Browsing by Author "Yürüsoy M."
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Item Symmetry groups of boundary layer equations of a class of non-newtonian fluids(Elsevier Ltd, 1996) Pakdemirli M.; Yürüsoy M.; Kücükbursa 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. Copyright © 1996 Elsevier Science Ltd.Item Symmetry reductions of unsteady three-dimensional boundary layers of some non-newtonian fluids(Elsevier Ltd, 1997) Yürüsoy 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 flow 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. © 1997 Elsevier Science Ltd.Item Lie-group analysis of boundary-layer equations of non-Newtonian fluids(1997) Yürüsoy M.; Pakdemirli M.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 infinitesimal 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 only 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.Item Exact solutions of boundary layer equations of a special non-Newtonian fluid over a stretching sheet(Elsevier Science Ltd, 1999) Yürüsoy M.; Pakdemirli M.This work focuses on the boundary layer equations of a special third grade fluid over a stretching sheet in which the second grade effects are negligible compared to third grade and viscous effects. As a first step, the general symmetries of the partial differential system are derived using Lie group analysis. Following this, the equations are reduced to an ordinary differential system via similarity transformations. Finally, the resulting ordinary differential systems are solved. The main observation is that, as the non-Newtonian behavior increases, the boundary layer gets thicker.Item Group classification of a non-Newtonian fluid model using classical approach and equivalence transformations(Elsevier Ltd, 1999) Yürüsoy 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. © 1998 Elsevier Science Ltd. All rights reserved.Item Equivalence transformations applied to exterior calculus approach for finding symmetries: An example of non-Newtonian fluid flow(Elsevier Ltd, 1999) Pakdemirli M.; Yürüsoy M.The exterior differential form approach for finding Lie-Point symmetries of differential equations is extended by implementing equivalence transformations to the formalism. The implementation is shown on a previously worked example of non-Newtonian fluid flow. Group classification of the equations are performed using this method. © 1998 Elsevier Science Ltd. All rights reserved.Item Lie group analysis of creeping flow of a second grade fluid(2001) Yürüsoy M.; Pakdemirli M.; Noyan Ö.F.The two-dimensional equations of motion for the slowly flowing second grade fluid are written in cartesian coordinates neglecting the inertial terms. By employing Lie group analysis, the symmetries of the equations are calculated. The Lie algebra consists of four finite parameter Lie group transformations, one being the scaling symmetry and the others being translations. Two different types of solutions are found using the symmetries. Using the translations in x and y coordinates, an exponential type of exact solution is constructed. For the scaling symmetry, the outcoming ordinary differential equations are more involved and only a series type of approximate solution is presented. Finally, some boundary value problems are discussed. © 2001 Elsevier Science Ltd.Item Approximate analytical solutions for the flow of a third-grade fluid in a pipe(2002) Yürüsoy M.; Pakdemirli M.The flow of a third-grade fluid in a pipe with heat transfer is considered. Constant viscosity, Reynold's model viscosity and Vogel's model viscosity cases are treated separately. Approximate analytical solutions are presented for each case using perturbations. The criteria for which the solutions are valid are determined for the dimensionless parameters involved. The analytical solutions are contrasted with the finite difference solutions given in Massoudi and Christie (Int. J. Non-Linear Mech. 30 (1995) 687-699) and within admissible parameter range, a close match is achieved. © 2001 Elsevier Science Ltd. All rights reserved.Item Comparison of Approximate Symmetry Methods for Differential Equations(2004) Pakdemirli M.; Yürüsoy M.; Dolapçi I.T.Two current approximate symmetry methods and a modified new one are contrasted. Approximate symmetries of potential Burgers equation and non-Newtonian creeping flow equations are calculated using different methods. Approximate solutions corresponding to the approximate symmetries are derived for each method. Symmetries and solutions are compared and advantages and disadvantages of each method are discussed in detail.Item The analysis approach of boundary layer equations of power-law fluids of second grade(Verlag der Zeitschrift fur Naturforschung, 2008) Abbasbandy S.; Yürüsoy M.; Pakdemirli M.A powerful analytic technique for nonlinear problems, the homotopy analysis method (HAM), is employed to give analytic solutions of power-law fluids of second grade. For the so-called second-order power-law fluids, the explicit analytic solutions are given by recursive formulas with constant coefficients. Also, for the real power-law index in a quite large range an analytic approach is proposed. It is demonstrated that the approximate solution agrees well with the finite difference solution. This provides further evidence that the homotopy analysis method is a powerful tool for finding excellent approximations to nonlinear equations of the power-law fluids of second grade. © 2008 Verlag der Zeitschrift für Naturforschung, Tübingen.Item Symmetries of boundary layer equations of power-law fluids of second grade(2008) Pakdemirli M.; Aksoy Y.; Yürüsoy M.; Khalique C.M.A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions. © 2008 The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH.Item Perturbation solution for a third-grade fluid flowing between parallel plates(2008) Yürüsoy M.; Pakdemirli M.; Yilbaş B.S.The flow of non-Newtonian fluid in between two parallel plates at different temperatures is considered. A third-grade fluid with temperature-dependent viscosity is considered in the analysis and the Reynolds model used to account for it. Approximate analytical solutions for the velocity and temperature profiles are found using perturbation techniques. It is found that the influence of the non-Newtonian parameter and viscosity index is more pronounced in the region of the plate surfaces where the rate of fluid strain and temperature gradients are high. © IMechE 2008.