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

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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.

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Acknowledgements

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

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Authors and Affiliations

  1. Beijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Hongxia Guo & Ping Lin

  2. Division of Mathematics, University of Dundee, Dundee, DD1 4HN, United Kingdom

    Ping Lin

  3. School of Mathematics and Physics, University of South China, Hengyang, 421001, Hunan Province, China

    Lin Li

Authors
  1. Hongxia Guo
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  2. Ping Lin
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  3. Lin Li
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Correspondence to Ping Lin.

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Citation: GUO, H. X., LIN, P., and LI, L. Asymptotic solutions for the asymmetric flow in a channel with porous retractable walls under a transverse magnetic field. Applied Mathematics and Mechanics (English Edition), 39(8), 1147–1164 (2018) https://doi.org/10.1007/s10483-018-2355-6

Project supported by the National Natural Science Foundation of China (Nos. 91430106 and 11771040) and the Fundamental Research Funds for the Central Universities of China (No. 06500073)

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Guo, H., Lin, P. & Li, L. Asymptotic solutions for the asymmetric flow in a channel with porous retractable walls under a transverse magnetic field. Appl. Math. Mech.-Engl. Ed. 39, 1147–1164 (2018). https://doi.org/10.1007/s10483-018-2355-6

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  • DOI: https://doi.org/10.1007/s10483-018-2355-6

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