Advertisement

MHD free convection flow of a viscous fluid in a rotating system with damped thermal transport, Hall current and slip effects

  • Waqas Ali Azhar
  • Constantin Fetecau
  • Dumitru VieruEmail author
Regular Article
  • 40 Downloads

Abstract.

Unsteady hydromagnetic free convection flows of a rotating incompressible viscous fluid over an infinite moving plate with fractional thermal transport are studied in the presence of heat source, Hall current and slip velocity effects. The modern definition of the fractional integral Caputo-Fabrizio operator with non-singular kernel is used in the constitutive equation for the thermal flux and closed form solutions for the dimensionless temperature and velocity components are established by using the Laplace transform technique. For comparison, the solutions for the ordinary fluid as well as those corresponding to the no-slip condition on the boundary are also determined. The influence of fractional, magnetic, Hall and rotation parameters as well as that of heat generation/absorption coefficient on the fluid motion and the heat transfer is graphically underlined and discussed. It is found that the damping of the thermal transport has significant influence on the fluid temperature and motion. The Hall current mainly affects the secondary flow.

References

  1. 1.
    G.W. Sutton, A. Sherman, Engineering Magnetohydrodynamics (McGraw-Hill, New York, 1965)Google Scholar
  2. 2.
    L. Debnath, S.C. Ray, A.K. Chatlerjee, Z. Angew. Math. Mech. 59, 469 (1979)CrossRefGoogle Scholar
  3. 3.
    H.S. Takhar, B.K. Jha, Magnetohydrodyn. Plasma Res. J. 8, 61 (1998)Google Scholar
  4. 4.
    H.S. Takhar, A.J. Chamkha, G. Nath, Int. J. Eng. Sci. 40, 1511 (2002)CrossRefGoogle Scholar
  5. 5.
    S.K. Gosh, I. Pop, Int. J. Appl. Mech. Eng. 8, 43 (2003)Google Scholar
  6. 6.
    S.K. Gosh, I. Pop, Int. J. Appl. Mech. Eng. 9, 293 (2004)Google Scholar
  7. 7.
    R.K. Deka, Theor. Appl. Mech. 35, 333 (2008)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    T. Hayat, Maryam Shafique, A. Tanveer, A. Alsaedi, J. Magn. & Magn. Mater. 407, 51 (2016)ADSCrossRefGoogle Scholar
  9. 9.
    T. Linga Raju, V.V. Ramana Rao, Int. J. Eng. Sci. 31, 1073 (1993)CrossRefGoogle Scholar
  10. 10.
    P.C. Ram, A. Singh, H.S. Takhar, Magnetohydrodyn. Plasma Res. J. 5, 1 (1995)Google Scholar
  11. 11.
    S.K. Ghosh, O.A. Beg, M. Narahari, Meccanica 44, 741 (2009)MathSciNetCrossRefGoogle Scholar
  12. 12.
    J.K. Sundarnath, R. Muthucumarswamy, Int. J. Appl. Mech. Eng. 20, 171 (2015)CrossRefGoogle Scholar
  13. 13.
    G.S. Seth, S.M. Hussain, S. Sarkar, Bulg. Chem. Commun. 46, 704 (2014)Google Scholar
  14. 14.
    G.S. Seth, S. Sarkar, S.M. Hussain, Ain Shams Eng. J. 5, 489 (2014)CrossRefGoogle Scholar
  15. 15.
    G.S. Seth, B. Kumbhakar, S. Sarkar, Int. J. Eng. Sci. Technol. 7, 94 (2015)CrossRefGoogle Scholar
  16. 16.
    G.S. Seth, R. Tripathi, R. Sharma, Bulg. Chem. Commun. 48, 770 (2016)Google Scholar
  17. 17.
    Q. Hussain, T. Hayat, S. Asghar, F. Alsaedi, J. Mech. Med. Biol. 16, 1650047 (2016)CrossRefGoogle Scholar
  18. 18.
    I.J. Rao, K.R. Rajagopal, Acta Mech. 135, 113 (1999)MathSciNetCrossRefGoogle Scholar
  19. 19.
    A.R.A. Khaled, K. Vafai, Int. J. Non-Linear Mech. 39, 795 (2004)ADSCrossRefGoogle Scholar
  20. 20.
    O.D. Makinde, E. Osalusi, Rom. J. Phys. 51, 319 (2006)Google Scholar
  21. 21.
    M.M. Hamza, B.Y. Isah, H. Usman, Int. J. Comput. Appl. 33, 12 (2011)Google Scholar
  22. 22.
    C. Fetecau, D. Vieru, Corina Fetecau, S. Akhter, Z. Naturforsch. 68a, 659 (2013)ADSGoogle Scholar
  23. 23.
    C. Fetecau, D. Vieru, Corina Fetecau, I. Pop, Eur. Phys. J. Plus 130, 6 (2015)CrossRefGoogle Scholar
  24. 24.
    A. Sohail, Samiulhaq, D. Vieru, Eur. Phys. J. Plus 129, 28 (2014)CrossRefGoogle Scholar
  25. 25.
    S.U. Haq, I. Khan, F. Ali, A. Khan, T.N.A. Abdelhameed, Abstr.Appl. Anal. 2015, 327975 (2015)CrossRefGoogle Scholar
  26. 26.
    M.M. Hamza, Ain Shams Eng. J. (2016)  https://doi.org/10.1016/j.asej.2016.08.011
  27. 27.
    S. Mukhopadhyay, I.C. Mandal, Eng. Sci. Technol. Int. J. 18, 98 (2015)CrossRefGoogle Scholar
  28. 28.
    R.L. Bagley, P.J. Torvik, J. Rheol 27, 201 (1983)ADSCrossRefGoogle Scholar
  29. 29.
    M. Caputo, F. Mainardi, Pure Appl. Geophys. 91, 134 (1971)ADSCrossRefGoogle Scholar
  30. 30.
    M. Caputo F. Mainardi, Riv. Nuovo Cimento 1, 161 (1971)CrossRefGoogle Scholar
  31. 31.
    N. Makris, G.F. Dargush, M.C. Constantinou, Dynamic analysis of generalized viscoelastic systems with the boundary element method, in Advances in Computational Mechanics, edited by M. Papadrakakis, B.H.V. Topping (Civil-Comp Press, Edinburgh, UK, 1994) pp. 283--290Google Scholar
  32. 32.
    S.S. Sheoran, P. Kundu, Int. J. Adv. Appl. Math. Mech. 3, 76 (2016)MathSciNetGoogle Scholar
  33. 33.
    K.R. Cramer, S.I. Pai, Magnetofluid Dynamics for Engineers and Applied Physicists (McGraw Hill, NewYork, 1973)Google Scholar
  34. 34.
    J. Hristov, in Frontiers in Fractional Calculus, 1st edition, edited by Sachin Bhalekar (Bentham Science Publishers 2017) chap. 10, pp. 235--295Google Scholar
  35. 35.
    M. Caputo, M. Fabrizio, Prog. Fract. Differ. Appl. 2, 1 (2016)CrossRefGoogle Scholar
  36. 36.
    M. Caputo, Prog. Fract. Differ. Appl. 2, 77 (2016)CrossRefGoogle Scholar
  37. 37.
    J. Losada, J.J. Nieto, Prog. Fract. Differ. Appl. 1, 87 (2015)Google Scholar
  38. 38.
    C.J. Toki, J.N. Tokis, Z. Angew. Math. Mech. 87, 4 (2007)CrossRefGoogle Scholar
  39. 39.
    M. Narahari, L. Debnath, Z. Angew. Math. Mech. 93, 38 (2013)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Waqas Ali Azhar
    • 1
  • Constantin Fetecau
    • 2
  • Dumitru Vieru
    • 3
    Email author
  1. 1.Abdus Salam School of Mathematical ScienceGC UniversityLahorePakistan
  2. 2.Academy of Romanian ScientistsBucharestRomania
  3. 3.Department of Theoretical MechanicsTechnical University of IasiIasiRomania

Personalised recommendations