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Homotopy analysis solutions for the asymmetric laminar flow in a porous channel with expanding or contracting walls

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Abstract

In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homotopy analysis method (HAM) is employed to obtain the expressions for velocity fields. Graphs are sketched for values of parameters and associated dynamic characteristics, especially the expansion ratio, are analyzed in detail.

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References

  1. Berman, A.S.: Laminar flow in channels with porous walls. Journal of Applied Physics 24, 1232–1235 (1953)

    Article  MATH  Google Scholar 

  2. Terrill, R.M., Thomas, P.W.: Laminar flow in a uniformly porous pipe. Applied Science Research 21, 37–67 (1969)

    Article  MATH  Google Scholar 

  3. Terrill, R.M.: On some exponentially small terms arising in flow through a porous pipe. The Quarterly Journal of Mechanics and Applied Mathematics 26, 347–354 (1973)

    Article  MATH  Google Scholar 

  4. Terrill, R.M.: Laminar flow in a uniformly porous channel. Article title. The Aeronautical Quarterly 15, 299–310 (1964)

    MathSciNet  Google Scholar 

  5. Robinson, W.A.: The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls. Journal of Engineering Mathematics 10, 23–40 (1976)

    Article  MATH  Google Scholar 

  6. Lu, C.: On the asymptotic behavior of laminar flow through a porous pipe. In: Proceeding of the First World Congress of Nonlinear Analysis, Tampa, Florida, 201–209 (1996)

  7. Terrill, R.M., Shrestha, G.M.: Laminar flow through parallel and uniformly porous walls of different permeability. ZAMP 16, 470–482 (1965)

    Article  MathSciNet  Google Scholar 

  8. Chang, H.N., Ha, J.S., Park, J.K., et al.: Velocity field of pulsatile flow in a porous tube. Journal of Biomechanics 22, 1257–1262 (1989)

    Article  Google Scholar 

  9. Uchida, S, Aoki, H.: Unsteady flows in a semi-infinite contract ing or expanding pipe. Journal of FluidMechanics 82, 371–387 (1977)

    MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  11. Goto, M., Uchida, S.: Unsteady flows in a semi-infinite expanding pipe with injection through wall. Japan Society for Aeronautical and Space Science 33, 14–27 (1990)

    Google Scholar 

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

    Article  MATH  Google Scholar 

  13. Ma, Y., van Moorhem, W.K., Shorthill, R.W.: Experimental investigation of velocity coupling in combustion instability. Journal of Propulsion and Power 7, 692–699 (1991)

    Article  Google Scholar 

  14. Ma, Y., van Moorhem, W.K., Shorthill. R.W.: Innovative method of investigating the role of turbulence in the velocity coupling phenomenon. ASME Journal of Vibration and Acoustics 112, 550–555 (1990)

    Article  Google Scholar 

  15. Barron, J., Majdalani, J., van Moorhem, W.K.: A novel investigation of the oscillatory field over a transpiring surface. Journal of Sound and Vibration 235, 281–297 (2000)

    Article  Google Scholar 

  16. Majdalani, J., Zhou, C., Dawson, C.A.: Two-dimensional viscous flows between slowly expanding or contracting walls with weak permeability. Journal of Biomechanics 35, 1399–1403 (2002)

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  19. Asghar, S., Mushtaq, M., Hayat, T.: Flow in a slowly deforming channel with weak permeability: an analytical approach. Nonlinear Analysis: Real World Applications 11, 555–561 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  20. Si, X.H., Zheng L.C., Zhang X.X., et al.: Asymptotic solution for unsteady flow in expanding or contracting channel with large suction Reynolds number. Journal of University of Science and Technology Beijing 31 1463–1466 (2009) (in Chinese)

    Google Scholar 

  21. Villarroel, F., Lanham, C.E., Bischoff, K.B., et al.: Gas transfer to blood flowing in semipermeable tubes under steady and pulsatile flow cinditions. CEP Symp. Ser 67, 94–104 (1971)

    Google Scholar 

  22. Wang, C.Y.: Pulsatile flow in a porous channel. Transactions of the ASME, Journal of Applied Mechanics 38, 553–555 (1971)

    Article  Google Scholar 

  23. Bhatnager, R.K.: Fluctuating flow of a viscoelastic fluid in a porous channel. Transactions of the ASME, Journal of Applied Mechanics 46, 21–25 (1979)

    Article  Google Scholar 

  24. Muhammad Ashraf, Anwar Kamal, M., Syed, K.S.: Numerical study of asymmetric laminar flow of micropolar fluids in a porous channel. Computers & Fluids 38, 1895–1902 (2009)

    Article  Google Scholar 

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

    Book  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  28. Hayat, T., Khan, M., Asghar, S.: Magnetohydrodynamic flow of an oldroyd 6-constant fluid. Applied Mathematics and Computation 155, 417–225 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  29. Hayat, T., Khan, M., Asghar, S., et al.: Transient flows of a second grade fluid. International Journal of Nonlinear Mechanics 39, 1621–1633 (2004)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

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Authors and Affiliations

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

    Xin-Hui Si & Lian-Cun Zheng

  2. Department of Mechanical Engineering, University of Science and Technology Beijing, 100083, Beijing, China

    Xin-Xin Zhang

  3. Research Institute of Chemical Defense of the P.L.A., 102205, Beijing, China

    Ying Chao

Authors
  1. Xin-Hui Si
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  2. Lian-Cun Zheng
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  3. Xin-Xin Zhang
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  4. Ying Chao
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Corresponding author

Correspondence to Xin-Hui Si.

Additional information

The project was supported by the National Natural Science Foundations of China (50936003, 50905013). The Open Project of State Key Lab. for Adv. Matals and Materials (2009Z-02) and Research Foundation of Engineering Research Institute of USTB.

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Si, XH., Zheng, LC., Zhang, XX. et al. Homotopy analysis solutions for the asymmetric laminar flow in a porous channel with expanding or contracting walls. Acta Mech Sin 27, 208–214 (2011). https://doi.org/10.1007/s10409-011-0430-3

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  • DOI: https://doi.org/10.1007/s10409-011-0430-3

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