M.Sheikholeslami, D.D.Ganji, H.R.Ashorynejad, Houman B.Rokni. Analytical Investigation of Jeffery-Hamel Flow With High Magnetic Field and Nano Particle by Adomian Decomposition Method[J]. Applied Mathematics and Mechanics, 2012, 33(1): 24-34. doi: 10.3879/j.issn.1000-0887.2012.01.003
Citation: M.Sheikholeslami, D.D.Ganji, H.R.Ashorynejad, Houman B.Rokni. Analytical Investigation of Jeffery-Hamel Flow With High Magnetic Field and Nano Particle by Adomian Decomposition Method[J]. Applied Mathematics and Mechanics, 2012, 33(1): 24-34. doi: 10.3879/j.issn.1000-0887.2012.01.003

Analytical Investigation of Jeffery-Hamel Flow With High Magnetic Field and Nano Particle by Adomian Decomposition Method

doi: 10.3879/j.issn.1000-0887.2012.01.003
  • Received Date: 2010-12-20
  • Rev Recd Date: 2011-09-15
  • Publish Date: 2012-01-15
  • The effect of magnetic field and nano particle on the Jeffery-Hamel flow were studied by a powerful analytical method that was called Adomian decomposition method (ADM). The traditional Navier-Stokes equation of fluid mechanics and Maxwell’s electromagnetism governing equations were reduced to nonlinear ordinary differential equations to model this problem. The obtained results by this method are well agreed with the numerical (Runge-Kutta method) results and tabulated in a table. The plots confirm that the used method is in high accuracy for different α,Ha and Re numbers. First the flow field inside the divergent channel was studied for various values of Hartmann number and angle of channel and at last the effect of nanoparticle volume fraction in absence of magnetic field was investigated.
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  • [1]
    Jeffery G B. The two-dimensional steady motion of a viscous fluid[J]. Phil Mag, 1915, 6: 455-465.
    [2]
    Hamel G. Spiralfrmige bewgeungen zher flüssigkeiten[J]. Jahresber Deutsch Math-Verein, 1916, 25: 34-60.
    [3]
    Bansal L. Magnetofluiddynamics of Viscous Fluids[M]. Jaipur, India: Jaipur Publishing House. OCLC 70267818, 1994.
    [4]
    Cha J E, Ahn Y C, Moo-Hwan Kim. Flow measurement with an electromagnetic flowmeter in two-phase bubbly and slug flow regimes[J]. Flow Measurement and Instrumentation, 2002,12(5/6): 329-339.
    [5]
    Tendler M. Confinement and related transport in extrap geometry[J]. Nuclear Instruments and Methods in Physics Research, 1983, 207(1/2): 233-240.
    [6]
    Makinde O D, Motsa S S. Hydromagnetic stability of plane Poiseuille flow using Chebyshev spectral collocation method[J]. J Ins Math Comput Sci, 2001, 12(2): 175-183.
    [7]
    Makinde O D. Magneto-hydrodynamic stability of plane—Poiseuille flow using multi-deck asymptotic technique[J]. Math Comput Modelling, 2003, 37(3/4): 251-259.
    [8]
    Anwari M, Harada N, Takahashi S. Performance of a magnetohydrodynamic accelerator using air-plasma as working gas[J]. Energy Conversion Management, 2005, 4: 2605-2613.
    [9]
    Homsy A, Koster S, Eijkel J C T, van der Berg A, Lucklum F, Verpoorte E, de Rooij N F. A high current density DC magnetohydrodynamic (MHD) micropump[J]. Lab Chip, 2005, 5(4): 466-471.
    [10]
    Kaka S. Pramuanjaroenkij A. Review of convective heat transfer enhancement with nanofluids[J]. Int J Heat Mass Transf, 2009, 52(13/14): 3187-3196.
    [11]
    Aminossadati S M, Ghasemi B. Natural convection cooling of a localized heat source at the bottom of a nanofluid-filled enclosure[J]. European J Mech B/Fluids, 2009, 28(5): 630-640.
    [12]
    Yacob N, Ishak A, Nazar R, Pop I. Falkner-Skan problem for a static and moving wedge with prescribed surface heat flux in a nanofluid[J]. International Communications in Heat and Mass Transfer, 2011, 38(2): 149-153.
    [13]
    Adomian G. A review of the decomposition method in applied mathematics[J]. Journal of Mathematical Analysis and Applications, 1988, 135(2): 501-544.
    [14]
    Ghosh S, Roy A, Roy D. An adaptation of adomian decomposition for numeric-analytic integration of strongly nonlinear and chaotic oscillators[J]. Comput Meth Appl Mech Engrg, 2007, 196(4/6): 1133-1153.
    [15]
    Jafari H, Daftardar-Gejji V. Revised Adomian decomposition method for solving a system of nonlinear equations[J]. Appl Math Comput, 2006, 175(1): 1-7.
    [16]
    Allan F M, Syam M I. On the analytic solutions of the nonhomogeneous Blasius problem[J]. J Comput Appl Math[J]. 2005, 182(2): 362-371.
    [17]
    Hashim I. Adomian decomposition method for solving BVPs for fourth-order integro-differential equations[J]. J Comput Appl Math, 2006, 193(2): 658-664.
    [18]
    Hashim I. Comments on a new algorithm for solving classical Blasius equation[J]. J Com Appl Math, 2005, 182: 362-371.
    [19]
    Kechil S A, Hashim I. Non-perturbative solution of free-convective boundary-layer equation by Adomian decomposition method[J]. Phys Lett A, 2007, 363(1/2): 110-114.
    [20]
    Arslanturk C. A decomposition method for fins efficiency of convective straight fins with temperature-dependent thermal conductivity[J]. Int Commun Heat Mass Transfer, 2005, 32(6): 831-841.
    [21]
    Pamuk S. Solution of the porous media equation by Adomian’s decomposition method[J]. Phys Lett A, 2005, 344(2/4): 184-188.
    [22]
    Daftardar-Gejji V, Jafari H. An iterative method for solving nonlinear functional equations[J]. J Math Anal Appl, 2006, 316(2): 753-763.
    [23]
    Lesnic D. Decomposition methods for non-linear non-characteristic Cauchy heat problems[J]. Commun Nonlinear Sci Numer Simulat, 2005, 10(6): 581-596.
    [24]
    LUO Xing-guo. A two-step adomian decomposition method[J]. Appl Math Comput, 2005, 170(1): 570-583.
    [25]
    ZHANG Xin-hua. A modification of the Adomian decomposition method for a class of nonlinear singular boundary value problems[J]. J Comput Appl Math, 2005, 180(2): 377-389.
    [26]
    Kaya D, Yokus A. A comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations[J]. Math Comput Simul, 2002, 60(6): 507-512.
    [27]
    Ganji Z Z, Ganji D D, Rostamiyan Y. Solitary wave solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by an analytical technique[J]. Applied Mathematical Modelling, 2009, 33(7): 3107-3113.
    [28]
    Esmaeilpour M, Ganji D D. Solution of the Jeffery-Hamel flow problem by optimal homotopy asymptotic method[J]. Computers and Mathematics With Applications, 2010, 59(11): 3405-3411.
    [29]
    Moghimi S M, Ganji D D, Bararnia H, Hosseini M, Jalaal M. Homotopy perturbation method for nonlinear MHD Jeffery-Hamel problem [J]. Computers & Mathematics With Applications, 2011, 61(8): 2213-2216.
    [30]
    Babazadeh H, Ganji D D, Akbarzade M. He’s energy balance method to evaluate the effect of amplitude on the natural frequency in nonlinear vibration systems[J]. Journal of Electromagnetic Waves and Applications (JEMWA) Progress in Electromagnetic Research, 2008, 4: 143-154.
    [31]
    Ganji D D, Babazadeh H, Jalaei M H, Tashakkorian H. Application of he’s variational iteration methods for solving nonlinear BBMB equations and free vibrations of systems[J]. Acta Appl Math, 2009, 106(3): 359-367.
    [32]
    司新辉, 郑连存, 张欣欣, 晁莹. 磁场力作用下胀缩可渗透壁面管道非稳态流动摄动解[J]. 应用数学和力学, 2010, 31(2): 143-149.(SI Xin-hui, ZHENG Lian-cun, ZHANG Xin-xin, CHAO Ying. Perturbation solution to unsteady flow in a porous channel with expanding or contracting walls in the presence of a transverse magnetic field[J]. Applied Mathematics and Mechanics(English Edition), 2010, 31(2): 151-158.)
    [33]
    Ganji D D, Rokni Houman B, Sfahani M G, Ganji S S. Approximate traveling wave solutions for coupled shallow water[J]. Advances in Engineering Software, 2010, 41: 956-961.
    [34]
    Tari Hafez, Ganji D D, Babazadeh H. The application of he’s variational iteration method to nonlinear equations arising in heat transfer[J]. Physics Letters A, 2007, 363(3): 213 -217.
    [35]
    Ganji S S, Ganji D D, Babazadeh H, Sadoughi N. Application of amplitude-frequency formulation to nonlinear oscillation system of the motion of a rigid rod rocking back[J]. Mathematical Methods in the Applied Sciences, 2009, 33(2): 157-166.
    [36]
    原培新, 李永强. 强非线性多自由度动力系统主共振同伦分析法研究[J]. 应用数学和力学, 2010, 31(10): 1229-1248.(YUAN Pei-xin, LI Yong-qiang. Primary resonance of multiple degree-of-freedom dynamic systems with strong non-linearity using the homotopy analysis method[J]. Applied Mathematics and Mechanics(English Edition), 2010, 31(10): 1293-1304.)
    [37]
    Ganji S S, Ganji D D, Karimpour S, Babazadeh H. Applications of he’s homotopy perturbation method to obtain second-order approximations of coupled two-degree-of-freedom system[J]. International Journal of Nonlinear Science and Numerical Simulation, 2009,10(3): 303-312.
    [38]
    Ganji D D, Rokni Houman B, Rafiee M Hadi, Imani A A, Esfandyaripour M, Sheikholeslami M. Reconstruction of variational iteration method for boundary value problems in structural engineering and fluid mechanics[J]. International Journal of Nonlinear Dynamics in Engineering and Sciences, 2011, 3: 1-10.
    [39]
    冯少东, 陈立群. Duffing简谐振子同伦分析法求解[J]. 应用数学和力学, 2009, 30(9): 1015-1020.( FENG Shao-dong, CHEN Li-qun. Homotopy analysis approach to the Duffing harmonic oscillator[J]. Applied Mathematics and Mechanics(English Edition), 2009, 30(9): 1083-1089.)
    [40]
    Ganji D D, Nezhad H R Ashory, Hasanpour A. Effect of variable viscosity and viscous dissipation on the Hagen-Poiseuille flow and entrop
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