Browsing by Author "Aksoy Y."
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Item Boundary layer equations and stretching sheet solutions for the modified second grade fluid(2007) Aksoy Y.; Pakdemirli M.; Khalique C.M.A modified second grade non-Newtonian fluid model is considered. The model is a combination of power-law and second grade fluids 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. The boundary layer equations are derived from the equations. Symmetries of the boundary layer equations are calculated using Lie Group theory. For a special power law index of m = -1, the principal Lie algebra extends. Using one of the symmetries, the partial differential system is transferred to an ordinary differential system. The ordinary differential equations are numerically integrated for the stretching sheet boundary 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. The shear stress on the boundary is also calculated. © 2007 Elsevier Ltd. All rights reserved.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 Approximate analytical solutions for flow of a third-grade fluid through a parallel-plate channel filled with a porous medium(2010) Aksoy Y.; Pakdemirli M.The flow of a non-Newtonian fluid through a porous media in between two parallel plates at different temperatures is considered. The governing momentum equation of third-grade fluid with modified Darcy's law and energy equation have been derived. Approximate analytical solutions of momentum and energy equations are obtained by using perturbation techniques. Constant viscosity, Reynold's model viscosity, and Vogel's model viscosity cases are treated separately. The criteria for validity of approximate solutions are derived. A numerical residual error analysis is performed for the solutions. Within the validity range, analytical and numerical solutions are in good agreement. © 2009 Springer Science+Business Media B.V.Item Group classification for path equation describing minimum drag work and symmetry reductions(2010) Pakdemirli M.; Aksoy Y.The path equation describing the minimum drag work first proposed by Pakdemirli is reconsidered (Pakdemirli, M. The drag work minimization path for a flying object with altitude-dependent drag parameters. P roceedin gs of the I nstituti on of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 223 (5), 1113-1116 (2009)). The Lie group theory is applied to the general equation. The group classification with respect to an altitude-dependent arbitrary function is presented. Using the symmetries, the group-invariant solutions are determined, and the reduction of order is performed by the canonical coordinates. © Shanghai University and Springer-Verlag.Item New perturbation-iteration solutions for Bratu-type equations(2010) Aksoy Y.; Pakdemirli M.Perturbation-iteration theory is systematically generated for both linear and nonlinear second-order differential equations and applied to Bratu-type equations. Different perturbation-iteration algorithms depending upon the number of Taylor expansion terms are proposed. Using the iteration formulas derived using different perturbation-iteration algorithms, new solutions of Bratu-type equations are obtained. Solutions constructed using different perturbation-iteration algorithms are contrasted with each other as well as with numerical solutions. It is found that algorithms with more Taylor series expansion terms yield more accurate results. © 2010 Elsevier Ltd. All rights reserved.Item Symmetry analysis of boundary layer equations of an upper convected Maxwell fluid with magnetohydrodynamic flow(Verlag der Zeitschrift fur Naturforschung, 2011) Deǧer G.; Pakdemirli M.; Aksoy Y.Steady state boundary layer equations of an upper convected Maxwell fluid with magnetohydrodynamic (MHD) flow are considered. The strength of the magnetic field is assumed to be variable with respect to the location. Using Lie group theory, group classification of the equations with respect to the variable magnetic field is performed. General boundary conditions including stretching sheet and injection are taken. Restrictions imposed by the boundary conditions on the symmetries are discussed. Special functional forms of boundary conditions for which similarity solutions may exist are derived. Using the symmetries, similarity solutions are presented for the case of constant strength magnetic field. Stretching sheet solutions with or without injection are presented. Effects of physical parameters on the solutions are depicted. © 2011 Verlag der Zeitschrift für Naturforschung, Tübingen.Item A new perturbation-iteration approach for first order differential equations(Association for Scientific Research, 2011) Pakdemirli M.; Aksoy Y.; Boyaci H.Two new perturbation-iteration algorithms for solving differential equations of first order are proposed. Variants of the algorithm are developed depending on the differential order of Taylor series expansions. The iteration algorithms are tested on a number of first order equations. Much better solutions than the regular perturbation solutions are achieved. © Association for Scientific Research.Item Boundary layer theory and symmetry analysis of a Williamson fluid(2012) Aksoy Y.; Hayat T.; Pakdemirli M.Boundary layer equations are derived for the first time for a Williamson fluid. Using Lie group theory, a symmetry analysis of the equations is performed. The partial differential system is transferred to an ordinary differential system via symmetries, and the resulting equations are numerically solved. Finally, the effects of the non-Newtonian parameters on the solutions are discussed. © 2012 Verlag der Zeitschrift für Naturforschung, Tübingen.Item New perturbation-iteration solutions for nonlinear heat transfer equations(2012) Aksoy Y.; Pakdemirli M.; Abbasbandy S.; Boyaci H.Purpose - The purpose of this paper is to apply, for the first time, the authors' newly developed perturbation iteration method to heat transfer problems. The effectiveness of the new method in nonlinear heat transfer problems will be tested. Design/methodology/approach - Nonlinear heat transfer problems are solved by perturbation iteration method. They are also solved by the well-known technique variational iteration method in the literature. Findings - It is found that perturbation iteration solutions converge faster to the numerical solutions. More accurate results can be achieved with this new method for nonlinear heat transfer problems. Research limitations/implications - A few iterations are actually sufficient. Further iterations need symbolic packages to calculate the solutions. Practical implications - This new technique can practically be applied to many heat and flow problems. Originality/value - The new perturbation iteration technique is successfully implemented to nonlinear heat transfer problems. Results show good agreement with the direct numerical simulations and the method performs better than the existing variational iteration method. © Emerald Group Publishing Limited.Item Boundary layer equations and lie group analysis of a sisko fluid(2012) Sari G.; Pakdemirli M.; Hayat T.; Aksoy Y.Boundary layer equations are derived for the Sisko fluid. Using Lie group theory, a symmetry analysis of the equations is performed. A partial differential system is transferred to an ordinary differential system via symmetries. Resulting equations are numerically solved. Effects of non-Newtonian parameters on the solutions are discussed. © 2012 Gözde Sari et al.Item Group-theoretic approach to boundary layer equations of an Oldroy-B fluid(2013) Pakdemirli M.; Hayat T.; Aksoy Y.Boundary layer equations are derived for the first time for an Oldroy-B fluid. The symmetry analysis of the equations is performed using Lie Group theory and the partial differential system is transferred to an ordinary differential system via symmetries. Resulting equations are numerically solved for the case of the stretching sheet problem. Effects of non-Newtonian parameters on the solutions are discussed. © 2013 Verlag der Zeitschrift für Naturforschung.Item Perturbation-iteration method for first-order differential equations and systems(2013) Şenol M.; Timuçin Dolapçi I.; Aksoy Y.; Pakdemirli M.The previously developed new perturbation-iteration algorithm has been applied to differential equation systems for the first time. The iteration algorithm for systems is developed first. The algorithm is tested for a single equation, coupled two equations, and coupled three equations. Solutions are compared with those of variational iteration method and numerical solutions, and a good agreement is found. The method can be applied to differential equation systems with success. © 2013 Mehmet Şenol et al.Item Similarity solutions for boundary layer equations of a Powel-Eyring fluid(Association for Scientific Research, 2013) Hayat T.; Pakdemirli M.; Aksoy Y.Boundary layer equations are derived for the first time for the Powel-Eyring fluid model, a non-Newtonian model proposed for pseudoplastic behavior. Using a scaling symmetry of the equations, partial differential system is transferred to an ordinary differential system. Resulting equations are numerically solved using a finite difference algorithm. Effects of non-Newtonian parameters on the solutions are discussed.Item Determining the velocities and angles for a free kick problem(Canadian Science Publishing, 2015) Pakdemirli M.; Aksoy Y.The free kick problem is considered for three distinct cases: (i) no air drag or lift, (ii) linear drag, and (iii) linear drag and lift. For the first case, closed form formulas are derived for the initial velocities and angles. For the second case, two coupled algebraic equations written from the trajectory equation are given and solved numerically for the initial velocities and angles. For the third case, the equations of motion are solved approximately using perturbation techniques assuming the lift coefficient to be small compared to the drag coefficient. Because the time variable cannot be eliminated between the equations, four coupled sets of algebraic equations are solved numerically for the initial velocities and angles. All three results are compared with each other and the influences of drag and lift coefficients on the velocities and angles are outlined. © 2015 Published by NRC Research Press.Item Perturbation-iteration solution for a third-grade fluid flowing between parallel plates(Begell House Inc., 2015) Yildiz V.; Pakdemirli M.; Aksoy Y.Two dimensional flow of a third grade non-Newtonian fluid between parallel plates is considered. Two different perturbation-iteration algorithms are employed in search of approximate solutions of the differential equations. Velocity and temperature profiles are obtained. Perturbation-iteration solutions are contrasted with regular perturbation and numerical solutions. It is found that the perturbation-iteration solutions seem to converge better to the numerical solutions compared to the regular perturbation solutions, especially when the validity criteria of the regular perturbation solution are not satisfied. Among the perturbation-iteration solutions, the algorithm with higher Taylor series expansion terms produce more accurate results. © 2015 Begell House Inc.. All rights reserved.Item Effects of couple stresses on the heat transfer and entropy generation rates for a flow between parallel plates with constant heat flux(Elsevier Masson SAS, 2016) Aksoy Y.In this study, the flow and heat transfer of a fluid with couple stresses is investigated. The flow caused by the pressure gradient between parallel plates is considered as incompressible, steady and fully developed while the bottom plate is adiabatic and the upper plate is exposed to a constant heat flux. Governing equations, i.e. momentum and energy, are derived and solved analytically. Using the analytical results, effects of couple stresses on the Nusselt number as a heat transfer performance parameter and entropy generation rates in the channel are presented via graphs and tables. In addition, second law analysis is performed by calculating mean entropy generation rates and Bejan number along the channel height. © 2016 Elsevier Masson SAS. All rights reserved.Item Parallel Plate Flow of a Third-Grade Fluid and a Newtonian Fluid with Variable Viscosity(Walter de Gruyter GmbH, 2016) Ylldlz V.; Pakdemirli M.; Aksoy Y.Steady-state parallel plate flow of a third-grade fluid and a Newtonian fluid with temperature-dependent viscosity is considered. Approximate analytical solutions are constructed using the newly developed perturbation-iteration algorithms. Two different perturbation-iteration algorithms are used. The velocity and temperature profiles obtained by the iteration algorithms are contrasted with the numerical solutions as well as with the regular perturbation solutions. It is found that the perturbation-iteration solutions converge better to the numerical solutions than the regular perturbation solutions, in particular when the validity criteria of the regular perturbation solution are not satisfied. The new analytical approach produces promising results in solving complex fluid problems. © 2016 by De Gruyter.Item Application of pert urbation-iteration method to Lotka-Volterra equations(Elsevier B.V., 2016) Aksoy Y.; Göktaş U.; Pakdemirli M.; Dolapçi I.T.Perturbation-iteration method is generalized for systems of first order differential equations. Approximate solutions of Lotka-Volterra systems are obtained using the method. Comparisons of our results with each other and with numerical solutions are given. The method is implemented in Mathematica, a major computer algebra system. The package PerturbationIteration.m automatically carries out the tedious calculations of the method. © 2016 Faculty of Engineering, Alexandria University.Item Perturbation iteration method solutions of a nonlinear fin equation(American Institute of Physics Inc., 2016) Aksoy Y.; Pakdemirli M.Recently developed perturbation iteration method is successfully applied to a nonlinear fin equation. Approximate solutions are obtained using the perturbation iteration method as well as the classical perturbation method. Solutions obtained from the classical and the perturbation iteration method are compared with the numerical solutions. Perturbation iteration method yields very accurate results whereas the classical perturbation method fails to produce acceptable results for large parameters of perturbation. © 2016 Author(s).Item Erratum: Determining the velocities and angles for a free kick problem (Canadian Journal of Physics (2015) 93:11 (1434) DOI: 10.1139/cjp-2015-0274)(National Research Council of Canada, 2016) Pakdemirli M.; Aksoy Y.[No abstract available]