Skip to main content
Log in

Cross-diffusion and heat source effects on a three-dimensional MHD flow of Maxwell nanofluid over a stretching surface with chemical reaction

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

This paper investigates the three-dimensional magnetohydrodynamic (MHD) flow of an upper convected Maxwell (UCM) nanofluid with the thermal radiation, cross-diffusion and heat source effects along a stretching sheet. The effects of chemical reaction, thermophoresis and Brownian motion are also studied. We have applied suitable similarity variables and transformed the governing boundary layer equations into a system of non-linear ordinary differential equations. The present problem is solved numerically by R–K-based shooting technique. The variations of the velocity, temperature and concentration profiles are shown graphically and discussed in detail. The numerical results of skin friction coefficient, Nusselt and Sherwood numbers are presented in tabular form for different physical parameters. It is noticed that the Dufour and thermal radiation parameters decrease the temperature field and raise the concentration field. The rising values of Deborah number and magnetic field reduce the friction factors, Nusselt and Sherwood numbers. Heat source and chemical reaction parameters decline the Nusselt number and boost the Sherwood number. Also, noticed that the Dufour and Soret numbers enhance the Nusselt number but they decrease the Sherwood number.

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

Access this article

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

Similar content being viewed by others

References

  1. T. Hayat, R. Sajjad, Z. Abbas, M. Sajid, Awatif A. Hendi, Radiation effects on MHD flow of Maxwell fluid in a channel with porous medium. Int. J. Heat Mass Transf. 54, 854–862 (2011)

    Article  Google Scholar 

  2. T. Hayat, Z. Iqbal, M. Mustafa, A. Alsaedi, Momentum and heat transfer of an upper-convected Maxwell fluid over a moving surface with convective boundary conditions. Nucl. Eng. Des. 252, 242–247 (2012)

    Article  Google Scholar 

  3. M.Y. Malik, A. Hussain, S. Nadeem, Flow of a non-Newtonian nano fluid between coaxial cylinders with variable viscosity. Zeitschrift für Naturforschung A 67(5), 255–261 (2012)

    Article  ADS  Google Scholar 

  4. R. Ellahi, Effects of the slip boundary condition on non- Newtonian flows in a channel. Commun. Nonlinear Sci. Numer. Simul. 14(4), 1377–1384 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  5. G. Sucharitha, M.M. Rashidi, S. Sreenadh, P. Lakshminarayana, Effects of magnetic field and slip on convective peristaltic flow of a non-Newtonian fluid in an inclined non-uniform porous channel with flexible walls. J. Porous Media 21(10), 895–910 (2018)

    Article  Google Scholar 

  6. J.V. Ramana Reddy, K. Anantha Kumar, V. Sugunamma, N. Sandeep, Effect of cross diffusion on MHD non-Newtonian fluids flow past a stretching sheet with non-uniform heat source/sink: A comparative study. Alex. Eng. J. 57, 1829–1838 (2018)

    Article  Google Scholar 

  7. T. Hayat, Z. Abbas, N. Ali, MHD flow and mass transfer of a upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species. Phys. Lett. A 372, 4698–4704 (2008)

    Article  ADS  Google Scholar 

  8. G. Sucharitha, K. Vajravelu, P. Lakshminarayana, Effect of heat and mass transfer on the peristaltic flow of a Jeffrey nanofluid in a tapered flexible channel in the presence of aligned magnetic field. Eur. Phys. J. Spec. Top. 228, 2713–2728 (2019)

    Article  Google Scholar 

  9. G.K. Ramesh, B.J. Gireesha, T. Hayat, A. Alsaedi, Stagnation point flow of Maxwell fluid towards a permeable surface in the presence of nanoparticles. Alex. Eng. J. 55, 857–865 (2016)

    Article  Google Scholar 

  10. T. Hayat, T. Muhammad, S.A. Shehzad, G.Q. Chen, A. Abbas Ibrahim, Interaction of magnetic field in flow of Maxwell nanofluid with convective effect. J. Magn. Magn. Mater. (2015). https://doi.org/10.1016/j.jmmm.2015.04.019

    Article  Google Scholar 

  11. R. Meenakumari, P. Lakshminarayana, K. Vajravelu, Influence of induced magnetic field and slip conditions on convective Prandtl fluid flow over a stretching surface with homogeneous and heterogeneous reactions. Multidiscip. Model. Mater. Struct. (2020). https://doi.org/10.1108/MMMS-02-2020-0040

    Article  Google Scholar 

  12. Noreen Sher Akbar, S. Nadeem, Rizwan Ul Haq, Z.H. Khan, Radiation effects on MHD stagnation point flow of nano fluid towards a stretching surface with convective boundary condition. Chin. J. Aeronaut. 26(6), 1389–1397 (2013)

    Article  Google Scholar 

  13. Macha Madhu, Naikoti Kishan, Ali J. Chamkha, Unsteady flow of a Maxwell nanofluid over a stretching surface in the presence of magnetohydrodynamic and thermal radiation effects. Propuls. Power Res. 6(1), 31–40 (2017)

    Article  Google Scholar 

  14. M. Sathish Kumar, N. Sandeep, Kumar B. Rushi, Three-dimensional magnetohydrodynamic rotating flow past a stretched surface with cross diffusion. Chin. J. Phys. (2017). https://doi.org/10.1016/j.cjph.2017.09.014

    Article  MathSciNet  Google Scholar 

  15. R. Meenakumari, P. Lakshminarayana, Radiation and Hall effects on a 3D flow of MHD Williamson fluid over a stretchable surface. Heat Transf. (2020). https://doi.org/10.1002/htj.21833

    Article  Google Scholar 

  16. G.K. Ramesh, B.C. Prasannakumara, B.J. Gireesha, S.A. Shehzad, F.M. Abbasi, Three dimensional flow of Maxwell fluid with suspended nanoparticles past a bidirectional porous stretching surface with thermal radiation. Therm. Sci. Eng. Prog. (2017). https://doi.org/10.1016/j.tsep.2017.02.006

    Article  Google Scholar 

  17. A.A. Afify, Similarity solution in MHD: effects of thermal diffusion and diffusion thermo on free convective heat and mass transfer over a stretching surface considering suction or injection. Commun. Non-linear Sci. Numer. Simul. 14, 2202–2214 (2009)

  18. M. Krishna Murthy, S. Sreenadh, P. Lakshminarayana, G. Sucharitha, Kumar B. Rushi, Thermophoresis and brownian motion effects on three dimensional magnetohydrodynamics slip flow of a Casson nanofluid over an exponentially stretching surface. J. Nanofluids 8(6), 1267–1272 (2019)

    Article  Google Scholar 

  19. M. Bilal, M. Sagheer, S. Hussain, Three dimensional MHD upper-convected Maxwell nanofluid flow with nonlinear radiative heat flux. Alex. Eng. J. 57, 1917–1925 (2018)

    Article  Google Scholar 

  20. S. Nadeem, S. Akhtar, A. Nadeem, Heat transfer of Maxwell base fluid flow of nanomaterial with MHD over a vertical moving surface. Alex. Eng. J. 59, 1847–1856 (2020)

    Article  Google Scholar 

  21. H. Mondal, D. Pal, C. Sewli, P. Sibanda, Thermophoresis and Soret-Dufour on MHD mixed convection mass transfer over an inclined plate with non-uniform heat source/sink and chemical reaction. Ain Shams Eng. J. 9, 2111–2121 (2018)

    Article  Google Scholar 

  22. W. Ibrahim, M. Negera, MHD slip flow of upper-convected Maxwell nanofluid over a stretching sheet with chemical reaction. J. Egypt. Math. Soc. (2020). https://doi.org/10.1186/s42787-019-0057-2

    Article  MathSciNet  MATH  Google Scholar 

  23. M. Vinodkumar Reddy, P. Lakshminarayana, K. Kajravelu, MHD radiative flow of a maxwell fluid on an expanding surface with the effects of Dufour and Soret and chemical reaction. Comput. Therm. Sci. 12(4), 317–327 (2020)

    Article  Google Scholar 

  24. W.I.A. Okuyade, T.M. Abbey, A.T. Gima-Laabel, Unsteady MHD free convective chemically reacting fluid flow over a vertical plate with thermal radiation, Dufour, Soret and constant suction effects. Alex. Eng. J. 57, 3863–3871 (2018)

    Article  Google Scholar 

  25. Y. Shagaiya Daniel, Z. Abdul Aziz, Z. Ismail, F. Salah, Entropy analysis in the electrical magnetohydrodynamic flow of nanofluid with the effects of thermal radiation, viscous dissipation, and chemical reaction. Theor. App. Mech. Lett. 7, 235–242 (2017)

    Article  Google Scholar 

  26. K. Ganesh Kumar, G.K. Ramesh, B.J. Gireesha, R.S.R. Gorla, Characteristics of Joule heating and viscous dissipation on three-dimensional flow of Oldroyd B nanofluid with thermal radiation. Alex. Eng. J. 57, 2139–2149 (2018)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. Lakshminarayana.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Reddy, M.V., Lakshminarayana, P. Cross-diffusion and heat source effects on a three-dimensional MHD flow of Maxwell nanofluid over a stretching surface with chemical reaction. Eur. Phys. J. Spec. Top. 230, 1371–1379 (2021). https://doi.org/10.1140/epjs/s11734-021-00037-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-021-00037-9

Navigation