Browsing by Author "Pakdemirli, M"

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    The Analysis Approach of Boundary Layer Equations of Power-Law Fluids of Second Grade
    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 formulas with constant coefficients. Also, for the real power-law index in a quite large range,e 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 the power-law fluids second grade.
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    Symmetries of boundary layer equations of power-law fluids of second grade
    Pakdemirli, M; Aksoy, Y; Yürüsoy, M; Khalique, CM
    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.
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    Entropy generation for pipe flow of a third grade fluid with Vogel model viscosity
    Pakdemirli, M; Yilbas, BS
    The flow of fluid-solid mixtures in a pipe can be treated as non-Newtonian fluids of third grade. Depending upon the fluid viscosity, entropy generation in the flow system varies. In the present study, flow of third grade fluid in a pipe is considered. The Vogel model is introduced to account for the temperature-dependent viscosity. Entropy generation due to fluid friction and heat transfer in the flow system is formulated. The influence of viscosity parameters A and B on the entropy generation number is investigated. It is found that increasing viscosity parameter A reduces the entropy generation number and opposite is true for increasing viscosity parameter B. (c) 2005 Elsevier Ltd. All rights reserved.
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    Group classification of fin equation with variable thermal properties
    Pakdemirli, M; Sahin, AZ
    A nonlinear fin equation in which thermal conductivity is an arbitrary function of temperature and, heat transfer coefficient is an arbitrary function of spatial variable is considered. Lie Group theory is applied to the equation. Group classification with respect to the thermal conductivity and heat transfer coefficient is performed. Results are summarized in a table for convenience. Some similarity transformations are used to convert the partial differential equation into an ordinary differential equation. (C) 2004 Elsevier Ltd. All rights reserved.
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    Entropy generation in a pipe due to non-Newtonian fluid flow: Constant viscosity case
    Pakdemirli, M; Yilbas, BS
    Non-Newtonian fluid flow in a pipe system is considered and a third grade non-Newtonian fluid is employed in the analysis. The velocity and temperature distributions across the pipe are presented. Entropy generation number due to heat transfer and fluid friction is formulated. The influences of non-Newtonian parameter and Brinkman number on entropy generation number are examined. It is found that increasing the non-Newtonian parameter reduces the fluid friction in the region close to the pipe wall. This in turn results in low entropy generation with increasing non-Newtonian parameter. Increasing Brinkman number enhances the fluid friction and heat transfer rates; in which case, entropy number increases with increasing Brinkman number.
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    Group-Theoretic Approach to Boundary Layer Equations of an Oldroy-B Fluid
    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.
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    Comparison of approximate symmetry methods for differential equations
    Pakdemirli, M; Yürüsoy, M; Dolapçi, IT
    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.
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    Estimating roots of polynomials using perturbation theory
    Pakdemirli, M; Yurtsever, HA
    Perturbation theory and the order of magnitude of terms are employed to develop two theorems. The theorems may be useful to estimate the order of magnitude of the roots of a polynomial a priori before solving the equation. The theorems are developed for two special types of polynomials of arbitrary order with their coefficients satisfying certain conditions. Numerical applications of the theorems are presented as examples. (c) 2006 Elsevier Inc. All rights reserved.
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    Analytical solution for temperature field in electron and lattice sub-systems during heating of solid film
    Yilbas, BS; Pakdemirli, M
    The analytical solution for non-equilibrium temperature field in solid substrate is presented. Closed form solutions for electron and lattice site temperature rise are obtained for a solid layer heated at the surface with a time-decaying intensity pulse. In the analytical solutions, a perturbation method of strained parameters is introduced. Temperature simulations are carried out for a gold layer with different thicknesses. It is found that increasing layer thickness lowers electron and lattice site temperatures at the surface. Electron temperature at the surface decays sharply with progressing heating period, which is more pronounced for thin layer. Moreover, lattice site temperature continues to rise despite reducing electron temperature in the surface region. The results obtained from the analytical solution for the lattice site temperature agrees well with the numerical predictions. (c) 2006 Elsevier B.V. All rights reserved.
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    Infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations
    Pakdemirli, M; Öz, HR
    The transverse vibrations of simply supported axially moving Euler-Bernoulli beams are investigated. The beam has a time-varying axial velocity with viscous damping. Traveling beam eigenfunctions with infinite number of modes are considered. Approximate analytical solutions are sought using the method of Multiple Scales, a perturbation technique. A detailed analysis of the resonances in which upto four modes of vibration involved are performed. Stability analysis is treated for each type of resonance. Approximate stability borders are given for the resonances involving only two modes. For higher number of modes involved in a resonance, sample numerical examples are presented for stabilities. (c) 2007 Elsevier Ltd. All rights reserved.
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    Boundary layer equations and stretching sheet solutions for the modified second grade fluid
    Aksoy, Y; Pakdemirli, M; Khalique, CM
    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. (C) 2007 Elsevier Ltd. All rights reserved.
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    Approximate symmetries of creeping flow equations of a second grade fluid
    Dolapçi, IT; Pakdemirli, M
    Creeping flow equations of a second grade fluid are considered. Two current approximate symmetry methods and a modified new one are applied to the equations of motion. Approximate symmetries obtained by different methods and the exact symmetries are contrasted. 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. (C) 2004 Elsevier Ltd. All rights reserved.
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    New Perturbation Iteration Solutions for Fredholm and Volterra Integral Equations
    Dolapçi, IT; Senol, M; Pakdemirli, M
    In this paper, recently developed perturbation iteration method is used to solve Fredholm and Volterra integral equations. The study shows that the new method can be applied to both types of integral equations. Some numerical examples are given, and results are compared with other studies to illustrate the efficiency of the method.
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    Two-to-one internal resonances in a shallow curved beam resting on an elastic foundation
    Öz, HR; Pakdemirli, M
    Vibrations of shallow curved beams are investigated. The rise function of the beam is assumed to be small. Sinusoidal and parabolic curvature functions are examined. The immovable end conditions result in mid-plane stretching of the beam which leads to nonlinearities. The beam is resting on an elastic foundation. The method of multiple scales, a perturbation technique, is used in search of approximate solutions of the problem. Two-to-one internal resonances between any two modes of vibration are studied. Amplitude and phase modulation equations are obtained. Steady state solutions and stability are discussed, and a bifurcation analysis of the amplitude and phase modulation equations are given. Conditions for internal resonance to occur are discussed, and it is found that internal resonance is possible for the case of parabolic curvature but not for that of sinusoidal curvature.
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    Optimum Path of a Flying Object with Exponentially Decaying Density Medium
    Abbasbandy, S; Pakdemirli, M; Shivanian, E
    In this paper, a differential equation describing the optimum path of a flying object is derived. The density of the fluid is assumed to be exponentially decaying with altitude. The equation is cast in to a dimensionless form and the exact solution is given. This equation is then analyzed by homotopy analysis method (HAM). The results showed in the figures reveal that this method is very effective and convenient.
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    Stability analysis of an axially accelerating string
    Pakdemirli, M; Ulsoy, AG
    The dynamic response of an axially accelerating string is investigated. The time dependent velocity is assumed to vary harmonically about a constant mean velocity. Approximate analytical solutions are sought using two different approaches. In the first approach, the equations are discretized first and then the method of multiple scales is applied to the resulting equations. In the second approach, the method of multiple scales is applied directly to the partial differential system. Principal parametric resonances and combination resonances are investigated in detail. Stability boundaries are determined analytically. It is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies. When the velocity variation frequency is close to zero or to the difference of two natural frequencies, however, no instabilities are detected up to the first order of perturbation. Numerical results are presented for a band-saw and a threadline problem. (C) 1997 Academic Press Limited.
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    A GEOMETRICAL OPTIMIZATION PROBLEM ASSOCIATED WITH FRUITS OF POPPY FLOWER
    Deger, G; Pakdemirli, M; Candan, F
    Inspired from the poppy fruit (Papaver rhoeas L.), a geometrical optimization problem is posed. The aim is to minimize the surface area for a given volume. The poppy fruit geometry is selected as the optimization geometry. The mathematical problem is solved using calculus. The optimum solutions obtained from mathematical model are contrasted with measurements of the fruit. A good agreement with difference in areas less than 1% in most of the cases is observed between the results.
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    Perturbation-Iteration Method for First-Order Differential Equations and Systems
    Senol, M; Dolapçi, IT; 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.
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    Non-linear vibrations of suspension bridges with external excitation
    Çevik, M; Pakdemirli, M
    Non-linear coupled vertical and torsional vibrations of suspension bridges are investigated. Method of Multiple Scales, a perturbation technique, is applied to the equations to find approximate analytical solutions. The equations are not discretized as usually done, rather the perturbation method is applied directly to the partial differential equations. Free and forced vibrations with damping are investigated in detail. Amplitude and phase modulation equations are obtained. The dependence of nonlinear frequency on amplitude is described. Steady-state solutions are analyzed. Frequency-response equation is derived and the jump phenomenon in the frequency-response curves resulting from non-linearity is considered. Effects of initial amplitude and phase values, amplitude of excitation, and damping coefficient on modal amplitudes, are determined. (c) 2005 Elsevier Ltd. All rights reserved.