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Applied Mathematics and Mechanics

, Volume 33, Issue 12, pp 1555–1568 | Cite as

DTM-BF method and dual solutions for unsteady MHD flow over permeable shrinking sheet with velocity slip

  • Xiao-hong Su (苏晓红)
  • Lian-cun Zheng (郑连存)Email author
  • Xin-xin Zhang (张欣欣)
Article

Abstract

An unsteady magnetohydrodynamic (MHD) boundary layer flow over a shrinking permeable sheet embedded in a moving viscous electrically conducting fluid is investigated both analytically and numerically. The velocity slip at the solid surface is taken into account in the boundary conditions. A novel analytical method named DTMBF is proposed and used to get the approximate analytical solutions to the nonlinear governing equation along with the boundary conditions at infinity. All analytical results are compared with those obtained by a numerical method. The comparison shows good agreement, which validates the accuracy of the DTM-BF method. Moreover, the existence ranges of the dual solutions and the unique solution for various parameters are obtained. The effects of the velocity slip parameter, the unsteadiness parameter, the magnetic parameter, the suction/injection parameter, and the velocity ratio parameter on the skin friction, the unique velocity, and the dual velocity profiles are explored, respectively.

Key words

unsteady magnetohydrodynamic (MHD) flow shrinking sheet analytical solution slip condition dual solutions 

Chinese Library Classification

O357 O175 

2010 Mathematics Subject Classification

34B40 34B15 76D10 76W05 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Xiao-hong Su (苏晓红)
    • 1
    • 2
    • 3
  • Lian-cun Zheng (郑连存)
    • 1
    Email author
  • Xin-xin Zhang (张欣欣)
    • 3
  1. 1.Department of Mathematics and MechanicsUniversity of Science and Technology BeijingBeijingP. R. China
  2. 2.Department of Mathematics and PhysicsNorth China Electric Power UniversityBaodingHebei Province, P. R. China
  3. 3.Mechanical Engineering SchoolUniversity of Science and Technology BeijingBeijingP. R. China

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