Neural Computing and Applications

, Volume 31, Issue 4, pp 967–977 | Cite as

Magnetohydrodynamic three-dimensional nonlinear convective flow of viscoelastic nanofluid with heat and mass flux conditions

  • Tasawar Hayat
  • Sajid Qayyum
  • Sabir Ali ShehzadEmail author
  • Ahmed Alsaedi
Original Article


The present research focuses on three-dimensional nonlinear convective flow of viscoelastic nanofluid. Here, the flow is generated due to stretching of a impermeable surface. The phenomenon of heat transport is analyzed by considering thermal radiation and prescribed heat flux condition. Nanofluid model comprises of Brownian motion and thermophoresis. An electrically conducting fluid is accounted due to consideration of an applied magnetic field. The dimensionless variables are introduced for the conversion of partial differential equations into sets of ordinary differential systems. The transformed expressions are explored through homotopic algorithm. Behavior of different dimensionless parameters on the non-dimensional velocities, temperature and concentration are scrutinized graphically. The values of skin friction coefficients, Nusselt and Sherwood numbers are also calculated and elaborated. It is visualized that the heat transfer rate increases with Prandtl number and radiation parameter is higher.


Viscoelastic nanofluid Nonlinear convection Thermal radiation Flux conditions 


Compliance with ethical standards

Conflict of interest

All the authors declare that they have no conflict of interest.


  1. 1.
    Cortell R (2006) Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to suction and to a transverse magnetic field. Int J Heat Mass Transf 49:1851–8156CrossRefzbMATHGoogle Scholar
  2. 2.
    Hayat T, Shehzad SA, Qasim M, Obaidat S (2011) Flow of a second grade fluid with convective boundary conditions. Therm Sci 15:253–261CrossRefGoogle Scholar
  3. 3.
    Turkyilmazoglu M (2013) The analytical solution of mixed convection heat transfer and fluid flow of a MHD viscoelastic fluid over a permeable stretching surface. Int J Mech Sci 77:263–268CrossRefGoogle Scholar
  4. 4.
    Sahoo B, Labropulu F (2012) Steady Homann flow and heat transfer of an electrically conducting second grade fluid. Comput Math Appl 63:1244–1255MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Akinbobola TE, Okoya SS (2015) The flow of second grade fluid over a stretching sheet with variable thermal conductivity and viscosity in the presence of heat source/sink. J Nigerian Math Soc 34:331–342MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Hayat T, Shafiq A, Imtiaz M, Alsaedi A (2016) Impact of melting phenomenon in the Falkner-Skan wedge flow of second grade nanofluid: a revised model. J Mol Liq 215:664–670CrossRefGoogle Scholar
  7. 7.
    Ramzan M, Bilal M (2015) Time dependent MHD nano-second grade fluid flow induced by permeable vertical sheet with mixed convection and thermal radiation. PLoS ONE 10:e0124929CrossRefGoogle Scholar
  8. 8.
    Hayat T, Qasim M, Shehzad SA, Alsaedi A (2014) Unsteady stagnation point flow of second grade fluid with variable free stream. Alex Eng J 53:455–461CrossRefGoogle Scholar
  9. 9.
    Choudhury R, Das UJ (2012) Viscoelastic effects on free convective three-dimensional flow with heat and mass transfer. Comput Math 2012:402037zbMATHGoogle Scholar
  10. 10.
    Alhuthali MS, Shehzad SA, Malaikah H, Hayat T (2014) Three dimensional flow of viscoelastic fluid by an exponentially stretching surface with mass transfer. J Petrol Sci Eng 119:221–226CrossRefGoogle Scholar
  11. 11.
    Turkyilmazoglu M (2014) Three dimensional MHD flow and heat transfer over a stretching/shrinking surface in a viscoelastic fluid with various physical effects. Int J Heat Mass Transf 78:150–155CrossRefGoogle Scholar
  12. 12.
    Hayat T, Sajid M, Pop I (2008) Three-dimensional flow over a stretching surface in a viscoelastic fluid. Nonlinear Anal Real World Appl 9:1811–1822MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Gorla RSR, Gireesha BJ (2015) Convective heat transfer in three-dimensional boundary-layer flow of viscoelastic nanofluid. J Thermophys Heat Transf 30:334–341CrossRefGoogle Scholar
  14. 14.
    Krishnamurthy MR, Prasannakumara BC, Gireesha BJ, Gorla RSR (2016) Effect of chemical reaction on MHD boundary layer flow and melting heat transfer of Williamson nanofluid in porous medium. Eng Sci Tech Int J 19:53–61CrossRefGoogle Scholar
  15. 15.
    Sui J, Zheng L, Zhang X (2016) Boundary layer heat and mass transfer with Cattaneo-Christov double-diffusion in upper-convected Maxwell nanofluid past a stretching sheet with slip velocity. Int J Therm Sci 104:461–468CrossRefGoogle Scholar
  16. 16.
    Hayat T, Abbas T, Ayub M, Farooq M, Alsaedi A (2016) Flow of nanofluid due to convectively heated Riga plate with variable thickness. J Mol Liq 222:854–862CrossRefGoogle Scholar
  17. 17.
    Sheikholeslami M, Mustafa MT, Ganji DD (2016) Effect of Lorentz forces on forced-convection nanofluid flow over a stretched surface. Particuology 26:108–113CrossRefGoogle Scholar
  18. 18.
    Hayat T, Waqas M, Shehzad SA, Alsaedi A (2016) A model of solar radiation and Joule heating in magnetohydrodynamic (MHD) convective flow of thixotropic nanofluid. J Mol Liq 215:704–710CrossRefGoogle Scholar
  19. 19.
    Lin Y, Zheng L, Zhang X (2014) Radiation effects on Marangoni convection flow and heat transfer in pseudo-plastic non-Newtonian nanofluids with variable thermal conductivity. Int J Heat Mass Transf 77:708–716CrossRefGoogle Scholar
  20. 20.
    Turkyilmazoglu M (2012) Exact analytical solutions for heat and mass transfer of MHD slip flow in nanofluids. Chem Eng Sci 84:182–187CrossRefGoogle Scholar
  21. 21.
    Hayat T, Qayyum S, Alsaedi A, Shafiq A (2016) Inclined magnetic field and heat source/sink aspects in flow of nanofluid with nonlinear thermal radiation. Int J Heat Mass Transf 103:99–107CrossRefGoogle Scholar
  22. 22.
    Shehzad SA, Abdullah Z, Alsaedi A, Abbasi FM, Hayat T (2016) Thermally radiative three-dimensional flow of Jeffrey nanofluid with internal heat generation and magnetic field. J Magn Magn Mater 397:108–114CrossRefGoogle Scholar
  23. 23.
    Rashidi MM, Ali M, Freidoonimehr N, Rostami B, Hossain MA (2014) Mixed convective heat transfer for MHD viscoelastic fluid flow over a porous wedge with thermal radiation. Adv Mech Eng 2014:10Google Scholar
  24. 24.
    Hayat T, Shafiq A, Alsaedi A (2016) Hydromagnetic boundary layer flow of Williamson fluid in the presence of thermal radiation and Ohmic dissipation. Alex Eng J 55:2229–2240Google Scholar
  25. 25.
    Turkyilmazoglu M, Pop I (2013) Heat and mass transfer of unsteady natural convection flow of some nanofluids past a vertical infinite flat plate with radiation effect. Int J Heat Mass Transf 59:167–171CrossRefGoogle Scholar
  26. 26.
    Sheikholeslami M, Ganji DD, Javed MY, Ellahi R (2015) Effect of thermal radiation on MHD nanofluid flow and heat transfer by means of two phase model. J Magn Magn Mater 374:36–43CrossRefGoogle Scholar
  27. 27.
    Shehzad SA, Hayat T, Alsaedi A (2014) MHD three dimensional flow of viscoelastic fluid with thermal radiation and variable thermal conductivity. J Cent South Univ 21:3911–3917CrossRefzbMATHGoogle Scholar
  28. 28.
    Liao S (2012) Homotopy analysis method in nonlinear differential equations. Springer & Higher Education Press, BerlinCrossRefzbMATHGoogle Scholar
  29. 29.
    Turkyilmazoglu M (2012) Solution of Thomas–Fermi equation with a convergent approach. Commun Nonlinear Sci Numer Simulat 17:4097–4410MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Hayat T, Shafiq A, Alsaedi A (2016) Characteristics of magnetic field and melting heat transfer in stagnation point flow of Tangent-hyperbolic liquid. J Magn Magn Mater 405:97–106CrossRefGoogle Scholar
  31. 31.
    Sui J, Zheng L, Zhang X, Chen G (2015) Mixed convection heat transfer in power law fluids over a moving conveyor along an inclined plate. Int J Heat Mass Transf 85:1023–1033CrossRefGoogle Scholar
  32. 32.
    Shehzad SA, Hayat T, Abbasi FM, Javed T, Kutbi MA (2016) Three-dimensional Oldroyd-B fluid flow with Cattaneo-Christov heat flux model. Eur Phys J Plus 131:112CrossRefGoogle Scholar
  33. 33.
    Farooq U, Zhao YL, Hayat T, Alsaedi A, Liao SJ (2015) Application of the HAM-based mathematica package BVPh 2.0 on MHD Falkner-Skan flow of nanoflui. Comput Fluids 111:69–75MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Abbasi FM, Shehzad SA, Hayat T, Ahmad B (2016) Doubly stratified mixed convection flow of Maxwell nanofluid with heat generation/absorption. J Magn Magn Mater 404:159–165CrossRefGoogle Scholar
  35. 35.
    Hayat T, Qayyum S, Shehzad SA, Alsaedi A (2017) Simultaneous effects of heat generation/absorption and thermal radiation in magnetohydrodynamics (MHD) flow of Maxwell nanofluid towards a stretched surface. Results Phys 7:562–573CrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  • Tasawar Hayat
    • 1
    • 2
  • Sajid Qayyum
    • 1
  • Sabir Ali Shehzad
    • 3
    Email author
  • Ahmed Alsaedi
    • 2
  1. 1.Department of MathematicsQuaid-I-Azam UniversityIslamabadPakistan
  2. 2.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of MathematicsCOMSATS Institute of Information TechnologySahiwalPakistan

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