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MHD boundary-layer flow due to a moving extensible surface

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Abstract

The flow due to a moving extensible sheet that obeys a more general stretching law is considered. The sheet occupies the negative x-axis and is moving continually in the positive x-direction, in an incompressible viscous and electrically conducting fluid. The sheet somehow disappears in a sink that is located at (x, y) = (0, 0). The governing system of partial differential equations is first transformed into a system of ordinary differential equations, and the transformed equations are solved numerically using a finite-difference scheme, namely the Keller-box method. The features of the flow and heat-transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that dual solutions exist for the flow near x = 0, where the velocity profiles show a reversed flow.

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References

  1. Sakiadis BC (1961). Boundary layer behavior on continuous solid surfaces: I. The boundary layer equations for two-dimensional and axisymmetric flow. AIChE J 7: 26–28

    Article  Google Scholar 

  2. Sakiadis BC (1961). Boundary-layer behavior on continuous solid surfaces: II. The boundary-layer on a continuous flat surface. AIChE J 7: 221–225

    Google Scholar 

  3. Gupta PS and Gupta AS (1977). Heat and mass transfer on a stretching sheet with suction and blowing. Can J Chem Engng 55: 744–746

    Article  Google Scholar 

  4. Dutta BK, Roy P and Gupta AS (1985). Temperature field in flow over a stretching sheet with uniform heat flux. Int Commun Heat Mass Transfer 12: 89–94

    Article  Google Scholar 

  5. Grubka LJ and Bobba KM (1985). Heat transfer characteristics of a continuous stretching surface with variable temperature. Trans ASME J Heat Transfer 107: 248–250

    Article  Google Scholar 

  6. Kumari M, Takhar HS and Nath G (1990). MHD flow and heat transfer over a stretching surface with prescribed wall temperature or heat flux. Wärme- und Stoffübertr 25: 331–336

    Article  ADS  Google Scholar 

  7. Liao S-J and Pop I (2004). On explicit analytic solutions of boundary-layer equations about flows in a porous medium or for a stretching wall. Int J Heat Mass Transfer 47: 75–85

    Article  Google Scholar 

  8. Nazar R, Amin N, Filip D and Pop I (2004). Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet. Int J Engng Sci 42: 1241–1253

    Article  MathSciNet  Google Scholar 

  9. Crane LJ (1970). Flow past a stretching plate. J Appl Math Phys (ZAMP) 21: 645–647

    Article  Google Scholar 

  10. Banks WHH (1983). Similarity solution of the boundary layer equations for a stretching wall. J Mech Theor Appl 2: 375–392

    MATH  Google Scholar 

  11. Magyari E and Keller B (1999). Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface. J Phys D: Appl Phys 32: 577–585

    Article  ADS  Google Scholar 

  12. Magyari E and Keller B (2000). Exact solutions for self-similar boundary-layer flows induced by permeable stretching surfaces. Eur J Mech B-Fluids 19: 109–122

    Article  MATH  MathSciNet  Google Scholar 

  13. Magyari E, Ali ME and Keller B (2001). Heat and mass transfer characteristics of the self-similar boundary-layer flows induced by continuous surfaces stretched with rapidly decreasing velocities. Heat Mass Transfer 38: 65–74

    Article  ADS  Google Scholar 

  14. Carragher P and Crane LJ (1982). Heat transfer on a continuous stretching sheet. J Appl Math Mech (ZAMM) 62: 564–565

    Google Scholar 

  15. Kuiken HK (1981). On boundary layers in fluid mechanics that decay algebraically along stretches of wall that are not vanishingly small. IMA J Appl Math 27: 387–405

    Article  MATH  MathSciNet  Google Scholar 

  16. Shercliff JA (1965) A textbook of magnetohydrodynamic. Oxford Pergamon Press

  17. Cobble MH (1977). Magnetohydrodynamic flow with a pressure gradient and fluid injection. J Eng Math 11: 249–256

    Article  MATH  Google Scholar 

  18. Cobble MH (1980). Magnetohydrodynamic flow for a non-Newtonian power-law fluid having a pressure gradient and fluid injection. J Eng Math 14: 47–55

    Article  MATH  Google Scholar 

  19. Helmy KA (1994). Solution of the boundary layer equation for a power law fluid in magneto-hydrodynamics. Acta Mech 102: 25–37

    Article  MATH  MathSciNet  Google Scholar 

  20. Cebeci T and Bradshaw P (1988). Physical and computational aspects of convective heat transfer. Springer, New York

    MATH  Google Scholar 

  21. Ariel PD (1994). Hiemenz flow in hydromagnetics. Acta Mech 103: 31–43

    Article  MATH  MathSciNet  Google Scholar 

  22. Chiam TC (1995). Hydromagnetic flow over a surface stretching with a power-law velocity. Int J Engng Sci 33: 429–435

    Article  MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor, Malaysia

    Anuar Ishak & Roslinda Nazar

  2. Faculty of Mathematics, University of Cluj, CP 253, Cluj, 3400, Romania

    Ioan Pop

Authors
  1. Anuar Ishak
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  2. Roslinda Nazar
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  3. Ioan Pop
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Correspondence to Ioan Pop.

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Ishak, A., Nazar, R. & Pop, I. MHD boundary-layer flow due to a moving extensible surface. J Eng Math 62, 23–33 (2008). https://doi.org/10.1007/s10665-007-9169-z

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  • DOI: https://doi.org/10.1007/s10665-007-9169-z

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