New Analytical Study for Nanofluid between Two Non-Parallel ‎Plane Walls (Jeffery-Hamel Flow)‎

Document Type : Research Paper

Author

Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq

Abstract

The aim of this paper is to analyze the problem of magneto hydrodynamic Jeffrey-Hamel flow (JHF) with nanoparticles. The governing equations for this problem are reduced to an ordinary differential equation and it is solved using new analytical method (NAM) and fourth-order Runge-Kutta Method (RK ∼ 4). The NAM is an iterative method that relies mainly on derivatives with Taylor expansion interference. In addition, the velocity profile has been computed and shown for various values of physical parameters. The objective of the present work is to investigate the effect of the angles between the plates, Reynold number, magnetic number and nanoparticles volume fraction on the velocity profile.

Keywords

Main Subjects

[1]‎ Jeffery, G.B., The two-dimensional steady motion of a viscous fluid, Philos. Mag., 1915, 6, 45565.‎
[2]‎ Hamel, G., Bewgungen Spiralformige, Flussigkeiten Zaher, DersDeutschen Jahresbericht, Math. Ver., 25, 1916, 34-60.‎
[3]‎ Nayfeh, A.H., Perturbation methods, New York, USA, Wiley, 2000.‎
[4]‎ Sheikholeslami, M., Ganji D.D., Ashorynejad, H.R., Rokni, H.B., Analytical investigation of Jeffery Hamel flow with ‎high ‎magnetic field and nanoparticle by Adomian decomposition method, Appl. Math. Mech., 33(11), 2012, 25-36.‎
[5]‎ He, J.H., New interpretation of homotopy-perturbation method, Int. J. Mod. Phys. B, 20, 2006, 2561-8.‎
[6]‎ Moghimi, S.M., Ganji, D.D., Bararnia, H., Hosseini, M., Jalaal, M., Homotopy perturbation method for ‎nonlinear MHD Jeffery Hamel ‎problem, Adv. Eng. Soft., 42, 2011, 108-113.‎
[7]‎ Rahimi Petroudi, I., Ganji, D.D., Shotorban, A.B., Khazayi Nejad, Ganji, N., Rahimi, E., Rohollahtabar, R., Taherinia, F., Semi ‎analytical ‎method for solving nonlinear equation arising of natural convection porous fin, Therm. Sci., 16(5), 2012, 13-38.‎
[8]‎ Ganji, Z.Z., Ganji, D.D., Esmaeilpour, M., Study on nonlinear Jeffery Hamel flow by He’s semi-analytical methods and comparison ‎with ‎numerical results, Comput. Math. Appl., 58(1112), 2009, 2107-2116.‎
[9]‎ Rahimi Petroudi, I., Ganji, D.D., Khazayi Nejad, M., Rahimi, J., Rahimi, E., Rahimifar, A., Transverse magnetic field on Jeffery-‎Hamel ‎problem with Cu-water nanoflid between two nonparallel plane walls by using collocation method, Case Studies in Thermal Engineering‎‎, 4, 2014, 193-201.‎
[10]‎ Ganji, D.D., Azimi, M., Application of DTM on MHD Jeffery Hamel problem with nanoparticles, U.P.B. Sci. Bull. Ser. A, 6, 2013, 75-81.‎
[11]‎ Abbasi, M., Ganji, D.D., Rahimi Petroudi, I., Khaki, M., Comparative analysis of MHD boundary-layer flow of ‎viscoelastic fluid ‎in permeable channel with slip boundaries by using HAM, VIM, HPM, Walailak J. Sci. Tech., 11(7), 2014, 55167.‎
[12]‎ Khidir, A.A., A new spectral homotopy perturbation method and its application to Jeffery-Hamel nanofluid flow with ‎high ‎magnetic field, Journal of Computational Method in Physics, 2013, 2013, 10 pages.‎
[13]‎ Motsa, S.S., Sibanda, P.F., Awad, G., Shateyi, S., A new spectral-homotopy analysis method for the MHD Jeffery-‎‎Hamel problem, Computers and Fluids, 39(7), 2010, 1219-1225.‎
[14]‎ Al-Saif, A.J.A., Jasim, A.M., A new analytical-approximate solution for the viscoelastic squeezing flow between two ‎parallel ‎plates, Applied Mathematics and Information Sciences, 13(2), 2019, 173-182.‎
[15]‎ Al-Saif, A.J.A., Jasim, A.M., A novel algorithm for studying the effects of squeezing flow of a Casson Fluid between ‎parallel ‎plates on magnetic field, Journal of Applied Mathematics, 2019, 2019, 3679373.‎
[16]‎ Al-Saif, A.J.A., Jasim, A.M., New Analytical Study of the Effects Thermo- Diffusion, Diffusion-Thermo and Chemical ‎Reaction ‎of Viscous Fluid on Magneto Hydrodynamics Flow in Divergent and Convergent Channels, Applied Mathematics, 10, 2019, ‎‎268300.‎
[17]‎ Al-Saif, A.J.A., Jasim, A.M., Analytical Investigation of the MHD Jeffery-Hamel Flow Through Convergent and Divergent ‎Channel ‎by New Scheme, Engineering Letters, 27(3), 2019, 27-3-28.‎
[18]‎ Jasim, A.M., Al-Saif, A.J.A., New Analytical Solution Formula for Heat Transfer of Unsteady Two-Dimensional Squeezing Flow ‎of a ‎Casson Fluid between Parallel Circular Plates, Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, ‎‎64(2), 2019, 219-243.‎
[19]‎ Jasim, A.M., Analytical approximation of the first grade MHD squeezing fluid flow with slip boundary condition using a ‎new ‎iterative method, Heat Transfer, 10, 2020, 1-21.‎
[20]‎ Sheikholesalmi, M., Jafaryar, M., Said, Z., Alsabery, A., Babazadeh, H., Shafee, A., Modification for helical turbulator to ‎augment ‎heat transfer behavior of nanomaterial via numerical approach, Applied Thermal Engineering, 2020, DOI: 10.1016/j.applthermaleng.2020.115935.
[21]‎ Sheikholesalmi, M., Farshad, S.A., Shafee, A., Babazadeh, H., Influence of Al2o3 nano power on performance of ‎solar ‎collector considering turbulent flow, Advanced Powder Technology, 2020.‎
[22]‎ Sheikholesalmi, M., Farshad, S.A., Shafee, A., Babazadeh, H., Performance of solar collector with turbulator ‎involving ‎nanomaterial turbulent regime, Renewable Energy, 163, 2021, 1222-1237.‎
[23]‎ Ganji, Z.Z., Ganji, D.D., Esmaeilpour, M., Study on nonlinear Jeffery- Hamel flow by He’s semi-analytical methods ‎and ‎comparison with numerical results, Computers and Mathematics with Applications, 58(12), 2009, 2107-2116.
‎[24]‎ Petroudi, I.R., Ganji, D.D., Nejad, M.K., Rahimi, J., Rahimi, E., Rahimifar, A., Transverse magnetic field on Jeffery-Hamel ‎problem ‎with Cu-water nanofluid between two non-parallel plane walls by using collocation method, Case Studies in Thermal Engineering, 4, ‎‎2014 ,193-201.‎
[25]‎ Akinbowale, T.A., Adeleke, I., Hafiz M.A., Abdul-Jalil S., Heat transfer analysis of nanofluid flow with porous ‎medium through ‎Jeffery Hamel diverging/converging channel, J. Appl. Comput. Mech., 6(3) 2020, 433-444.‎