Modeling and numerical analysis of viscoelastic fluid flow in a permeable channel

Document Type : Mechanics article

Author

Department of Engineering Sciences, Hakim Sabzevari University, Sabzevar, Iran

Abstract

In this article, the laminar flow of an incompressible and viscoelastic fluid inside a channel with porous walls has been investigated using optimal asymptotic homotopy method (OHAM). The flow inside the channel is considered steady and the Darcy model is used to simulate the effects of drag on the flow caused by the porous medium. The governing equations of the problem are converted into non-linear ordinary differential equations and solved. To prove the correctness of the solution, some of the results have been compared with the obtained numerical results. The effects of Darcy number, Deborah number and Reynolds number on the velocity distribution are analyzed. Based on the comparison, the ability and high accuracy of this method to solve the problem has been determined. Finally, it can be concluded that this method can be used as a reliable method to solve the internal flow of fluid inside a channel with a porous wall.

Keywords

Main Subjects

References

[1] G. Hou, J. Wang, and A. Layton, “NumericalMethods for Fluid-Structure Interaction— A Review”, Commun. Comput. Phys., vol. 12, no. 1, 2012, pp. 337-377.
[2] F. Gao and T. Matsuzawa, “FSI within Aortic Arch Model over Cardiac Cycle and Influence of Wall Stiffness on Wall Stress in Layered Wall”, Engineering Letters, vol. 13, no. 2, Aug. 2006, 13_2_15.
[3] D.V. Le, B.C. Khoo, and J. Peraire, “An immersed interface method for viscous incompressible flows involving rigid and flexible boundaries”, Journal of Computational Physics, vol. 220, 2006, pp. 109–138.
]4[ حبیب الله سایه وند و رضا نعمتی، "حل عددی اثر افزایش دمای دیواره بر جریان و انتقال حرارت در لوله حرارتی نوسانی"، نشریه مدل سازی در مهندسی، دوره 18، شماره60 ، خرداد 1399 ، صفحه 13-25.
]5[ رسول محبی، "بررسی جریان سیال و انتقال حرارت جابجایی آزاد حفره مربعی با وجود مانع گرم مثلثی با روش المان محدود"، نشریه مدل سازی در مهندسی، دوره 16، شماره 55، دی 1397، صفحه 361-373.
]6[ مازیار دهقان، یوسف رحمانی، سیف الله سعدالدین، محمدصادق ولیپور و داوود دومیری گنجی، "بررسی انتقال حرارت در فوم‌های فلزی در حضور جابجایی اجباری و تشعشع حرارتی به روش اغتشاش هموتوپی"، نشریه مدل سازی در مهندسی، دوره 14، شماره 46، مهر 1395، صفحه 1-9.
[7] J. Mandeep Singh, “An iterative technique based on HPM for a class of one dimensional Bratu’s type problem”, Mathematics and Computers in Simulation, vol. 200, 2022, pp. 50-64.
[8] S. Momani, G.H. Erjaee, and M.H. Alnasr, “The modified homotopy perturbation method for solving strongly nonlinear oscillators”, Computers & Mathematics with Applications, vol. 58, no. 11–12,2009, pp. 2209-2220.
[9] A.M. Siddiqui, T. Haroon, and S. Irum, “Torsional flow of third grade fluid using modified homotopy perturbation method”, Computers & Mathematics with Applications, vol. 58, no. 11–12 ,2009, pp. 2274-2285.
[10] S. Bhatti, M. Zahid, R. Ali, A. Sarwar, and H.A. Wahab, “Blade coating analysis of a viscoelastic Carreau fluid using Adomian decomposition method”, Mathematics and Computers in Simulation, vol. 190, 2021, pp. 659-677.
[11] K. M. Ewis, “A New Approach in Differential transformation method with application on MHD flow in non-Darcy medium between porous parallel plates considering hall current”, Advances in Water Resources, vol. 143, 2020, p. 103677.
[12] R. Abazari, A. Borhanifar, “Numerical study of the solution of the Burgers and coupled Burgers equations by a differential transformation method”, Computers & Mathematics with Applications, vol. 59, no. 8, 2010, pp. 2711-2722.
[13] J.W. Zhou, W. Zhang, X. Jiang, and E.D. Zhai, “Investigation on dynamics of rotating wind turbine blade using transferred differential transformation method”, Renewable Energy, vol. 188, 2022, pp. 96-113.
[14] W. Alhejaili, R.S. Varun Kumar, E. Roshdy El-Zahar, G. Sowmya, B.C. Prasannakumara, M. Ijaz Khan, K.M. Yogeesha, and S. Qayyum, “Analytical solution for temperature equation of a fin problem with variable temperature dependent thermal properties: Application of LSM and DTM-Pade approximant”, Chemical Physics Letters, vol. 793, 2022, p. 139409.
[15] O. Doeva, P. Khaneh Masjedi, P. M. Weaver, “A semi-analytical approach based on the variational iteration method for static analysis of composite beams”, Composite Structures, vol. 257, 2021, p. 113110.
[16] S. J. Liao, “The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems”, Ph.D. Thesis, Shanghai Jiao Tong University, 1992.
[17] S.J. Liao, “Beyond Perturbation: Introduction to Homotopy Analysis Method”, Chapman & Hall/CRC Press, Boca Raton, 2003.
[18] S.J.Liao,” On the homotopy analysis method for nonlinear problems”, Applied Mathematics and Computation, vol. 147, 2004, pp. 499–513.
[19] V. Marinca, N. Herisanu, and I. Nemes, “Optimal homotopy asymptotic method with application to thin film flow”, Central European Journal of Physics, vol. 6, 2008, pp. 648–653.
[20] V. Marinca, N. Herisanu, “Application of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer”, International Communication in Heat and Mass Transfer, vol.  35, no.  8, 2008, pp. 710–715.
[21] V. Marinca, and N. Herisanu, “An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate”, Applied Mathematics Letters, vol. 22, 2009, pp. 245–251.
[22] V. Marinca, and N. Herisanu, “Optimal homotopy perturbation method for strongly nonlinear differential equations”, Nonlinear Science Letters A, vol. 1, no. 3, 2010, pp.  273–280.
[23] O. Anwar Bég, and O.D. Makinde, “Viscoelastic flow and species transfer in a Darcian high-permeability channel”, Journal of Petroleum Science and Engineering, vol. 76, no. 3–4, 2011, pp. 93-99.
Journal of Modeling in Engineering
Volume 21, Issue 73
June 2023
Pages 255-262

Files

Share

How to cite

Statistics