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Perturbation solutions for asymmetric laminar flow in porous channel with expanding and contracting walls

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Abstract

The cases of large Reynolds number and small expansion ratio for the asymmetric laminar flow through a two-dimensional porous expanding channel are considered. The Navier-Stokes equations are reduced to a nonlinear fourth-order ordinary differential equation by introducing a time and space similar transformation. A singular perturbation method is used for the large suction Reynolds case to obtain an asymptotic solution by matching outer and inner solutions. For the case of small expansion ratios, we are able to obtain asymptotic solutions by double parameter expansion in either a small Reynolds number or a small asymmetric parameter. The asymptotic solutions indicate that the Reynolds number and expansion ratio play an important role in the flow behavior. Numerical methods are also designed to confirm the correctness of the present asymptotic solutions.

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Authors and Affiliations

  1. Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing, 100083, P. R. China

    Yan Zhang  (张 燕), Ping Lin  (林 平) & Xin-hui Si  (司新辉)

  2. Department of Mathematics, University of Dundee, Dundee, DD1 4HN, UK

    Ping Lin  (林 平)

Authors
  1. Yan Zhang  (张 燕)
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  2. Ping Lin  (林 平)
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  3. Xin-hui Si  (司新辉)
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Corresponding author

Correspondence to Xin-hui Si  (司新辉).

Additional information

Project supported by the Beijing Higher Education Young Elite Teacher Project (No.YETP0387), the Fundamental Research Funds for the Central Universities (Nos.FRF-TP-12-108A and FRF-BR-13-023), and the National Natural Science Foundation of China (Nos. 51174028 and 11302024)

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Zhang, Y., Lin, P. & Si, Xh. Perturbation solutions for asymmetric laminar flow in porous channel with expanding and contracting walls. Appl. Math. Mech.-Engl. Ed. 35, 203–220 (2014). https://doi.org/10.1007/s10483-014-1784-8

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  • DOI: https://doi.org/10.1007/s10483-014-1784-8

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Chinese Library Classification

2010 Mathematics Subject Classification

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