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Analytic solution to the micropolar-fluid flow through a semi-porous channel with an expanding or contracting wall

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Abstract

The flow of a micropolar fluid in a semi-porous channel with an expanding or contracting wall is investigated. The governing equations are reduced to ordinary ones by using similar transformations. To get the analytic solution to the problem, the homotopy analysis method (HAM) is employed to obtain the expressions for velocity fields. Graphs are sketched and discussed for various parameters, especially the effect of the expansion ratio on velocity and micro-rotation fields.

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References

  1. Uchida, S. and Aoki, H. Unsteady flows in a semi-infinite contracting or expanding pipe. Journal of Fluid Mechanics 82(2), 371–387 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ohki, M. Unsteady flows in a porous, elastic, circular tube: part 1, the wall contracting or expanding in an axial direction. Bulletin of the JSME 23(179), 679–686 (1980)

    Google Scholar 

  3. Goto, M. and Uchida, S. Unsteady flow in a semi-infinite expanding pipe with injection through wall. Journal of the Japan Society for Aeronautical and Space Science 33(9), 14–27 (1990)

    Google Scholar 

  4. Bujurke, N. M., Pai, N. P., and Jayaraman, G. Computer extended series solution for unsteady flow in a contracting or expanding pipe. IMA Journal of Applied Mathematics 60(2), 151–165 (1998)

    Article  MATH  Google Scholar 

  5. Majdalani, J., Zhou, C., and Dawson, C. D. Two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability. Journal of Biomechanics 35(10), 1399–1403 (2002)

    Article  Google Scholar 

  6. Dauenhauer, C. E. and Majdalani, J. Exact self-similarity solution of the Navier-Stokes equations for a porous channel with orthogonally moving walls. Physics of Fluids 15(6), 1485–1495 (2003)

    Article  MathSciNet  Google Scholar 

  7. Majdalani, J. and Zhou, C. Moderate-to-large injection and suction driven channel flows with expanding or contracting walls. Zeitschrift für Angewandte Mathematik und Mechanik 83(3), 181–196 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Eringen, A. C. Theory of micropolar fluids. Journal of Mathematics and Mechanics 16(1), 1–18 (1966)

    MathSciNet  Google Scholar 

  9. Eringen, A. C. Theory of thermomicropolar fluids. Journal of Mathematical Analysis and Applications 38(1), 480–496 (1972)

    Article  MATH  Google Scholar 

  10. Ariman, T., Turk, M. A., and Sylvester, N. D. Microcontinuum fluid mechanics—a review. International Journal of Engineering Science 11(8), 905–930 (1973)

    Article  MATH  Google Scholar 

  11. Ariman, T., Turk, M. A., and Sylvester, N. D. Application of microcontinuum fluid mechanics—a review. International Journal of Engineering Science 12(4), 273–293 (1974)

    Article  MATH  Google Scholar 

  12. Eringen, A. C. Microcontinuum Field Theories II: Fluent Media, Springer, New York (2001)

    Google Scholar 

  13. Ramachandran, P. S., Mathur, M. N., and Ojha, S. K. Heat transfer in boundary layer flow of a micropolar fluid past a curved surface with suction and injection. International Journal of Engineering Science 17(5), 625–639 (1979)

    Article  MATH  Google Scholar 

  14. Takhar, H. S., Bhargava, R., Agrawal, R. S., and Balaji, A. V. S. Finite element solution of micropolar fluid flow and heat transfer between two porous discs. International Journal of Engineering Science 38(17), 1907–1922 (2000)

    Article  Google Scholar 

  15. Kelson, N. A. and Farrell, T. W. Micropolar fluid flow over a porous stretching sheet with strong suction or injection. International Communications in Heat and Mass Transfer 28(4), 479–488 (2001)

    Article  Google Scholar 

  16. Ashraf, M., Kamal, M. A., and Syed, K. S. Numerical study of asymmetric laminar flow of a micropolar fluid in a porous channel. Computers and Fluids 38(10), 1895–1902 (2009)

    Article  Google Scholar 

  17. Ashraf, M., Kamal, M. A., and Syed, K. S. Numerical simulation of flow of a micropolar fluid between a porous disk and a non-porous disk. Applied Mathematical Modelling 33(4), 1933–1943 (2009)

    Article  MATH  Google Scholar 

  18. Liao, S. J. Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman Hall/CRC Press, Boca Raton (2003)

    Google Scholar 

  19. Liao, S. J. On the homotopy analysis method for nonlinear problems. Applied Mathematics and Computation 147(2), 499–513 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  20. Hayat, T. and Khan, M. Homotopy solution for a generalized second grade fluid past a porous plate. Nonlinear Dynamics 42(4), 395–405 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  21. Hayat, T., Khan, M., and Asghar, S. Magnetohydrodynamic flow of an oldroyd 6-constant fluid. Applied Mathematics and Computation 155(2), 417–425 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  22. Hayat, T., Khana, M., Siddiquib, A. M., and Asghar, S. Transient flows of a second grade fluid. International Journal of Non-Linear Mechanics 39(10), 1621–1633 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  23. Abbas, Z., Sajid, M., and Hayat, T. MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel. Theoretical and Computational Fluid Dynamics 20(4), 229–238 (2006)

    Article  MATH  Google Scholar 

  24. Sajid, M., Hayat, T., and Asghar, S. On the analytic solution of the steady flow of a fourth grade fluid. Physics Letters A 355(1), 18–26 (2006)

    Article  Google Scholar 

  25. Sajid, M., Abbas, Z., and Hayat, T. Homotopy analysis for boundary layer flow of a micropolar fluid through a porous channel. Applied Mathematical Modelling 33(11), 4120–4125 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  26. Scrinivasacharya, D., Murthy, J. V. R., and Venugopalam, D. Unsteady stokes flow of micropolar fluid between two parallel porous plates. International Journal of Engineering Science 39(14), 1557–1563 (2001)

    Article  Google Scholar 

  27. Rees, D. and Pop, I. Free convection boundary layer flow of a micropolar fluid from a vertical flat plate. IMA Journal of Applied Mathematics 61(2), 179–191 (2001)

    Article  MathSciNet  Google Scholar 

  28. Guram, G. S. and Smith, A. C. Stagnation flows of micropolar fluids with strong and weak interactions. Computers and Mathematics with Applications 6(2), 213–233 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  29. Liao, S. J. An optimal homotopy-analysis approach for strongly nonlinear differential equations. Communications in Nonlinear Science and Numerical Simulation 15(8), 2003–2016 (2010)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Applied Science School, University of Science and Technology Beijing, Beijing, 100083, P. R. China

    Xin-hui Si  (司新辉) & Lian-cun Zheng  (郑连存)

  2. Mechanical Engineering School, University of Science and Technology Beijing, Beijing, 100083, P. R. China

    Xin-xin Zhang  (张欣欣)

  3. Research Institute of Chemical Defense, Beijing, 102205, P. R. China

    Ying Chao  (晁 莹)

Authors
  1. Xin-hui Si  (司新辉)
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  2. Lian-cun Zheng  (郑连存)
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  3. Xin-xin Zhang  (张欣欣)
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  4. Ying Chao  (晁 莹)
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Corresponding author

Correspondence to Xin-hui Si  (司新辉).

Additional information

Communicated by Zhe-wei ZHOU

Project supported by the National Natural Science Foundation of China (Nos. 50936003 and 50905013), the Open Project of State Key Laboratory for Advanced Metals and Materials (No. 2009Z-02)

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Si, Xh., Zheng, Lc., Zhang, Xx. et al. Analytic solution to the micropolar-fluid flow through a semi-porous channel with an expanding or contracting wall. Appl. Math. Mech.-Engl. Ed. 31, 1073–1080 (2010). https://doi.org/10.1007/s10483-010-1343-6

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  • DOI: https://doi.org/10.1007/s10483-010-1343-6

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2000 Mathematics Subject Classification

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