Journal of Mathematical Chemistry

, Volume 55, Issue 7, pp 1407–1426 | Cite as

DRBEM solution of biomagnetic fluid flow and heat transfer in cavities-CMMSE2016

  • P. Senel
  • M. Tezer-Sezgin
Original Paper


In this paper, we investigate the fully developed, laminar, forced convection flow of an electrically non-conducting, viscous, biomagnetic fluid in the 2D cross-section (cavity) of a long impermeable pipe. The fluid is under the influence of a point magnetic source placed below the cavity. The dual reciprocity boundary element method (DRBEM) with constant and linear elements is used for solving the governing equations resulting from the Navier–Stokes and energy equations together with magnetization and buoyancy forces. The fundamental solution of Laplace equation is made use of converting differential equations to boundary integral equations by taking all the terms other than Laplacian as inhomogeneity in the Poisson’s equations for the velocity components, pressure and the temperature of the fluid. The unknown pressure boundary conditions are approximated through momentum equations by using finite difference approximation for the pressure gradients and DRBEM coordinate matrix for the other terms. All the space derivatives are also calculated by DRBEM coordinate matrix which is one of the main advantages of DRBEM. Pipe axis velocity is also computed. The effects of magnetization and the buoyancy force on the fluid with or without viscous dissipation term in the energy equation are investigated in square and lid-driven cavities for several values of magnetic (Mn) and Rayleigh (Ra) numbers. It is observed that the flow and heat transfer are significantly affected with increasing values of Mn and Ra. DRBEM gives small sized linear systems due to its boundary only nature at a considerably low computational expense.


DRBEM Biomagnetic fluid Forced convection Magnetization 


  1. 1.
    Y. Haik, V. Pai, C.J. Chen, J. Magn. Magn. Mater. 194, 254 (1999)Google Scholar
  2. 2.
    R.E. Rosensweig, Ferrohydrodynamics (Dover Publications, Mineola, 2014)Google Scholar
  3. 3.
    V.C. Loukopoulos, E.E. Tzirtzilakis, Int. J. Eng. Sci. 42, 571 (2004)Google Scholar
  4. 4.
    E.E. Tzirtzilakis, V.D. Sakalis, N.G. Kafoussias, P.M. Hatzikonstantinou, Int. J. Numer. Methods Fluids 44, 1279 (2004)Google Scholar
  5. 5.
    E.E. Tzirtzilakis, Phys. Fluids 17, 077103 (2005)Google Scholar
  6. 6.
    P.K. Papadopoulos, Int. J. Numer. Methods Heat Fluid Flow 20(3), 298 (2010)Google Scholar
  7. 7.
    N.A. Idris, N. Amin, H. Rahmat, Appl. Comput. Math. 3(6), 285 (2014)Google Scholar
  8. 8.
    A. Zaman, N. Ali, O.A. Beg, M. Sajid, Int. J. Heat. Mass Transf. 95, 1084 (2016)Google Scholar
  9. 9.
    P.K. Papadopoulos, E.E. Tzirtzilakis, Phys. Fluids 16, 2952 (2004)Google Scholar
  10. 10.
    S.A. Khashan, Y. Haik, Phys. Fluids 18, 113601 (2006)Google Scholar
  11. 11.
    S. Kenjeres, Int. J. Heat Fluid Flow 29, 752 (2008)Google Scholar
  12. 12.
    E.E. Tzirtzilakis, M.A. Xenos, Meccanica 48, 187 (2013)Google Scholar
  13. 13.
    R. Bhargava, O.A. Beg, S. Sharma, J. Zueco, Commun. Nonlinear Sci. Numer. Simul. 15, 1210 (2010)Google Scholar
  14. 14.
    K. Tzirakis, Y. Papaharilaou, D. Giordano, J. Ekaterinaris, Int. J. Numer. Method Biomed. Eng. 30, 297 (2014)Google Scholar
  15. 15.
    O. Turk, C. Bozkaya, M. Tezer-Sezgin, Comput. Fluids 97, 40 (2014)Google Scholar
  16. 16.
    M. Tezer-Sezgin, C. Bozkaya, O. Turk, Eng. Anal. Bound. Elem. 37, 1127 (2013)Google Scholar
  17. 17.
    P. Senel, M. Tezer-Sezgin, Eng. Anal. Bound. Elem. 64, 158 (2016)Google Scholar
  18. 18.
    P. Senel, M. Tezer-Sezgin, in Advances in Boundary Element and Meshless Techniques, 11–13 July 2016, Ankara, Turkey, pp. 139–145Google Scholar
  19. 19.
    C.A.J. Fletcher, Computational Techniques for Fluid Dynamics 2 (Springer, Berlin, 1991)Google Scholar
  20. 20.
    P.W. Partridge, C.A. Brebbia, L.C. Wrobel, The Dual Reciprocity Boundary Element Method (Computational Mechanics Publications, Sauthampton, 1992)Google Scholar
  21. 21.
    D.C. Lo, D.L. Young, C.C. Tsai, J. Comput. Appl. Math. 203(1), 219 (2007)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey

Personalised recommendations