Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (12): 124702-124702.doi: 10.1088/1674-1056/22/12/124702

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

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Khaled S. Mekheimera b, Soliman R. Komyc, Sara I. Abdelsalamd   

  1. a Mathematics & Statistics Department, Faculty of Science, Taif University, Hawia (888) Taif, Saudi Arabia;
    b Department of Mathematics, Faculty of Science (Men), Al-Azhar University, Nasr City, Cairo, Egypt;
    c Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt;
    d Basic Science Department, Faculty of Engineering, The British University in Egypt, Al-Shorouk City, Misr-Suez Desert Road, P. O. Box 43, Cairo 11837, Egypt
  • 收稿日期:2013-02-06 修回日期:2013-05-05 出版日期:2013-10-25 发布日期:2013-10-25

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Khaled S. Mekheimera b, Soliman R. Komyc, Sara I. Abdelsalamd   

  1. a Mathematics & Statistics Department, Faculty of Science, Taif University, Hawia (888) Taif, Saudi Arabia;
    b Department of Mathematics, Faculty of Science (Men), Al-Azhar University, Nasr City, Cairo, Egypt;
    c Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt;
    d Basic Science Department, Faculty of Engineering, The British University in Egypt, Al-Shorouk City, Misr-Suez Desert Road, P. O. Box 43, Cairo 11837, Egypt
  • Received:2013-02-06 Revised:2013-05-05 Online:2013-10-25 Published:2013-10-25
  • Contact: Sara I. Abdelsalam E-mail:sara.abdelsalam@bue.edu.eg, siabdelsalam@yahoo.com

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摘要： Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.

关键词: peristaltic flow, Maxwell fluid, porous medium, slip flow, microchannel

Abstract: Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.

Key words: peristaltic flow, Maxwell fluid, porous medium, slip flow, microchannel

中图分类号:  (Compressible flows; shock waves)

  • 47.40.-x
47.45.Gx (Slip flows and accommodation) 47.56.+r (Flows through porous media) 52.30.Cv (Magnetohydrodynamics (including electron magnetohydrodynamics))