Muhammad Ashraf, M. M. Ashraf. MHD Stagnation Point Flow of a Micropolar Fluid Towards a Heated Surface[J]. Applied Mathematics and Mechanics, 2011, 32(1): 44-52. doi: 10.3879/j.issn.1000-0887.2011.01.005
Citation: Muhammad Ashraf, M. M. Ashraf. MHD Stagnation Point Flow of a Micropolar Fluid Towards a Heated Surface[J]. Applied Mathematics and Mechanics, 2011, 32(1): 44-52. doi: 10.3879/j.issn.1000-0887.2011.01.005

MHD Stagnation Point Flow of a Micropolar Fluid Towards a Heated Surface

doi: 10.3879/j.issn.1000-0887.2011.01.005
  • Received Date: 2010-08-05
  • Rev Recd Date: 2010-11-10
  • Publish Date: 2011-01-15
  • The problem of two dimensional stagnation point flow of an electrically conducting micropolar fluid impinging normally on a heated surface in the presence of a uniform transverse magnetic field was analyzed.The governing continuity,momentum,angular momentum,and heat equations together with the associated boundary conditions were reduced to dimensionless form using suitable similarity transformations.The reduced self similar non-linear equations were then solved numerically by an algorithm based on finite difference discretization.The results were further refined by Richardson's extrapolation.The effects of the magnetic parameter,the micropolar parameters,and the Prandtl number on the flow and temperature fields were predicted in tabular and graphical forms to show the important features of the solution.The study shows that the velocity and thermal boundary layers become thinner as the magnetic parameter is increased.The micropolar fluids display more reduction in shear stress as well as heat transfer rate than that exhibited by Newtonian fluids,which is beneficial in the flow and thermal control of polymeric processing.
  • loading
  • [1]
    Hiemenz K. Die Grenzschicht in einem in dem gleichformingen flussigkeitsstrom eingetauchten gerade kreiszylinder[J]. Dingler Polytechnic Journal, 1911, 326: 321-340.
    Homann F. Der einfluss grosser zahigkeit bei der stromung um den zylinder und um die kugel[J].ZAMM , 1936, 16: 153-164. doi: 10.1002/zamm.19360160304
    Wang C Y. Impinging stagnation flows[J]. Phys Fluids , 1987, 30(3): 915-917. doi: 10.1063/1.866345
    Ariel P D. Hiemenz flow in hydromagnetics[J]. Acta Mech, 1994, 103(1/4): 31-43. doi: 10.1007/BF01180216
    Mahapatra T R, Gupta A S. Magnetohydrodynamic stagnation point flow towards a stretching sheet[J].Acta Mech, 2001, 152(1/4): 191-196. doi: 10.1007/BF01176953
    Chamkha A J, Issa Camille. Effects of heat generation/absorption and thermophoresis on hydromagnatic flow with heat and mass transfer over a flat surface[J]. International Journal of Numerical Method for Heat and Fluid Flow, 2000, 10(4): 432-449. doi: 10.1108/09615530010327404
    朱婧,郑连存,张欣欣. 具有延伸表面的驻点流动和传热问题的级数解[J]. 应用数学和力学,2009, 30(4): 432-456.(ZHU Jing, ZHENG Lian-cun, ZHANG Xin-xin. Analytic solution to stagnation point flow and heat transfer over a stretching sheet based on homotopy analysis[J]. Applied Mathematics and Mechanics(English Edition), 2009, 30(4): 463-474.)
    Hoyt J W, Fabula A G. The effect of additives on fluid friction[R]. U S Naval Ordinance Test Station Report, 1964.
    Eringen A C. Theory of micropolar continua[C] Proceedings of the Ninth Midwestern Conference, 1965: 23.
    Eringen A C. Simple microfluids[J]. Int J Eng Sci, 1964, 2(2): 205-217. doi: 10.1016/0020-7225(64)90005-9
    Eringen A C. Theory of micropolar fluids[J]. J Math, 1966, 16: 1-18.
    Ariman T, Turk M A, Sylvester N D. Microcontinum fluid mechanics—a review[J]. Int J Eng Sci, 1973, 11(8): 905- 930. doi: 10.1016/0020-7225(73)90038-4
    Ariman T, Turk M A, Sylvester N D. Application of microcontinum fluid mechanics[J]. Int J Eng Sci, 1974, 12: 273-293. doi: 10.1016/0020-7225(74)90059-7
    Guram G S, Smith C. Stagnation flows of micropolar fluids with strong and weak interactions[J]. Comp Math Appl, 1980, 6(2): 213-233.
    Ahmadi G. Self-similar solution of incompressible micropolar boundary layer flow over a semi infinite plate[J]. Int J Eng Sci, 1972, 14(7): 639-646.
    CHENG Long-chang. Numerical simulation of micropolar fluid flow along a flat plate with wall conduction and boundary effects[J]. J Phys D: Appl Phys, 2006, 39(6): 1132-1140. doi: 10.1088/0022-3727/39/6/019
    Lok Y Y, Pop I, Chamkha A J. Non-orthognal stagnation point flow of a micropolar fluid[J]. Int J Eng Sci, 2007, 45(1): 173-184. doi: 10.1016/j.ijengsci.2006.04.016
    Seddeek M A. Flow of a magneto micropolar fluid past a continuously moving plate[J]. Physics Letters A, 2003, 306(4): 255-257. doi: 10.1016/S0375-9601(02)01513-X
    Ishak A, Nazar R, Pop I. Stagnation flow of a micropolar fluid towards a vertical permeable surface[J]. International Communications in Heat and Mass Transfer, 2008, 35(3): 276-281. doi: 10.1016/j.icheatmasstransfer.2007.07.007
    Ashraf Muhammad, Anwar Kamal M, Syed K S. Numerical study of asymmetric laminar flow of micropolar fluids in a porous channel[J]. Computers and Fluids, 2009, 38(10): 1895-1902. doi: 10.1016/j.compfluid.2009.04.009
    Ashraf Muhammad, Anwar Kamal M, Syed K S. Numerical investigations of asymmetric flow of a micropolar fluid between two porous disks[J]. Acta Mechanica Sinica , 2009, 25(6): 787-794. doi: 10.1007/s10409-009-0307-x
    Ishak A, Jafar K, Nazar R, Pop I. MHD stagnation point flow towards a stretching sheet[J]. Physica A , 2009, 388(17): 3377-3383. doi: 10.1016/j.physa.2009.05.026
    Ishak A, Lok Y Y, Pop I. Stagnation point flow over a shrinking sheet in a micropolar fluid[J]. Chem Eng Comm, 2010, 197(11): 1417-1427. doi: 10.1080/00986441003626169
    Shercliff J A. A Text Book of Magnetohydrodynamics[M]. Oxford: Pergamon Press, 1965.
    Rossow V J. On flow of electrically conducting fluids over a flat plate in the presence of a transverse magnetic field[R]. NACA, Tech Report 1358, 1958.
    Gerald C F. Applied Numerical Analysis[M]. Massachusetts: Addison Wesley Publishing Company Reading, 1974.
    Milne W E. Numerical Solutions of Different Equations[M]. New York: John Willy and Sons Inc,1953.
    Hildebrand F B. Introduction to Numerical Analysis[M]. Tata McGraw Hill Publishing Company Ltd, 1978.
    Syed K S, Tupholme G E, Wood A S. Iterative solution of fluid flow in finned tubes[C]Taylor C, Cross J T. Proceeding of the 10th International Conference on Numerical Methods in Laminar and Turbulent Flow.Swansea, UK 429-440: Pineridge Press, 1997: 21-25.
    Deuflhard P. Order and step size control in extrapolation methods[J]. Numer Math, 1983, 41(3): 399-422 . doi: 10.1007/BF01418332
    Guram G S, Anwar M. Micropolar flow due to a rotating disc with suction and injection[J].ZAMM, 1981, 61(11): 589-605. doi: 10.1002/zamm.19810611107
    Takhar H S, Bhargaval R, Agraval R S, Balaji A V S. Finite element solution of micropolar flow and heat transfer between two porous discs[J]. Int J Eng Sci, 2000, 38(17): 1907-1922. doi: 10.1016/S0020-7225(00)00019-7
    Ashraf Muhammad, Anwar Kamal M, Syed K S. Numerical simulation of a micropolar fluid between a porous disk and a non-porous disk[J]. Appl Math Modell, 2009, 33(4): 1933-1943. doi: 10.1016/j.apm.2008.05.002
    Pantokratoras A. Comment on “laminar boundary layer flow over a horizontal permeable flat plate” [J]. Appl Math Comput, 2006, 182(2): 1-2. doi: 10.1016/j.amc.2006.03.015
    Pantokratoras A. A common error made in investigation of boundary layer flows[J]. Appl Math Model, 2009, 33(1): 413-422. doi: 10.1016/j.apm.2007.11.009
  • 加载中


    通讯作者: 陈斌,
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1252) PDF downloads(718) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint