On DTM-BF Method and Dual Solutions for an Unsteady MHD Flow Over a Permeable Shrinking Sheet With Velocity Slip

SU Xiao-hong; ZHENG Lian-cun; ZHANG Xin-xin

doi:10.3879/j.issn.1000-0887.2012.12.007

Volume 33 Issue 12

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SU Xiao-hong, ZHENG Lian-cun, ZHANG Xin-xin. On DTM-BF Method and Dual Solutions for an Unsteady MHD Flow Over a Permeable Shrinking Sheet With Velocity Slip[J]. Applied Mathematics and Mechanics, 2012, 33(12): 1451-1464. doi: 10.3879/j.issn.1000-0887.2012.12.007

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On DTM-BF Method and Dual Solutions for an Unsteady MHD Flow Over a Permeable Shrinking Sheet With Velocity Slip

doi: 10.3879/j.issn.1000-0887.2012.12.007

¹ School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, P.R.China;² School of Mathematics and Physics, North China Electric Power University, Baoding, Hebei 071003, P.R.China;³Mechanical Engineering School, University of Science and Technology Beijing, Beijing 100083, P.R.China

Received Date: 2012-02-01
Rev Recd Date: 2012-05-06
Publish Date: 2012-12-15

Abstract

Abstract

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

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References(48)

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