Browsing by Author "Yurusoy, M"

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    Similarity transformations for partial differential equations
    (SIAM PUBLICATIONS) Pakdemirli, M; Yurusoy, M
    The importance of similarity transformations and their applications to partial differential equations is discussed. The theory has been presented in a simple manner so that it would be beneficial at the undergraduate level. Special group transformations useful for producing similarity solutions are investigated. Scaling, translation, and the spiral group of transformations are applied to well-known problems in mathematical physics, such as the boundary layer equations, the wave equation, and the heat conduction equation. Finally, a new transformation including the mentioned transformations as its special cases is also proposed.
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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.
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    Group classification of a non-Newtonian fluid model using classical approach and equivalence transformations
    (PERGAMON-ELSEVIER SCIENCE LTD) Yurusoy, M; Pakdemirli, M
    Boundary layer equations of a non-Newtonian fluid model in which the shear stress is an arbitrary function of the velocity gradient is considered. Group classification of the equations with respect to shear stress is done using two different approaches: (1) classical theory and (2) equivalence transformations. Both approaches yield identical results. It is found that the principle Lie algebra extends only for cases of Newtonian and Power-Law flows. (C) 1998 Elsevier Science Ltd. All rights reserved.