Advertisement

Magnetohydrodynamic instability of mixed convection in a differentially heated vertical channel

  • B. M. ShankarEmail author
  • Jai Kumar
  • I. S. Shivakumara
Regular Article
First Online:
  • 17 Downloads

Abstract.

The present paper investigates the instability of mixed convection in a differentially heated vertical layer of an electrically conducting fluid under the influence of a uniform horizontal magnetic field. The key parameters which influence the instability characteristics of the system are the Hartman number, the Reynolds number, the Grashof number and the Prandtl number. The computational results reveal that two-dimensional disturbances are more unstable than the three-dimensional disturbances. Further, influence of the Grashof number and the Hartmann number is analyzed on the basic flow. The effect of increasing the Hartman number shows stabilizing effect on the fluid flow and dissimilar is the case with an increase in the Reynolds number and the Prandtl number. In the presence of Reynolds number, Re, stationary instability disappears altogether which is contrary to the results observed in the case of pure natural convection (\( Re\rightarrow 0\)). The numerical results obtained under the limiting cases are shown to be in excellent agreement with the existing ones.

This is a preview of subscription content, log in to check access.

References

  1. 1.
    Y.C. Chen, J.N. Chung, J. Fluid Mech. 325, 29 (1996)ADSCrossRefGoogle Scholar
  2. 2.
    Y.C. Chen, J.N. Chung, C.S. Wu, Y.F. Lue, Int. J. Heat Mass Transfer 43, 2421 (2000)CrossRefGoogle Scholar
  3. 3.
    Y.C. Chen, Int. J. Heat Mass Transfer 47, 1257 (2004)CrossRefGoogle Scholar
  4. 4.
    Jai Kumar, P. Bera, A. Khalili, Int. J. Heat Mass Transfer 53, 5261 (2010)CrossRefGoogle Scholar
  5. 5.
    C.D. Dritselis, A.J. Iatridis, I.E. Sarris, N.S. Vlachos, Int. J. Therm. Sci. 65, 28 (2013)CrossRefGoogle Scholar
  6. 6.
    Y.C. Chen, J.N. Chung, ASME J. Heat Transf. 120, 127 (1998)CrossRefGoogle Scholar
  7. 7.
    R.C. Lock, Proc. R. Soc. A 233, 105 (1955)ADSGoogle Scholar
  8. 8.
    M.C. Potter, J.A. Kutchey, Phys. Fluids 16, 1848 (1973)ADSCrossRefGoogle Scholar
  9. 9.
    M. Takashima, Fluid Dyn. Res. 17, 293 (1996)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    O.D. Makinde, Math. Comp. Model. 37, 251 (2003)MathSciNetCrossRefGoogle Scholar
  11. 11.
    O.D. Makinde, P.Y. Mhone, Comp. Math. Appl. 53, 128 (2007)CrossRefGoogle Scholar
  12. 12.
    A. Proskurin, A. Sagalakov, J. Appl. Mech. Tech. Phys. 49, 383 (2008)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    O.D. Makinde, P.Y. Mhone, Flow Turb. Combust. 83, 21 (2009)CrossRefGoogle Scholar
  14. 14.
    J. Hagan, J. Priede, J. Fluid Mech. 760, 387 (2014)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    B.M. Shankar, I.S. Shivakumara, Appl. Math. Comput. 321, 752 (2018)MathSciNetGoogle Scholar
  16. 16.
    O. Zikanov, A. Thess, J. Fluid Mech. 358, 299 (1998)ADSCrossRefGoogle Scholar
  17. 17.
    M. Takashima, Fluid Dyn. Res. 14, 121 (1994)ADSCrossRefGoogle Scholar
  18. 18.
    B.M. Shankar, Jai Kumar, I.S. Shivakumara, J. Magn. & Magn. Mater. 421, 152 (2017)ADSCrossRefGoogle Scholar
  19. 19.
    M. Nagata, Eur. J. Mech.-B/Fluids 17, 33 (1998)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    O.D. Makinde, A. Aziz, Int. J. Therm. Sci. 49, 1813 (2010)CrossRefGoogle Scholar
  21. 21.
    S. Satake, K. Sone, K. Furumi, T. Kunugi, Fusion Eng. Design 87, 798 (2012)CrossRefGoogle Scholar
  22. 22.
    J.H. Son, I.S. Park, Numer. Heat Transf. Part A 71, 1004 (2017)ADSCrossRefGoogle Scholar
  23. 23.
    M. Sankar, M. Venkatachalappa, I.S. Shivakumara, Int. J. Eng. Sci. 44, 1556 (2006)CrossRefGoogle Scholar
  24. 24.
    D.S. Krasnov, E. Zienicke, O. Zinkanov, T. Boeck, A. Thess, J. Fluid Mech. 504, 183 (2004)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    B.M. Shankar, Jai Kumar, I.S. Shivakumara, Appl. Math. Model. 40, 5462 (2016)MathSciNetCrossRefGoogle Scholar
  26. 26.
    B.M. Shankar, I.S. Shivakumara, Transp. Porous Med. 124, 395 (2018)CrossRefGoogle Scholar
  27. 27.
    B.A. Singer, J.H. Ferziger, H.L. Read, J. Fluid Mech. 208, 45 (1989)ADSCrossRefGoogle Scholar
  28. 28.
    B.M. Shankar, Jai Kumar, I.S. Shivakumara, Int. J. Heat Mass Transfer 78, 447 (2014)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsPES UniversityBangaloreIndia
  2. 2.Space Applications CentreISROAhmedabadIndia
  3. 3.Department of MathematicsBangalore UniversityBangaloreIndia

Personalised recommendations

Cite article

Buy options