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Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (9): 1097-1106.doi: https://doi.org/10.1007/s10483-013-1730-8

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Oscillatory flow of second grade fluid in cylindrical tube

A. ALI1,2  S. ASGHAR2,3  H. H. ALSULAMI3   

  1. 1. Laboratoire Jean Alexandre Dieudonne, Universite de Nice Sophia Antipolis, Parc Valrose, Nice 06108, France;
    2. Department of Mathematics, Commission on Science and Technology for Sustainable Development in the South, Institute of Information Technology, Islamabad 44000, Pakistan;
    3. Department of Mathematics, King Abdulaziz University, Jeddah 21432, Saudi Arabia
  • 收稿日期:2012-03-01 修回日期:2013-04-08 出版日期:2013-09-02 发布日期:2013-09-02

Oscillatory flow of second grade fluid in cylindrical tube

A. ALI1,2  S. ASGHAR2,3  H. H. ALSULAMI3   

  1. 1. Laboratoire Jean Alexandre Dieudonne, Universite de Nice Sophia Antipolis, Parc Valrose, Nice 06108, France;
    2. Department of Mathematics, Commission on Science and Technology for Sustainable Development in the South, Institute of Information Technology, Islamabad 44000, Pakistan;
    3. Department of Mathematics, King Abdulaziz University, Jeddah 21432, Saudi Arabia
  • Received:2012-03-01 Revised:2013-04-08 Online:2013-09-02 Published:2013-09-02

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摘要： The unsteady oscillatory flow of an incompressible second grade fluid in a cylindrical tube with large wall suction is studied analytically. Flow in the tube is due to uniform suction at the permeable walls, and the oscillations in the velocity field are due to small amplitude time harmonic pressure waves. The physical quantities of interest are the velocity field, the amplitude of oscillation, and the penetration depth of the oscillatory wave. The analytical solution of the governing boundary value problem is obtained, and the effects of second grade fluid parameters are analyzed and discussed.

关键词: Oscillatory flow of second grade fluid in cylindrical tube

Abstract: The unsteady oscillatory flow of an incompressible second grade fluid in a cylindrical tube with large wall suction is studied analytically. Flow in the tube is due to uniform suction at the permeable walls, and the oscillations in the velocity field are due to small amplitude time harmonic pressure waves. The physical quantities of interest are the velocity field, the amplitude of oscillation, and the penetration depth of the oscillatory wave. The analytical solution of the governing boundary value problem is obtained, and the effects of second grade fluid parameters are analyzed and discussed.

Key words: analytical solutions, mode III interface crack, self-similar function, complex functions, second grade fluid, cylindrical coordinate, oscillatory flow, incompressible flow, laminar flow, Navier-Stokes equation, partial differential equation, Wentzel-Kramers-Brillouin (WKB) approximation

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