Study of polymeric liquid between stretching disks with chemical reaction

  • N. Khan
  • M. S. Hashmi
  • Sami Ullah Khan
  • Waqar Adil Syed
Technical Paper


An analysis has been carried out to investigate the heat and mass transfer effects in steady axi-symmetric flow of a polymeric liquid (Maxwell fluid) between two infinite stretching disks in the presence of chemical reaction. Particular attention is to compute similarity solution of the governing nonlinear partial differential equations. The series solution of transformed nonlinear ordinary differential equations are computed via homotopy analysis method. The convergence of the developed series solution is also discussed. The quantities of interest like fluid velocity, fluid pressure, temperature, concentration, skin friction coefficient, local Nusselt and local Sherwood numbers are analyzed for the influence of embedded parameters. It is observed that the skin friction coefficient is an increasing function of Deborah number and Reynolds number. It is also observed that effects of stretching parameter on skin friction coefficient at upper and lower disks are opposite. Moreover, the heat transfer rate at lower disk is increases by increasing Deborah number. It is also observed that the surface mass transfer at both disks decreases by increasing Schmidt number.


Maxwell fluid Stretching disks Chemical reaction Homotopy analysis method 



We are thankful to the anonymous reviewer for his/her useful comments to improve the earlier version of the paper.


  1. 1.
    Hayat T, Awais M, Qasim M, Hendi Awatif A (2011) Effects of mass transfer on the stagnation point flow of an upper-convected Maxwell (UCM) fluid. Int J Heat Mass Transf 54:3777–3782CrossRefMATHGoogle Scholar
  2. 2.
    Makinde OD, Chinyoka T, Rundora L (2011) Unsteady flow of a reactive variable viscosity non-Newtonian fluid through a porous saturated medium with asymmetric convective boundary conditions. Comput Math Appl 62:3343–3352MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Hayat T, Sajid M (2007) Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet. Int J Heat Mass Transf 50:75–84CrossRefMATHGoogle Scholar
  4. 4.
    Zhenga L, Li C, Zhang X, Gaoc Y (2011) Exact solutions for the unsteady rotating flows of a generalized Maxwell fluid with oscillating pressure gradient between coaxial cylinders. Comput Math Appl 62:1105–1115MathSciNetCrossRefGoogle Scholar
  5. 5.
    Ali N, Khan SU, Abbas Z (2015) Hydromagnetic flow and heat transfer of a Jeffrey fluid over an oscillatory stretching surface. Zeitschrift für Naturforschung A 70(7):567–576CrossRefGoogle Scholar
  6. 6.
    Ali N, Khan SU, Abbas Z, Sajid M (2016) Soret and Dufour effects on hydromagnetic flow of viscoelastic fluid over porous oscillatory stretching sheet with thermal radiation. J Braz Soc Mech Sci Eng 38:2533–2546CrossRefGoogle Scholar
  7. 7.
    Nadeem S, Asghar S, Hayat T, Hussain M (2008) The Rayleigh Stokes problem for rectangular pipe in Maxwell and second grade fluid. Meccanica 43:495–504MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Hashmi MS, Khan N, Mahmood T, Shehzad SA (2017) Effect of magnetic field on mixed convection flow of Oldroyd-B nanofluid induced by two infinite isothermal stretching disks. Int J Therm Sci 111:463–474CrossRefGoogle Scholar
  9. 9.
    Khan N, Mahmood T (2016) Thermophoresis particle deposition and internal heat generation on MHD flow of an Oldroyd-B nanofluid between radiative stretching disks. J Mol Liq 216:571–582CrossRefGoogle Scholar
  10. 10.
    Khan N, Sajid M, Mahmood T, Hashmi MS (2016) Heat and mass transfer on MHD mixed convection axisymmetric chemically reactive flow of Maxwell fluid driven by exothermal and isothermal stretching disks. Int J Heat Mass Transf 92:1090–1105CrossRefGoogle Scholar
  11. 11.
    Khan N, Sajid M, Mahmood T (2015) Flow of a hydromagnetic viscous fluid between parallel stretching disks with slip. J Mech 31(6):713–726CrossRefGoogle Scholar
  12. 12.
    Khan N, Sajid M, Mahmood T (2015) Heat transfer analysis for magnetohydrodynamics axisymmetric flow between stretching disks in the presence of viscous dissipation and Joule heating. AIP Adv 5:057115CrossRefGoogle Scholar
  13. 13.
    Hayat T, Sajjad R, Abbas Z, Sajid M, Hendi AA (2011) Radiation effects on MHD flow of Maxwell fluid in a channel with porous medium. Int J Heat Mass Transf 54:854–862CrossRefMATHGoogle Scholar
  14. 14.
    Awais M, Hayat T, Alsaedi A, Asghar S (2014) Time-dependent three-dimensional boundary layer flow of a Maxwell fluid. Comput Fluids 91:21–27MathSciNetCrossRefGoogle Scholar
  15. 15.
    Nadeem S, Ijaz S (2016) Impulsion of nanoparticles as a drug carrier for the theoretical investigation of stenosed arteries with induced magnetic effects. J Magn Magn Mater 410:230–241CrossRefGoogle Scholar
  16. 16.
    Changdar S, De S (2017) Analytical solution of mathematical model of MHD blood nanofluid flowing through an inclined multiple stenosed artery. J Nanofluids 6(6):1198–1205. CrossRefGoogle Scholar
  17. 17.
    Changdar S, De S (2017) Transport of spherical nanoparticles suspended in a blood flowing through stenose artery under the influence of Brownian motion. J Nanofluids 6(1):87–96CrossRefGoogle Scholar
  18. 18.
    Changdar S, De S (2016) Analysis of nonlinear pulsatile blood flow in artery through a generalized multiple stenosis. Arab J Math 5(1):51–61MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    S Changdar, S De (2015) Numerical simulation of nonlinear pulsatile Newtonian blood flow through a multiple stenosed artery. In: International scholarly research notices, Hindawi Publishing Corporation, Article ID 628605, p 10.
  20. 20.
    Von Karman T (1921) Uber, laminar and turbulente Reibung. Zeitschrift fur Angewandte Mathematic and Mechanic (ZAMM) 1(14):233–255CrossRefMATHGoogle Scholar
  21. 21.
    Cochran WG (1934) The flow due to a rotating disk. Math Proc Camb Philos Soc 30(3):365–375CrossRefMATHGoogle Scholar
  22. 22.
    Benton ER (1966) On the flow due to a rotating disk. J Fluid Mech 24(781–800):133–137MATHGoogle Scholar
  23. 23.
    Hayat T, Shafiq A, Nawaz M, Alsaedi A (2012) MHD axisymmetric flow of third grade fluid between porous disks with heat transfer. Appl Math Mech (English Edition) 33(6):749–764MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Khan N, Sajid M, Mahmood T (2015) Heat transfer analysis for magnetohydrodynamics axisymmetric flow between stretching disks in the presence of viscous dissipation and Joule heating. AIP Adv 5:057115CrossRefGoogle Scholar
  25. 25.
    Kendoush AA (1998) Theory of stagnation region heat and mass transfer to fluid jets impinging normally on solid surfaces. Chem Eng Process 37:223–228CrossRefGoogle Scholar
  26. 26.
    Cortell R (2007) Towards an understanding of the motion and mass transfer with chemically reactive species for two classes of viscoelastic fluid over a porous stretching sheet. Chem Eng Process Process Intensif 46:982–989CrossRefGoogle Scholar
  27. 27.
    Andersson HI, Hansen OR, Holmedal B (1994) Diffusion of a chemically reactive species from a stretching sheet. Int J Heat Mass Transf 37:659–664CrossRefMATHGoogle Scholar
  28. 28.
    Takhar HS, Chamkha AJ, Nath G (2000) Flow and mass transfer on a stretching sheet with magnetic field and chemical reactive species. Int J Eng Sci 38:1303–1314CrossRefMATHGoogle Scholar
  29. 29.
    Akyilidiz FT, Bellout H, Vajravelu K (2006) Diffusion of chemical reactive species in porous medium over a stretching sheet. J Math Anal Appl 320:322–339MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Layek GC, Mukhopadhyay S, Samad SA (2007) Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing. Int Commun Heat Mass Transf 34:347–356CrossRefGoogle Scholar
  31. 31.
    Hayat T, Awais M (2011) Simultaneous effects of heat and mass transfer on time dependent flow over a stretching surface. Int J Numer Methods Fluids. MathSciNetMATHGoogle Scholar
  32. 32.
    Ravindran R, Ganapathirao M, Pop I (2014) Effects of chemical reaction and heat generation/absorption on unsteady mixed convection MHD flow over a vertical cone with non-uniform slot mass transfer. Int J Heat Mass Transf 73:743–751CrossRefGoogle Scholar
  33. 33.
    Sajid M, Hayat T (2009) The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet. Chaos Solitons Fractals 39:1317–1323CrossRefMATHGoogle Scholar
  34. 34.
    Liao SJ (2003) Beyond perturbation: introduction to the homotopy analysis method. Chapman and Hall, Boca RatonCrossRefGoogle Scholar
  35. 35.
    Liao SJ (2003) On the analytic solution of magneto hydrodynamic flow of non-Newtonian fluids over a stretching sheet. J Fluid Mech 488:189–212MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Liao SJ (2010) An optimal homotopy analysis approach for strongly nonlinear differential equations. Commun Nonlinear Sci Numer Simul 15(8):2003–2016MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Harris J (1977) Rheology and non-Newtonian flow. Longman, New YorkMATHGoogle Scholar
  38. 38.
    Gorder RAV, Sweet E, Vajravelu K (2010) Analytical solutions of a coupled nonlinear system arising in a flow between stretching disks. Appl Math Comput 216:1513–1523MathSciNetMATHGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • N. Khan
    • 1
  • M. S. Hashmi
    • 2
  • Sami Ullah Khan
    • 3
  • Waqar Adil Syed
    • 4
  1. 1.Department of MathematicsThe Islamia University of BahawalpurBahawalpurPakistan
  2. 2.Department of MathematicsThe Govt. Sadiq College Women UniversityBahawalpurPakistan
  3. 3.Department of MathematicsCOMSATS Institute of Information TechnologySahiwalPakistan
  4. 4.Department of PhysicsInternational Islamic UniversityIslamabadPakistan

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