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Applied Mathematics and Mechanics

, Volume 39, Issue 8, pp 1147–1164 | Cite as

Asymptotic solutions for the asymmetric flow in a channel with porous retractable walls under a transverse magnetic field

  • Hongxia Guo
  • Ping LinEmail author
  • Lin Li
Article

Abstract

The self-similarity solutions of the Navier-Stokes equations are constructed for an incompressible laminar flow through a uniformly porous channel with retractable walls under a transverse magnetic field. The flow is driven by the expanding or contracting walls with different permeability. The velocities of the asymmetric flow at the upper and lower walls are different in not only the magnitude but also the direction. The asymptotic solutions are well constructed with the method of boundary layer correction in two cases with large Reynolds numbers, i.e., both walls of the channel are with suction, and one of the walls is with injection while the other one is with suction. For small Reynolds number cases, the double perturbation method is used to construct the asymptotic solution. All the asymptotic results are finally verified by numerical results.

Key words

laminar flow asymmetric flow asymptotic solution porous and retractable channel magnetic field 

Chinese Library Classification

O175.8 O357.1 

2000 Mathematics Subject Classification

76M45 76D10 

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Notes

Acknowledgements

The authors would like to thank the editors and reviewers for the valuable comments.

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Beijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science, School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijingChina
  2. 2.Division of MathematicsUniversity of DundeeDundeeUnited Kingdom
  3. 3.School of Mathematics and PhysicsUniversity of South ChinaHengyangChina

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