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Boundary element method solution of magnetohydrodynamic flow in a rectangular duct with conducting walls parallel to applied magnetic field

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Abstract

The magnetohydrodynamic (MHD) flow of an incompressible, viscous, electrically conducting fluid in a rectangular duct with one conducting and one insulating pair of opposite walls under an external magnetic field parallel to the conducting walls, is investigated. The MHD equations are coupled in terms of velocity and magnetic field and cannot be decoupled with conducting wall boundary conditions since then boundary conditions are coupled and involve an unknown function. The boundary element method (BEM) is applied here by using a fundamental solution which enables to treat the MHD equations in coupled form with the most general form of wall conductivities. Also, with this fundamental solution it is possible to obtain BEM solution for values of Hartmann number (M) up to 300 which was not available before. The equivelocity and induced magnetic field contours which show the well-known characteristics of MHD duct flow are presented for several values of M.

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References

  1. Barrett KE (2001) Duct flow with a transverse magnetic field at high Hartmann numbers. Int J Numer Meth Eng 50: 1893–1906

    Article  MATH  Google Scholar 

  2. Bozkaya C (2005) Fundamental solution for some equations in magnetohydrodynamic flow. In: Proceedings of UKBIM5 International Conference, Liverpool, England, pp. 90–99

  3. Bozkaya C, Tezer-Sezgin M (2006) Fundamental solution for coupled magnetohydrodynamic flow equations. J Comput Appl Math (in press)

  4. Brebbia CA, Dominguez J (1992) Boundary elements an introductory course. Comp. Mech. Pub. Southhampton, Boston

  5. Carabineanu A, Dinu A, Oprea I (1995) The application of the boundary element method to the MHD duct flow. ZAMP 46:971–981

    Article  MATH  MathSciNet  Google Scholar 

  6. Demendy Z, Nagy T (1997) A new algorithm for solution of equations of MHD channel flows at moderate Hartmann numbers. Acta Mech 123:135–149

    Article  MATH  Google Scholar 

  7. Dragoş L (1975) Magneto-fluid dynamics. Abacus Press, England

    Google Scholar 

  8. Liu HW, Zhu SP (2002) The dual reciprocity boundary element method for magnetohydrodynamic channel flows. ANZIAM J 44(2):305–322

    Article  MATH  MathSciNet  Google Scholar 

  9. NAG Fortran Library Manual (1993) Mark 16, vol 2, Edn 1. Oxford, UK

  10. Neslitürk AI, Tezer-Sezgin M (2005) The finite element method for MHD flow at high Hartmann numbers. Comput Meth Appl Mech Eng 194:1201–1224

    Article  Google Scholar 

  11. Shercliff JA (1953) Steady motion of conducting fluids in pipes under transverse fields. Proc Camb Phil Soc 49:136–144

    MATH  MathSciNet  Google Scholar 

  12. Singh B, Lal J (1978) MHD axial flow in a triangular pipe under transverse magnetic field. Ind J Pure Appl Math 9: 101–115

    MathSciNet  Google Scholar 

  13. Singh B, Lal J (1979) MHD axial flow in a triangular pipe under transverse magnetic field parallel to a side of the triangle. Ind J Tech 17:184–189

    MATH  Google Scholar 

  14. Singh B, Lal J (1982) Finite element method in MHD channel flow problems. Int J Numer Meth Eng 18:1104–1111

    Article  MATH  Google Scholar 

  15. Singh B, Lal J (1984) Finite element method of MHD channel flow with arbitrary wall conductivity. J Math Phys Sci 18: 501–516

    MATH  Google Scholar 

  16. Tezer-Sezgin M, Köksal S (1989) Finite element method for solving MHD flow in a rectangular duct. Int J Numer Meth Eng 28:445–459

    Article  MATH  Google Scholar 

  17. Tezer-Sezgin M (1994) BEM solution of MHD flow in a rectangular duct. Int J Numer Meth Fluids 18:937–952

    Article  MATH  Google Scholar 

  18. Tezer-Sezgin M, Dost S (1994) Boundary element method for MHD channel flow with arbitrary wall conductivity. Appl Math Modell 18:429–436

    Article  MATH  Google Scholar 

  19. Tezer-Sezgin M, Aydın SH (2002) Dual reciprocity BEM for MHD flow using radial basis functions. Int J Comput Fluid Dyn 16(1):49–63

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Middle East Technical University, 06531, Ankara, Turkey

    M. Tezer-Sezgin & C. Bozkaya

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  1. M. Tezer-Sezgin
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  2. C. Bozkaya
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Correspondence to M. Tezer-Sezgin.

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Tezer-Sezgin, M., Bozkaya, C. Boundary element method solution of magnetohydrodynamic flow in a rectangular duct with conducting walls parallel to applied magnetic field. Comput Mech 41, 769–775 (2008). https://doi.org/10.1007/s00466-006-0139-5

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  • DOI: https://doi.org/10.1007/s00466-006-0139-5

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