F. M. Ali, R. Nazar, N. M. Arifin, I. Pop. MHD Stagnation-Point Flow and Heat Transfer Towards a Stretching Sheet With Induced Magnetic Field[J]. Applied Mathematics and Mechanics, 2011, 32(4): 391-399. doi: 10.3879/j.issn.1000-0887.2011.04.003
Citation: F. M. Ali, R. Nazar, N. M. Arifin, I. Pop. MHD Stagnation-Point Flow and Heat Transfer Towards a Stretching Sheet With Induced Magnetic Field[J]. Applied Mathematics and Mechanics, 2011, 32(4): 391-399. doi: 10.3879/j.issn.1000-0887.2011.04.003

MHD Stagnation-Point Flow and Heat Transfer Towards a Stretching Sheet With Induced Magnetic Field

doi: 10.3879/j.issn.1000-0887.2011.04.003
  • Received Date: 2010-09-27
  • Rev Recd Date: 2011-01-24
  • Publish Date: 2011-04-15
  • The problem of steady magnetohydrodynamic (MHD) stagnation point flow of an incompressi-ble viscous fluid over a stretching sheet was studied.The effect of induced magnetic field was taken into account.The nonlinear partial differential equations were transformed into ordinary differential equations via the similarity transformation.The transformed boundary layer equations were solved numerically using the shooting method.Numerical results are obtained for various magnetic parameter β and Prandtl number Pr.The effects of induced magnetic field on the skin friction coefficient,local Nusselt number,velocity and temperature profiles for both a/c>1 and a/c<1,where a and c are positive constants,are presented graphically and discussed in detail.
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  • [1]
    Tzirtzilakis E E,Kafoussias N G. Biomagnetic fluid flow over a stretching sheet with non linear temperature dependent magnetization[J]. Journal of Applied Mathematics and Mechanics (ZAMP), 2003, 54(4): 551-565.
    [2]
    Tzirtzilakis E E, Tanoudis G B. Numerical study of biomagnetic fluid flow over a stretching sheet with heat transfer[J]. International Journal for Numerical Methods in Heat and Fluid Flow, 2003, 13(7): 830-848 . doi: 10.1108/09615530310502055
    [3]
    Tzirtzilakis E E, Kafoussias N G. Three-dimensional magnetic fluid boundary layer flow over a linearly stretching sheet[J]. ASME Journal of Heat Transfer, 2010, 132(1): 011702-1-011702-8. doi: 10.1115/1.3194765
    [4]
    Al-Odat M Q, Damseh R A, Al-Azab T A. Thermal boundary layer on an exponentially stretching continuous surface in the presence of magnetic field effect[J]. International Journal of Applied Mechanics and Engineering, 2006,11(2): 289-299.
    [5]
    Tongli B, Zheng L C, Zhang X X. Multiple solutions of laminar flow in channels with a transverse magnetic field[J]. Chinese Physics Letters, 2009, 26(9): 094101-1-094101-3. doi: 10.1088/0256-307X/26/9/094101
    [6]
    Hiemenz K. Die Grenzschicht an einem in den gleichfrmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder[J]. Dingler Polytech Journal, 1911, 326: 321-324.
    [7]
    Eckert E R G. Die Berechnung des Warmeubergangs in der laminaren Grenzschicht umstromter Korpe[J]. VDI Forschungsheft, 1942,416: 1-23.
    [8]
    Mahapatra T R, Gupta A S. Magnetohydrodynamic stagnation point flow towards a stretching sheet[J]. Acta Mechanica, 2001, 152(1/4): 191-196. doi: 10.1007/BF01176953
    [9]
    Mahapatra T R, Gupta A S. Heat tansfer in stagnation-point flow towards a stretching sheet[J]. Heat and Mass Transfer, 2002,38(6): 517-521. doi: 10.1007/s002310100215
    [10]
    Mahapatra T R, Gupta A S. Stagnation-point flow of a viscoelastic fluid towards a stretching surface[J]. International Journal of Non-Linear Mechanics, 2004, 39(5): 811-820. doi: 10.1016/S0020-7462(03)00044-1
    [11]
    Nazar R, Amin N, Filip D, Pop I. Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet[J]. International Journal of Engineering Science, 2004, 42(11/12): 1241-1253. doi: 10.1016/j.ijengsci.2003.12.002
    [12]
    Ishak A, Nazar R, Pop I. Mixed convection boundary layers in the stagnation-point flow towards a stretching vertical sheet[J]. Meccanica, 2006, 41(5): 509-518. doi: 10.1007/s11012-006-0009-4
    [13]
    Wang C Y. Stagnation slip flow and heat transfer on a moving plate[J]. Chemical Engineering Science, 2006, 61(23), 7668-7672.
    [14]
    Gorla R S R. Non-Newtonian fluid at a stagnation point in the presence of a transverse magnetic field[J]. Mechanics Research Communications, 1976, 3(1): 1-6. doi: 10.1016/0093-6413(76)90074-4
    [15]
    朱婧,郑连存,张欣欣. 具有伸展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): 432-442. (ZHU Jing, ZHENG Lian-cen, ZHANG Xin-xin. Analytical 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.)
    [16]
    朱婧,郑连存,张志刚. 幂律速度运动表面上磁流体在驻点附近的滑移流动[J] 应用数学和力学,2009, 31(4): 411-419. (ZHU Jing, ZHENG Lian-cen, ZHANG Zhi-gang. Effects of slip condition on MHD stagnation-point flow over a power-law stretching sheet[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(4): 439-448.) doi: 10.1007/s10483-010-0404-z
    [17]
    Kumari M, Takhar H S, Nath G. MHD flow and heat transfer over a stretching surface with prescribed wall temperature or heat flux[J]. Wrme-und Stoffübertr, 1990, 25(6): 331-336.
    [18]
    Takhar H S, Kumari M, Nath G. Unsteady free convection flow under the influence of a magnetic field[J]. Archive of Applied Mechanics, 1993, 63(4/5): 313-321. doi: 10.1007/BF00793897
    [19]
    Cowling T G. Magnetohydrodynamics[M]. New York : Interscience Publication, 1957.
    [20]
    Davies T V. The magneto-hydrodynamic boundary layer in the two-dimensional steady flow past a semi-infinite flat plate—Ⅰ: uniform conditions at infinity[J]. Proc Roy Soc A, 1962, 273(1355): 496-508.
    [21]
    Hartmann J. Theory of the laminar flow of an electrically conducting liquid in a homogenous magnetic field[J]. Math-Fys Medd, 1937,15(6): 1-28.
    [22]
    Meade D B, Haran B S, White R E. The shooting technique for the solution of two-point boundary value problems[J]. Maple Tech, 1996, 3(1): 85-93.
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