Browsing by Author "Yürüsoy, M"
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Item Item Approximate analytical solutions for the flow of a third-grade fluid in a pipe(PERGAMON-ELSEVIER SCIENCE LTD) Yürüsoy, M; Pakdemirli, MThe 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. (C) 2001 Elsevier Science Ltd. All rights reserved.Item Item Exact solutions of boundary layer equations of a special non-Newtonian fluid over a stretching sheet(PERGAMON-ELSEVIER SCIENCE LTD) Yürüsoy, M; Pakdemirli, MItem Item Lie group analysis of creeping flow of a second grade fluid(PERGAMON-ELSEVIER SCIENCE LTD) Yürüsoy, M; Pakdemirli, M; Noyan, ÖFThe 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 bring 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. (C) 2001 Elsevier Science Ltd. All rights reserved.Item Perturbation solution for a third-grade fluid flowing between parallel plates(SAGE PUBLICATIONS LTD) Yürüsoy, M; Pakdemirli, M; Yilbas, BSThe 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.Item Perturbation analysis of a modified second grade fluid over a porous plate(PERGAMON-ELSEVIER SCIENCE LTD) Pakdemirli, M; Hayat, T; Yürüsoy, M; Abbasbandy, S; Asghar, SA 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.Item Equivalence transformations applied to exterior calculus approach for finding symmetries(PERGAMON-ELSEVIER SCIENCE LTD) Pakdemirli, M; Yürüsoy, MThe 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. (C) 1998 Elsevier Science Ltd. All rights reserved.Item The Analysis Approach of Boundary Layer Equations of Power-Law Fluids of Second GradeAbbasbandy, S; Yürüsoy, M; Pakdemirli, MA 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.Item Symmetries of boundary layer equations of power-law fluids of second gradePakdemirli, M; Aksoy, Y; Yürüsoy, M; Khalique, CMA 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.Item Comparison of approximate symmetry methods for differential equationsPakdemirli, M; Yürüsoy, M; Dolapçi, ITTwo 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 Perturbation solution for a third-grade fluid flowing between parallel platesYürüsoy, M; Pakdemirli, M; Yilbas, BSThe 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.Item Lie group analysis of creeping flow of a second grade fluidYürüsoy, M; Pakdemirli, M; Noyan, ÖFThe 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 bring 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. (C) 2001 Elsevier Science Ltd. All rights reserved.Item Approximate analytical solutions for the flow of a third-grade fluid in a pipeYürüsoy, M; Pakdemirli, MThe 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. (C) 2001 Elsevier Science Ltd. All rights reserved.Item Equivalence transformations applied to exterior calculus approach for finding symmetriesPakdemirli, M; Yürüsoy, MThe 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. (C) 1998 Elsevier Science Ltd. All rights reserved.Item Perturbation analysis of a modified second grade fluid over a porous platePakdemirli, M; Hayat, T; Yürüsoy, M; Abbasbandy, S; Asghar, SA 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.