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Using Laguerre polynomials as a basis for a new differential quadrature methodology to solve magneto-hydrodynamic (MHD) fourth-grade fluid flow | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، Special Issue، اسفند 2021، صفحه 83-96 اصل مقاله (377.3 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4846 | ||
| نویسندگان | ||
| Abdul-Sattar Jaber Al-Saif* 1، 2؛ Afrah Abdul- Imam Almaziny2 | ||
| 1Department of Mathematics, College of Education for Pure Sciences, Basrah University, Basrah, Iraq | ||
| 2Department of Mathematics, College of Sciences, Basrah University, Basrah, Iraq | ||
| تاریخ دریافت: 25 مهر 1399، تاریخ بازنگری: 14 دی 1399، تاریخ پذیرش: 10 بهمن 1399 | ||
| چکیده | ||
| The addition of an application of a new version of the Differential Quadrature Method is the purpose of this work. The new method, tracing Laguerre polynomials, is applicable to test functions whose purpose is to establish the DQM weighting coefficients, focussing on the use of the DQM in investigating solving nonlinear differential equations numerically for the representation of the steady incompressible flow problem of a fourth-grade non-Newtonian fluid magnetic field between two stationary parallel plates. A series of graphs are used to demonstrate the ways a range of important physical parameters influence the velocity profile. The level of agreement when comparing a small number of grid points in the new technique with analytical solutions is remarkably high. | ||
| کلیدواژهها | ||
| MHD fluid؛ fourth-grade fluid؛ Laguerre polynomials؛ differential quadrature method | ||
| مراجع | ||
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[1] T.Hayat, Y. Wang and K. Hutter, Flow of a fourth grade fluid, Mathematical Models and Methods in Applied Sciences, 2002, 12, pp. 797-811. [2] M.Patel and M. G.Timol, Numerical solution of non-Newtonian fluids flow past an accelerated vertical infinite plate in the presence of free convection currents, Int. J. of Applied Mechanics and Engineering, 2013, 18, pp. 761-777. [3] P. G. Moakher, M. Abbasi and M. Khaki,New analytical solution of MHD fluid flow of fourth grade fluid through the channel with slip condition via collocation method. International Journal of Advances in Applied Mathematics and Mechanics, 2015, 3, pp. 87-94. [4] P. G. Moakher, M. Abbasi and M. Khaki, Fully developed flow of fourth grade through the channel with slip condition in the presence of a magnetic field, 2016, 5, pp. 2239-2245. [5] A.S.J. Al-Saif and J. Assma, MHD Flow of Fourth Grade Fluid Solve by Perturbation-Iteration Algorithm, J. of Advanced Research in Fluid Mechanics and Thermal Sciences, 2019, 2289-7879. [6] Z.Khan, N. Tairan, W. K. Mashwani and U. H. Rasheed, MHD and Slip Effect on Two-immiscible Third Grade Fluid on Thin Film Flow over a Vertical Moving Belt, Open Phys, 2019, 17, pp. 575–586. [7] R.Bellman and J. Casti, Differential quadrature and long-term integration, J.Math. Anal. Appl.,1971, 34, 235-238. [8] C. Shu, Differential Quadrature and its Application in Engineering, Athenaeum Press Ltd., Great Britain, 2000. [9] C. W. Bert and M. Malik, Differential Quadrature Method in computational mechanics, A review: Appl. Mech. Rev., 49, 1-27, 1996. [10] R. Bellman and J. Casti, Differential quadrature: A Technique for the Rapid solution of nonlinear partial differential equations, J. Compute. Phys. 1972, 10, pp. 40-52. [11] J. Quan, New insights in solving distributed system equations by the quadrature methods-I, Compute.Chem. Engineering, 1989a, 13, pp. 779-788. [12] C. Shu and B. Richards, Application of generalized differential quadrature to solve two dimensional incompressible Navier-Stokes equations, Int. J. Numer. Meth. Fluids, (1992), 15, pp. 791-798. [13] C. Shu and H. Xue, Explicit computation of weighting coefficients in the harmonic differential quadrature, Journal of Sound and Vibration, 1997, 204, pp. 549-555. [14] Q. Guo and H. Zhong, Non-linear Vibration analysis of beams by a spline based differential quadrature method, Journal of Sound and Vibration, 2004, 269, pp. 413-420. [15] H. Ding, C. Shu, K.S. Yeo and D. Xu, Numerical computation of three-dimensional incompressible viscous flows in the primitive variable form by local multiquadric differential quadrature method, Comput. Methods Appl. Mech. Engineering, 2006, 195, pp. 516-533. [16] C. Shu, and Y. Wu, Integrated radial basis functions-based Differential Quadrature Method and its performance, Int, J. Numer. Meth. Fluids, 2007, 53, pp. 969-984. [17] A. Korkmaz and I. Dag, A differential quadrature algorithm for nonlinear Schrodinger equations, Nonlinear Dyn, 2009, 56, pp. 69-83. [18] M. Janghorban and A. Zare, Harmonic Differential Quadrature Method for static analysis of functionally graded single walled carbon nanotubes based on Euler-Bernoulli beam theory, Latin American Journal of Solids and Structures, 2012, 9, pp. 633-641. [19] A., Gorgun,S. Ozen, and S. Helhel, Implementation of Fourier Expansion Based Differential Quadrature Method (FDQM) and Polynomial Based Differential Quadrature Method (PDQM) for the 2D Helmholtz Problem, Academic Journals, 2013, 8 (34), pp. 1670-1675.[20] A. Al-Saif and F. A. Al-Saadawi,new differential quadrature methodology based on Bernstein polynomials for solving the equations governing the unsteady flow of a polytropic gas, Indion J. of Physical Science and Application, 2015, 5, pp. 38-47. [21] D. Watson, Radial Basis Function Differential Quadrature Method for the Numerical Solution of Partial Differential Equations, Ph.D. Thesis, the University of Southern Mississippi, 2017. [22] A.Bashan, Quartic B-spline Differential Quadrature Method for Solving the Extended Fisher-Kolmogorov Equation, Journal of Science and Technology, 2019, 12 (1), pp. 56-62. [23] H. Yu and H.S. Nik, A Laguerre homotopy method for optimal control of nonlinear systems in semi-infinite interval, 2018. [24] C. Shu, Differential Quadrature and its Application in Engineering, Athenaeum Press Ltd., Great Britain, 2000. | ||
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