Browsing by Author "Abbasbandy, S"

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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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    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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    New perturbation-iteration solutions for nonlinear heat transfer equations
    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.
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    Perturbation analysis of a modified second grade fluid over a porous plate
    Pakdemirli, M; Hayat, T; Yürüsoy, M; Abbasbandy, S; Asghar, S
    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 flow of this fluid is considered over a porous plate. Equations of motion in dimensionless form are derived. When the power-law effects are small compared to second grade effects, a regular perturbation problem arises which is solved. The validity criterion for the solution is derived. When second grade effects are small compared to power-law effects, or when both effects are small, the problem becomes a boundary layer problem for which the solutions are also obtained. Perturbation solutions are contrasted with the numerical solutions. For the regular perturbation problem of small power-law effects, an excellent match is observed between the solutions if the validity criterion is met. For the boundary layer solution of vanishing second grade effects however, the agreement with the numerical data is not good. When both effects are considered small, the boundary layer solution leads to the same solution given in the case of a regular perturbation problem. (C) 2010 Elsevier Ltd. All rights reserved.