Electrically Driven MHD Flow Between Two Parallel Slipping and Partly Conducting Infinite Plates

  • Munevver Tezer-SezginEmail author
  • Pelin Senel
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


The magnetohydrodynamic (MHD) flow between two parallel slipping and conducting infinite plates containing symmetrically placed electrodes is solved by using the dual reciprocity boundary element method (DRBEM). The flow is driven by the current traveling between the plates and the external magnetic field applied perpendicular to the plates. The coupled MHD equations are solved for the velocity of the fluid and the induced magnetic field as a whole without introducing an iteration. The effects of both the slip ratio and the length of the electrodes are discussed on the flow and magnetic field behavior for increasing values of Hartmann number (Ha). It is found that, an increase in the Hartmann number produces Hartmann layers of thickness 1∕Ha near the conducting parts and shear layers of order of thickness \(1/\sqrt {Ha}\) in front of the end points of electrodes. When the slip ratio increases Hartmann layers are weakened and the increase in the length of the electrodes retards this weakening effect of the slip on the Hartmann layers. The DRBEM discretizes only a finite portion of the plates and provides the solution inside the infinite region which is mostly concentrated in front of the electrodes. The aim of the study is to numerically simulate the MHD flow under the influence of the slipping velocity on the partly conducting plates which can not be treated theoretically.


  1. 1.
    C. Bozkaya, M. Tezer-Sezgin, A numerical solution of the steady MHD flow through infinite strips with BEM. Eng. Anal. Bound. Elem. 36, 591–566 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    J.C.R. Hunt, D.G. Malcolm, Some electrically driven flows in magnetohydrodynamics part 2. Theory and experiment. J. Fluid Mech. 33(4), 775–801 (1968)CrossRefGoogle Scholar
  3. 3.
    J.C.R. Hunt, W.E. Williams, Some electrically driven flows in magnetohydrodynamics part 1. Theory. J. Fluid Mech. 31(4), 705–722 (1968)CrossRefGoogle Scholar
  4. 4.
    E. Ligere, I. Dzenite, A. Matvejevs, MHD flow in the duct with perfectly conducting Hartmann walls and slip condition on side walls, in 10th PAMIR International Conference-Fundamental and Applied MHD, Cagliari, Italy, 20–24 June 2016, pp. 279–283.Google Scholar
  5. 5.
    U. Muller, L. Buhler, Magnetofluiddynamics in Channels and Containers (Springer, Berlin, 2001)CrossRefGoogle Scholar
  6. 6.
    P.W. Partridge, C.A. Brebbia, L.C. Wrobel, The Dual Reciprocity Boundary Element Method (Computational Mechanics Publications, Sauthampton, 1992)zbMATHGoogle Scholar
  7. 7.
    B.A. Pint, K.L. More, H.M. Meyer, J.R. Distefano, Recent progress addressing compatibility issues relevant to fusion environments. Fusion Sci. Technol. 47, 851–855 (2005)CrossRefGoogle Scholar
  8. 8.
    M. Rivero, S. Cuevas, Analysis of the slip condition in magnetohydrodynamic (MHD) micropumps. Sensors Actuators B Chem. 166–167, 884–892 (2012)CrossRefGoogle Scholar
  9. 9.
    D. Sarma, P.N. Deka, Numerical study of liquid metal MHD duct flow under hydrodynamic “slip” condition. Int. J. Comput. Appl. 81(16), 7–10 (2013)Google Scholar
  10. 10.
    M. Sezgin, Magnetohydrodynamic flow in an infinite channel. Int J. Numer. Methods Fluids 6, 593–609 (1986)CrossRefGoogle Scholar
  11. 11.
    M. Sezgin, Magnetohydrodynamic flow on a half-plane. Int. J. Numer. Methods Fluids 8, 743–758 (1988)MathSciNetCrossRefGoogle Scholar
  12. 12.
    S. Smolentsev, MHD duct flows under hydrodynamic ‘slip’ condition. Theor. Comput. Fluid Dyn. 23, 557–570 (2009)CrossRefGoogle Scholar
  13. 13.
    M. Tezer-Sezgin, C. Bozkaya, The boundary element solution of the magnetohydrodynamic flow in an infinite region. J. Comput. Appl. Math. 225, 510–521 (2009)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey

Personalised recommendations