS OF SOME NON-NEWTONIAN FLUIDS

Three-dimensional, unsteady, laminar boundary layer equations of a gen eral model of non-Newtonian fluids are treated. In this model, the she ar stresses are considered to be arbitrary functions of velocity gradi ents. Using Lie Group analysis, the infinitesimal generators accepted by the equations are calculated for the arbitrary shear stress case. T he extension of the Lie algebra, for the case of Newtonian fluids, is also presented. A general boundary value problem modeling the flow ove r a moving surface with suction or injection is considered. The restri ctions imposed by the boundary conditions on the generators are calcul ated. Assuming all Bow quantities to be independent of the z-direction , the three-independent-variable partial differential system is conver ted first into a two-independent-variable system by using two differen t subgroups of the general group. Lie Group analysis is further applie d to the resulting equations, and final reductions to ordinary differe ntial systems are obtained. (C) 1997 Elsevier Science Ltd.