Applied Physics A

, 126:105 | Cite as

Magnetohydrodynamic thin film deposition of Carreau nanofluid over an unsteady stretching surface

  • Kaleem Iqbal
  • Jawad AhmedEmail author
  • Masood Khan
  • Latif Ahmad
  • Mehtib Alghamdi


Thin films are commonly used to improve the surface features of solids. Permeation, corrosion, hardness, reflection, transmission, absorption and electrical behavior are certain properties of a bulk material surface that can be made effective by use of a thin film. Thin film technology can also play a vital role in nanotechnology. In this study, an analysis is performed about the Carreau thin film flow over an electrically conducting elastic stretching sheet. The effects of Brownian motion and thermophoresis parameters are utilized to describe the characteristics of heat and mass transfer phenomena. The time-dependent thin film flow is modeled over a moving surface in the form of nonlinear PDEs and then converted into nonlinear ODEs using suitable transformations. The computational outcomes are captured with the help of numerical method and displayed in graphical form. Effects of various flow parameters like the magnetic, Brownian and thermophoresis parameters are tested and found to be very remarkable during the flow analysis. Moreover, a declining conduct is noted with the impact of magnetic and Brownian motion parameters on the velocity, temperature and concentration fields. On the other hand, the influence of the thermophoresis parameter on the temperature of the fluid is found to be in increasing order. Furthermore, the boundary layer thickness is varying during the flow and all the numerical values of film thickness obtained are in good agreement with the existing literature.



The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Saudi Arabia for funding this work through Research Groups Program under grant number (R.G.P2. /26/40).


  1. 1.
    C. Wang, Analytic solution for a liquid film on unsteady stretching surface. Heat Mass Transf. 42, 505–528 (2006)Google Scholar
  2. 2.
    B.C. Sakiadis, Boundary layer behaviour on continuous solid surface: I - Boundary layer equations for two dimensional and axisymmetric flow. J. AICHE 7, 26–28 (1961)CrossRefGoogle Scholar
  3. 3.
    L.J. Crane, Flow past a stretching plate. Math Phys. 21, 645–647 (1970)Google Scholar
  4. 4.
    H.I. Andersson, J.B. Aarseth, N. Braud, B.S. Dandapat, Flow of a power-law fluid film on unsteady stretching surface. J. Non-Newton Fluid Mech. 62, 1–8 (1996)CrossRefGoogle Scholar
  5. 5.
    K. Vajravelu, K.V. Prasad, Ng Chiu, On Unsteady flow and heat transfer in a thin film of Ostwald-de Waele liquid over a stretching surface. Common. Nonlinear Sci. Numer. Simulat. 17, 4163–4173 (2012)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    A.J. Roberts, The inertial dynamics of thin film flow of non-Newtonian fluids. Phys. Lett. A 332, 1607–1611 (2008)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    C.H. Chen, Marangoni effects on forced convection of power-law liquids in a thin film over a stretching surface. Phy. Lett. A 370, 51–57 (2007)ADSCrossRefGoogle Scholar
  8. 8.
    A.M. Siddiqui, M. Ahmed, Q.K. Ghori, Thin film flow of non-Newtonian fluids on a moving belt. Chaos Solitons Fract. 33, 1006–1016 (2007)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    M. Sajid, T. Hayat, Thin film flow of an Oldroyd 8-constant fluid: an exact solution. Phys. Lett. A 332, 1827–1830 (2008)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    N.S. Khan, S. Islam, T. Gul, I. Khan, W. Khan and L. Ali, Thin film flow of a second grade in a porous medium past a stretching sheet with heat transfer. Alex. Eng. J. CrossRefGoogle Scholar
  11. 11.
    J. Li, L. Liu, L. Zheng, B.B. Mohsin, Unsteady MHD flow and radiation heat transfer of nanofluid in a finite thin film with heat generation and thermophoresis. J. Taiwan Inst. Chem. Eng. 67, 226–234 (2016)CrossRefGoogle Scholar
  12. 12.
    M. Martin, T. Defraeyea, D. Derome, J. Carmeliet, A film flow model for analysing gravity-driven, thin wavy fluid films. Int. J. Multiph. Flow 73, 207–216 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    B.S. Dandapat, S.K. Singh, S. Maity, Thin film flow of bi-viscosity liquid over an unsteady stretching sheet: an analytical solution. Int. J. Mech. Sci. 130, 367–374 (2017)CrossRefGoogle Scholar
  14. 14.
    P.J. Carreau, Rheological equations from molecular network theories. Trans. Soc. Rheol. 116, 99–127 (1972)CrossRefGoogle Scholar
  15. 15.
    T. Hayat, R. Ellahi, F.M. Mahomed, Exact solutions for thin film flow of a third grade fluid down an inclined plane. Chaos Solitons Fract. 38, 1336–1341 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    C.Y. Wang, Liquid film on an unsteady stretching surface. Q. Appl. Math. 48, 601–610 (1990)MathSciNetCrossRefGoogle Scholar
  17. 17.
    C. Wang, I. Pop, Analysis of the flow of a power-law fluid film on an unsteady stretching surface by means of homotopy analysis method. J. Non-Newton. Fluid Mech. 138, 161–172 (2006)CrossRefGoogle Scholar
  18. 18.
    U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles. ASME Int. Mech. Eng. 66, 99–105 (1995)Google Scholar
  19. 19.
    T. Hayat, M. Imtiaz, A. Alsaedi, R. Mansoor, MHD flow of nanofluids over an exponentially stretching sheet in a porous medium with convective boundary conditions. Chin. Phys. B 23, 1–8 (2014)Google Scholar
  20. 20.
    N. Sandeep, A. Malvandi, Enhanced heat transfer in liquid thin film flow of non-Newtonian nanofluids embedded with graphene nanoparticles. Adv. Powd. Tech. 27, 2448–2456 (2016)CrossRefGoogle Scholar
  21. 21.
    M.S. Abel, J. Tawade, M.M. Nandeppanavar, Effect of non-uniform heat source on MHD heat transfer in a liquid film over an unsteady stretching sheet. Int. J. Nonlinear Mech. 44, 990–998 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    N.S. Akbar, S. Nadeem, Carreau fluid model for blood flow through a tapered artery with a stenosis. Ain Shams Eng. J. 5, 1307–1316 (2014)CrossRefGoogle Scholar
  23. 23.
    M. Khan, M. Azam, Unsteady heat and mass transfer mechanisms in MHD Carreau nanofluid flow. J. Mol. Liq. 225, 554–562 (2017)CrossRefGoogle Scholar
  24. 24.
    M. Khan, Hashim, Axisymmetric flow and heat transfer of the Carreau fluid due to a radially stretching sheet: numerical study. J. Appl. Mech. Tech. Phys 58, 410–418 (2017)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  • Kaleem Iqbal
    • 1
  • Jawad Ahmed
    • 1
    • 2
    Email author
  • Masood Khan
    • 1
  • Latif Ahmad
    • 1
    • 3
  • Mehtib Alghamdi
    • 4
  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan
  2. 2.Department of Basic SciencesUniversity of Engineering and TechnologyTaxilaPakistan
  3. 3.Department of MathematicsShaheed Benazir Bhutto UniversitySheringal Upper DirPakistan
  4. 4.Department of Mathematics, Faculty of ScienceKing Khalid UniversityAbhaSaudi Arabia

Personalised recommendations