Influence of cross-diffusion and radiation on mixed convection between rotating discs in the presence of a variable magnetic field

  • Aamir KhanEmail author
  • Rehan Ali Shah


In the present article, Navier-Stokes equations along with heat/mass transfers are taken into account for the squeezing flow of a viscous fluid between two rotating and parallel discs. The flow is also under the influence of an external applied magnetic field, \( M^{f}\), which will give rise to an induced magnetic field \( B(r, \theta, z)\) with components \( B_{r}\), \( B_{\theta}\) and \( B_{z}\) between the two discs. A similarity solution is obtained through the homotopy analysis method (HAM) with appropriate initial guesses and the auxiliary parameter to produce an algorithm with an accelerated and assured convergence. An investigation is made for the effects of the rotational motions of two discs, upward/downward motion of an upper disc, magnetic force on velocity components, the pressure and the torques that the fluid exerts on the discs. Tabulated and graphical results show that an increase in the rotational Reynolds number increases the pressure, torque and azimuthal/axial components of the induced magnetic field. HAM results are compared with numerical results obtained by BVP4c to assure the accuracy of HAM. A parametric study is tabulated and discussed with graphical results.


  1. 1.
    W.F. Hughes, R.A. Elco, J. Fluid Mech. 13, 21 (1962)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    R.J. Krieger, H.J. Day, W.S. Hughes, Lubr. TechnoL, Trans. ASME 89, 307 (1967)CrossRefGoogle Scholar
  3. 3.
    M. Rahimi-Gorji, O. Pourmehran, M. Gorji-Bandpy, D.D. Ganji, J. Taiwan Inst. Chem. Eng. 67, 467 (2016)CrossRefGoogle Scholar
  4. 4.
    N. Acharya, K. Das, P.K. Kundu, Alex. Eng. J. 55, 1177 (2016)CrossRefGoogle Scholar
  5. 5.
    M.H. Saidi, H. Tamim, Adv. Powder Technol. 27, 564 (2016)CrossRefGoogle Scholar
  6. 6.
    S.I. Khan, N. Ahmed, U. Khan, S.U. Jan, S.T. Mohyud-Din, J. Egypt. Math. Soc. 23, 445 (2015)CrossRefGoogle Scholar
  7. 7.
    S.S. Elshekh, M.K. Abdelhady, Int. J. Eng. Sci. 34, 1183 (1996)CrossRefGoogle Scholar
  8. 8.
    E.A. Hamza, J. Phys. D 24, 547 (1991)ADSCrossRefGoogle Scholar
  9. 9.
    L.G. Petrosyan, Magnetohydrodynamics 25, 119 (1989)Google Scholar
  10. 10.
    D.C. Kuzma, E.R. Mak, R.J. Donnelly, J. Fluid Mech. 19, 395 (1964)ADSCrossRefGoogle Scholar
  11. 11.
    J.D.G. Durán, G.R. Iglesias, A.V. Delgado, L.F. Ruiz-Morón, J. Insa, F. González-Caballero, Tribol. Trans. 51, 271 (2008)CrossRefGoogle Scholar
  12. 12.
    A.M. Siddiqui, S. Irum, A.R. Ansari, Math. Mod. Anal. 13, 565 (2008)CrossRefGoogle Scholar
  13. 13.
    M. Hatami, M. Sheikholeslami, D.D. Ganji, Powder Technol. 253, 769 (2014)CrossRefGoogle Scholar
  14. 14.
    M. Hatami, D.D. Ganji, J. Mol. Liq. 190, 159 (2014)CrossRefGoogle Scholar
  15. 15.
    A. Ting, T.Q. Hua, J.S. Walker, B.F. Picologlou, Int. J. Eng. Sci. 31, 357 (1993)CrossRefGoogle Scholar
  16. 16.
    M.M. Rashidi, B. Rostami, N. Freidoonimehr, S. Abbasbandy, Ain Shams Eng. J. 5, 901 (2014)CrossRefGoogle Scholar
  17. 17.
    A. Khan, R. Shah, M. Shuaib, Results Phys. 9, 923 (2018)ADSCrossRefGoogle Scholar
  18. 18.
    S.P. Anjali Devi, R. Uma Devi, Commun. Nonlinear Sci. Numer. Simul. 16, 1917 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    M. Turkyilmazoglu, Phys. Fluids 29, 013302 (2017)ADSCrossRefGoogle Scholar
  20. 20.
    M. Turkyilmazoglu, Phys. Fluids 30, 033601 (2018)ADSCrossRefGoogle Scholar
  21. 21.
    M. Turkyilmazoglu, Phys. Fluids 30, 063605 (2018)ADSCrossRefGoogle Scholar
  22. 22.
    S.J. Liao, Commun. Nonlinear Sci. Numer. Simul. 15, 2003 (2010)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    M. Turkyilmazoglu, Adv. Appl. Math. Mech. 10, 925 (2018)MathSciNetCrossRefGoogle Scholar
  24. 24.
    E.A. Hamza, D.A. McDonald, Quar. Appl. Math. 41, 495 (1984)CrossRefGoogle Scholar

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

Authors and Affiliations

  1. 1.Department of Basic Sciences and IslamiatUniversity of Engineering and Technology Peshawar, KPKPeshawarPakistan

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