Semi-Analytical Assessment of Magneto-Hydrodynamic Nano-Fluid Flow Jeffrey- Hamel Problem
Main Article Content
Abstract
In this paper, analyzing the non-dimensional Magnesium-hydrodynamics problem Using nanoparticles in Jeffrey-Hamel flow (JHF) has been studied. The fundamental equations for this issue are reduced to a three-order ordinary differential equation. The current project investigated the effect of the angles between the plates, Reynolds number, nanoparticles volume fraction parameter, and magnetic number on the velocity distribution by using analytical technique known as a perturbation iteration scheme (PIS). The effect of these parameters is similar in the converging and diverging channels except magnetic number that it is different in the divergent channel. Furthermore, the resulting solutions with good convergence and high accuracy for the different values of the physical parameters are in the form a power-series of the problem posed. The efficiency of this method is shown by comparison between for different cases between computed results with numerical solution and solutions by other methods.
Received 15/10/2022,
Revised 4/2/2023,
Accepted 5/2/2023,
Published Online First 20/5/2023
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite
References
Kaggwa A., and Carson JK. Developments and future insights of using nanofluids for heat transfer enhancements in thermal systems: a review of recent literature. Int Nano Lett . 2019; 9(4): 277–288. https://doi.org/10.1007/s40089-019-00281-x.
Younes H., Mao M., Sohel Murshed SM., Lou D., Hong H., and Peterson GP. Nanofluids: Key parameters to enhance thermal conductivity and its Appl. Therm. Eng . 2022; Vol. 207: Elsevier Ltd. https://doi.org/10.1016/j.applthermaleng.2022.118202.
Jeffery GBL. The two-dimensional steady motion of a viscous fluid. Lond. Edinb. Dublin philos. Mag. j. sci.1915;29(172):455–465. https://doi.org/10.1080/14786440408635327.
Hamel G. Spiralförmige Bewegungen zäher Flüssigkeiten. Jahresber Dtsch Math.-Ver,1917; 25: 34‐60. http://eudml.org/doc/145468.
Biswal U., and Chakraverty S. Investigation of Jeffery-Hamel Flow for Nanofluid in the Presence of Magnetic Field by a New Approach in the Optimal Homotopy Analysis Method. JACM . 2022; 8(1): 48–59. https://doi.org/10.22055/jacm.2020.31909.1937.
Singh J., Rashidi MM., Sushila, and Kumar DA. hybrid computational approach for Jeffery–Hamel flow in non-parallel walls. Neural. Comput. Appl. 2019; 31(7): 2407–2413. https://doi.org/10.1007/s00521-017-3198-y.
Chaharborj SS., and Moameni A. Spectral-homotopy analysis of MHD non-orthogonal stagnation point flow of a nanofluid. J. Appl. Math. Comput. Mech. 2018; 17(1): 15–28. https://doi.org/10.17512/jamcm.2018.1.02.
Petroudi IR., Ganji DD., Nejad MK., Rahimi J., Rahimi E., and Rahimifar A. Transverse magnetic field on Jeffery-Hamel problem with Cu-water nanofluid between two non-parallel plane walls by using collocation method. Case Stud. Therm. Eng. 2014; 4: 193–201. https://doi.org/10.1016/j.csite.2014.10.002 .
Rahman I UR., Sulaiman M., Alarfaj FK., Kumam P., and Laouini G. Investigation of non-linear MHD Jeffery–Hamel blood flow model using a hybrid metaheuristic approach. IEEE Access. 2021;9: 163214–163232. https://doi.org/10.1109/ACCESS.2021.3133815.
Ahmad I., and Ilyas H. Homotopy Perturbation Method for the nonlinear MHD Jeffery–Hamel blood flows problem. Appl. Numer. Math. 2019; 141: 124–132. https://doi.org/10.1016/j.apnum.2018.07.005.
Li Z., Khan I., Shafee A., Tlili I., and Asifa T. Energy transfer of Jeffery–Hamel nanofluid flow between non-parallel walls using Maxwell–Garnetts (MG) and Brinkman models. Energy Reports. 2018; 4: 393–399. https://doi.org/10.1016/j.egyr.2018.05.003.
Meher R., and Patel ND. Analytical Investigation of MHD Jeffery–Hamel flow problem with heat transfer by differential transform method. SN Appl. Sci. 2019; 1(7). https://doi.org/10.1007/s42452-019-0632-z.
Al-Saif, ASJ., and Harfash, AJ. Perturbation-iteration algorithm for solving heat and mass transfer in the unsteady squeezing flow between parallel plates. J. Appl. Comput. Mech. 2019; 5(4): 804–815. https://doi.org/10.22055/JACM.2019.28052.1453
Jasim A M. New Analytical Study for Nanofluid between Two Non-Parallel Plane Walls (Jeffery-Hamel Flow). J. Appl. Comput. Mech.. 2021; 7(1): 213–224. https://doi.org/10.22055/jacm.2020.34958.2520.
Jasim AM. New Analytical Study of Non-Newtonian Jeffery Hamel Flow of Casson Fluid in Divergent and Convergent Channels by Perturbation Iteration Algorithm. Baghdad J Sci. 2021; 39(1): 37–55. https://doi.org/10.29072/basjs.202113.
Kumbinarasaiah S., and Raghunatha KR. Numerical solution of the Jeffery–Hamel flow through the wavelet technique. Heat Transfer. 2022; 51(2): 1568–1584. https://doi.org/10.1002/htj.22364.
Umavathi J C., and Shekar M (n.d.). Effect of MHD on Jeffery-Hamel Flow in Nanofluids by Differential Transform Method. J. Eng. Res. Appl. . 2022 ;(Vol. 3). www.ijera.com.
Mehmood A., Ul-Haq N., Zameer A., Ling SH., Asif M., and Raja Z (n.d.). Design of Neuro-Computing Paradigms for Nonlinear Nanofluidic Systems of MHD Jeffery-Hamel Flow. J. Taiwan Inst. Chem. 2018;Vol.(91):57-85. https://www.sciencedirect.com/science/article/pii/S1876107018303201.
AL-Jizani, K H., and Al-Delfi J KK. An Analytic Solution for Riccati Matrix Delay Differential Equation using Coupled Homotopy-Adomian Approach. Baghdad Sci J. 2022; 19(4): 800–804. https://doi.org/10.21123/bsj.2022.19.4.0800.
Al-Jawary MA, and Salih OM.Effective Computational Methods for Solving the Jeffery-Hamel Flow Problem. Baghdad Sci J. 2022. https://doi.org/10.21123/bsj.2022.7326.
Noon, N J. Numerical Analysis of Least-Squares Group Finite Element Method for Coupled Burgers’ Problem. Baghdad Sci J.2022; 18(4): 1521–1535. https://doi.org/10.21123/bsj.2021.18.4(Suppl.).1521.
Swaidan W., and Ali H S. Numerical solution for linear state space systems using haar wavelets method. Baghdad Sci J. 2022; 19(1): 84–90. https://doi.org/10.21123/BSJ.2022.19.1.0084.
Tarrad AH. 3D Numerical Modeling to Evaluate the Thermal Performance of Single and Double U-tube Ground-coupled Heat Pump. High Tech Innov. J. 2022; 3(2): 115–129. https://doi.org/10.28991/HIJ-2022-03-02-01.
Hasan P M., and Sulaiman N A. Convergence Analysis for the Homotopy Perturbation Method for a Linear System of Mixed Volterra-Fredholm Integral Equations. Baghdad Sci J. 2020; 17(3(Suppl.)): 1010. https://doi.org/10.21123/bsj.2020.17.3(Suppl.).1010.
Hasim I, Kilicman A, Ismail AI, Azmi A, and Che Hussin CH.Approximate Analytical Solutions of Bright Optical Soliton for Nonlinear Schrödinger Equation of Power Law Nonlinearity. Baghdad Sci J.2021; 18(1(Suppl.)). https://doi.org/10.21123/bsj2021.18.1(Suppl.).0836.