Skip to main content
SpringerLink
Log in

Effect of homogeneous–heterogeneous reactions in stagnation point flow of third grade fluid past a variable thickness stretching sheet

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Present work addresses the stagnation point flow of third grade fluid past a variable thicked stretching sheet. Homogeneous and heterogeneous reactions are considered. Impact of thermal radiation and variable wall temperature is studied here. System of nonlinear ordinary differential equations is obtained by suitable transformations. Convergence of series solutions is achieved. Fluid flow, temperature and concentration field are deliberated through graphs for different parameters. It is seen that velocity and temperature fields increase for higher shape parameter. Increasing values of homogeneous parameter decline the concentration profile. Velocity profile enhances when wall thickness parameter and ratio of free stream velocity and stretching velocity are increased.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. Ramzan M, Bilal M, Chung JD (2016) Effects of MHD homogeneous–heterogeneous reactions on third grade fluid flow with Cattaneo–Christov heat flux. J Mol Liq 223:1284–1290

    Article  Google Scholar 

  2. Wang L, Jian Y, Liu Q, Li F, Chang L (2016) Electromagnetohydrodynamic flow and heat transfer of third grade fluids between two micro-parallel plates. Phys Eng Asp 494:87–94

    Article  Google Scholar 

  3. Hayat T, Khan MI, Waqas M, Alsaedi A, Yasmeen T (2016) Diffusion of chemically reactive species in third grade flow over an exponentially stretching sheet considering magnetic field effects. Chin J Chem Eng. doi:10.1016/j.cjche.2016.06.008

    Article  Google Scholar 

  4. Hussain T, Shehzad SA, Hayat T, Alsaedi A (2015) Hydromagnetic flow of third grade nanofluid with viscous dissipation and flux conditions. AIP Adv 5:087169

    Article  Google Scholar 

  5. Farooq U, Hayat T, Alsaedi A, Liao SJ (2014) Heat and mass transfer of two-layer flows of third-grade nano-fluids in a vertical channel. Appl Math Comput 242:528–540

    MathSciNet  MATH  Google Scholar 

  6. Li SX, Jian YJ, Xie ZY, Liu QS, Li FQ (2015) Rotating electro osmotic flow of third grade fluids between two microparallel plates. Physicochem Eng Asp 470:240–247

    Article  Google Scholar 

  7. Abbasbandy Hayat T (2011) On series solution for unsteady boundary layer equations in a special third grade fluid. Commun Nonlinear Sci Numer Simul 16:3140–3146

    Article  MathSciNet  Google Scholar 

  8. Keimanesh M, Rashidi MM, Chamkha AJ, Jafari R (2011) Study of a third grade non-Newtonian fluid flow between two parallel plates using the multi-step differential transform method. Comput Math Appl 62:2871–2891

    Article  MathSciNet  Google Scholar 

  9. Williams WR, Stenzel MT, Song X, Schmidt LD (1991) Bifurcation behavior in homogeneous–heterogeneous combustion: I experimental results over platinum. Combust Flame 84:277–291

    Article  Google Scholar 

  10. Song X, Williams WR, Schmidt LD, Aris R (1991) Bifurcation behavior in homogeneous–heterogeneous combustion. Combust Flame 84:292–311

    Article  Google Scholar 

  11. Williams WR, Zhao J, Schmidt LD (1991) Ignition and extinction of surface and homogeneous oxidation of NH3 and CH4. AlChE J 37:641–649

    Article  Google Scholar 

  12. Chaudhary MA, Merkin JH (1995) A simple isothermal model for homogeneousheterogeneous reactions in boundary-layer flow. Fluid Dyn Res 16:311–333

    Article  Google Scholar 

  13. Chaudhary MA, Merkin JH (1995) A simple isothermal model for homogeneousheterogeneous reactions in boundary-layer flow. Fluid Dyn Res 16:335–359

    Article  Google Scholar 

  14. Merkin JH (1996) A model for isothermal homogeneous–heterogeneous reactions in boundary layer flow. Math Comput Model 24:125–136

    Article  MathSciNet  Google Scholar 

  15. Hayat T, Farooq S, Ahmad B, Alsaedi A (2016) Homogeneous–heterogeneous reactions and heat source/sink effects in MHD peristaltic flow of micropolar fluid with Newtonian heating in a curved channel. J Mol Liq 223:469–488

    Article  Google Scholar 

  16. Khan WA, Pop I (2015) Effects of homogeneous–heterogeneous reactions on the viscoelastic fluid towards a stretching sheet. ASME J Heat Transf 134:064506

    Article  Google Scholar 

  17. Dogonchi AS, Ganji DD (2016) Thermal radiation effect on the nanofluid buoyancy flow and heat transfer over a stretching sheet considering Brownian motion. J Mol Liq 223:521–527

    Article  Google Scholar 

  18. Imtiaz M, Hayat T, Alsaedi A, Ahmad B (2016) Convective flow of carbon nanotubes between rotating stretchable disks with thermal radiation effects. Int J Heat Mass Transf 101:948–957

    Article  Google Scholar 

  19. Bhatti MM, Rashidi MM (2016) Effects of thermo-diffusion and thermal radiation on Williamson nanofluid over a porous shrinking/stretching sheet. J Mol Liq 221:567–573

    Article  Google Scholar 

  20. Sheikholeslami M, Hayat T, Alsaedi A (2016) MHD free convection of Al2O3 water nanofluid considering thermal radiation. Int J Heat Mass Transf 96:513–524

    Article  Google Scholar 

  21. Zeeshan A, Majeed A, Ellahi R (2016) Effect of magnetic dipole on viscous ferrofluid past a stretching surface with thermal radiation. J Mol Liq 215:549–554

    Article  Google Scholar 

  22. Crane LJ (1970) Flow past a stretching plate. J Appl Math Phys (ZAMP) 21:645–647

    Article  Google Scholar 

  23. Khan JA, Mustafa M, Hayat T, Alsaedi A (2015) Three-dimensional flow of nanofluid over a non-linearly stretching sheet. Int J Heat Mass Transf 86:158–164

    Article  Google Scholar 

  24. Hayat T, Asad S, Mustafa M, Alsaedi A (2015) MHD stagnation-point flow of Jeffrey fluid over a convectively heated stretching sheet. Comput Fluids 108:179–185

    Article  MathSciNet  Google Scholar 

  25. Li J, Zheng L, Liu L (2016) MHD viscoelastic flow and heat transfer over a vertical stretching sheet with Cattaneo–Christov heat flux effects. J Mol Liq 221:19–25

    Article  Google Scholar 

  26. Zhang Y, Zhang M, Bai Y (2016) Flow and heat transfer of an Oldroyd-B nanofluid thin film over an unsteady stretching sheet. J Mol Liq 220:665–670

    Article  Google Scholar 

  27. Mahmood A, Chen B, Ghaffari A (2016) Hydromagnetic Hiemenz flow of micropolar fluid over a nonlinearly stretching/shrinking sheet. J Magn Magn Mater 416:329–334

    Article  Google Scholar 

  28. Majeed A, Zeeshan A, Ellahi R (2016) Unsteady ferromagnetic liquid flow and heat transfer analysis over a stretching sheet with the effect of dipole and prescribed heat flux. J Mol Liq 223:528–533

    Article  Google Scholar 

  29. Nawaz M, Zeeshan A, Ellahi R, Abbasbandy Rashidi S (2015) Joule and Newtonian heating effects on stagnation point flow overa stretching sheet by means of genetic algorithm and Nelder–Mead method. Int J Numer Methods Heat Fluid Flow 25:665–684

    Article  Google Scholar 

  30. Maqbool K, Sohail A, Manzoor N, Ellahi R (2016) Hall effect on Falkner–Skan boundary layer flow of FENE-P fluid over a stretching sheet. Commun Theor Phys 66:547–554

    Article  MathSciNet  Google Scholar 

  31. Arqub OA, Ajou AEl (2013) Solution of the fractional epidemic model by homotopy analysis method. J King Saud Univ Sci 25(1):73–81

    Article  Google Scholar 

  32. Abbasbandy S, Yurusoy M, Gulluce H (2014) Analytical solutions of non-linear equations of power-law fluids of second grade over an infinite porous plate. Math Comput Appl 19(2):124

    MathSciNet  Google Scholar 

  33. 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 85:1023–1033

    Article  Google Scholar 

  34. Ellahi R, Hassan M, Zeeshan A (2015) Shape effects of nanosize particles in Cu–H2O nanofluid on entropy generation. Int J Heat Mass Transf 81:449–456

    Article  Google Scholar 

  35. 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 nanofluid. Comput Fluids 111:69–75

    Article  MathSciNet  Google Scholar 

  36. Hayat T, Qayyum S, Imtiaz M, Alsaedi A (2016) Impact of Cattaneo–Christov heat flux model on Jeffrey fluid flow with homogeneous–heterogeneous reaction. PLoS ONE 11:e0148662

    Article  Google Scholar 

  37. Shehzad SA, Hayat T, Alsaedi A, Chen B (2016) A useful model for solar radiation. Energy Ecol Environ 1:30–38

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan

    Tasawar Hayat, Asmara Kiran & Maria Imtiaz

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Tasawar Hayat & Ahmed Alsaedi

Authors
  1. Tasawar Hayat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Asmara Kiran
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maria Imtiaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ahmed Alsaedi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maria Imtiaz.

Ethics declarations

Conflict of interest

The authors confirm that this article content has no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hayat, T., Kiran, A., Imtiaz, M. et al. Effect of homogeneous–heterogeneous reactions in stagnation point flow of third grade fluid past a variable thickness stretching sheet. Neural Comput & Applic 30, 3071–3080 (2018). https://doi.org/10.1007/s00521-017-2913-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-017-2913-z

Keywords

Search

Navigation