中国物理B ›› 2017, Vol. 26 ›› Issue (1): 14704-014704.doi: 10.1088/1674-1056/26/1/014704

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Three-dimensional MHD flow over a shrinking sheet: Analytical solution and stability analysis

Sumaira Afzal, Saleem Asghar, Adeel Ahmad   

  1. 1. Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, 44000 Islamabad, Pakistan;
    2. Department of Mathematics, King Abdul Aziz University, Jeddah, Saudi Arabia
  • 收稿日期:2015-11-27 修回日期:2016-08-30 出版日期:2017-01-05 发布日期:2017-01-05
  • 通讯作者: Sumaira Afzal E-mail:sumairaafzal66@yahoo.com

Three-dimensional MHD flow over a shrinking sheet: Analytical solution and stability analysis

Sumaira Afzal1, Saleem Asghar1,2, Adeel Ahmad1   

  1. 1. Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, 44000 Islamabad, Pakistan;
    2. Department of Mathematics, King Abdul Aziz University, Jeddah, Saudi Arabia
  • Received:2015-11-27 Revised:2016-08-30 Online:2017-01-05 Published:2017-01-05
  • Contact: Sumaira Afzal E-mail:sumairaafzal66@yahoo.com

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摘要： The magnetohydrodynamic (MHD) steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt-Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.

关键词: steady and unsteady magnetohydrodynamic flows, two-directional shrinking sheet, exact and asymptotic solutions, stability analysis

Abstract: The magnetohydrodynamic (MHD) steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt-Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.

Key words: steady and unsteady magnetohydrodynamic flows, two-directional shrinking sheet, exact and asymptotic solutions, stability analysis

中图分类号:  (Magnetohydrodynamics and electrohydrodynamics)

  • 47.65.-d
04.20.Jb (Exact solutions) 04.25.-g (Approximation methods; equations of motion) 47.15.Fe (Stability of laminar flows)