Browsing by Subject "2ND-ORDER FLUIDS"

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    SIMILARITY ANALYSIS OF BOUNDARY-LAYER EQUATIONS OF A CLASS OF NON-NEWTONIAN FLUIDS
    (PERGAMON-ELSEVIER SCIENCE LTD) PAKDEMIRLI, M
    A similarity analysis of three-dimensional boundary layer equations of a class of non-Newtonian fluids in which the stress is an arbitrary function of rates of strain is made. It is shown that under scaling transformation, for an arbitrary stress function, only 90-degrees of wedge flow leads to similarity solutions, whereas for a specific more restricted form, similarity solutions exist for arbitrary wedge angles. In the case of spiral group transformation, no similarity solutions exist if we force the stress function to remain arbitrary after the transformation, whereas for a specific more restricted form, similarity solutions exist for arbitrary wedge angles. For both transformations, similarity equations for power-law and Newtonian fluids are presented as special cases of the analysis. Finally the conditions for invariance and the form of the stress function for a two-dimensional case are also presented.
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    Symmetry reductions of unsteady tree-dimensional boundary layers of some non-Newtonian fluids
    (PERGAMON-ELSEVIER SCIENCE LTD) Yurusoy, M; Pakdemirli, M
    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, the infinitesimal generators accepted by the equations are calculated for the arbitrary shear stress case. The extension of the Lie algebra, for the case of Newtonian fluids, is also presented. A general boundary value problem modeling the flow over a moving surface with suction or injection is considered. The restrictions imposed by the boundary conditions on the generators are calculated. Assuming all Bow quantities to be independent of the z-direction, the three-independent-variable partial differential system is converted first 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. (C) 1997 Elsevier Science Ltd.
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    Symmetry groups of boundary layer equations of a class of non-Newtonian fluids
    (PERGAMON-ELSEVIER SCIENCE LTD) Pakdemirli, M; Yurusoy, M; Kucukbursa, A
    A non-Newtonian fluid model in which the stress is an arbitrary function of the symmetric part of the velocity gradient is considered. Symmetry groups of the two-dimensional boundary layer equations of the model are found by using exterior calculus. The complete isovector field corresponding to some cases, such as arbitrary shear function, Newtonian fluids, and power-law fluids, are found. Similarly, solutions for some special transformations are presented. Results obtained in a previous paper [M. Pakdemirli, Int. J. Non-Linear Mech. 29, 187 (1994)] using special groups of transformations (scaling, spiral) are verified in this study using a general approach. (C) 1996 Elsevier Science Ltd.