Skip to main content
SpringerLink
Log in

Hybrid nanofluid MHD motion towards an exponentially stretching/shrinking sheet with the effect of thermal radiation, heat source and viscous dissipation

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

In this article, the heat transfer of Al\(_2 \textrm{O}_3\)–Cu/H\(_2\)O in the magnetohydrodynamic (MHD) stagnation point flow in the direction of an exponentially stretching/shrinking sheet with the effect of heat source, thermal radiation and viscous dissipation is examined. The inclusion of dissipative heat, thermal radiation and additional heat source enriches the study as well. Using suitable similarity transformations, the governing partial differential equations are transformed into ordinary differential equations (ODEs). The ODEs are solved numerically by the built-in function bvp4c in MATLAB. By the addition of nanoparticle, effects of various parameters were studied, and the outcomes revealed that the skin friction coefficient decreases and the local Nusselt number increases. In comparison, viscous dissipation causes an improvement in the fluid thermal state and, as a result, triggers the thermal boundary layer to rise.

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

Similar content being viewed by others

References

  1. S S U Choi and J A Eastman, ASME Publ. Fed. 231, 99 (1995)

    Google Scholar 

  2. D Singh, J Tourbort and G Chen, Argo. Nat. Lab. (2006).

  3. M U Sajid and H M Ali, Int. J. Heat Mass Transf. 126, 211 (2018)

    Article  Google Scholar 

  4. G Huminic and A Huminic, Int. J. Heat Mass Transf. 125, 82 (2018)

    Article  Google Scholar 

  5. T R Shah and H M Ali, Sol. Energy 183, 173 (2019)

    Article  ADS  Google Scholar 

  6. N A C Sidik, I M Adamu, M M Jamil, G H R Kefayati, R Mamat and G Najafi, Int. Commun. Heat Mass Transf. 78, 68 (2016)

    Article  Google Scholar 

  7. M Gupta, V Singh, S Kumar, S Kumar and N Dilbaghi, J. Clean. Prod. 190, 169 (2018)

    Article  Google Scholar 

  8. G Huminic and A Huminic, J. Mol. Liq. 302, 112533 (2020)

    Article  Google Scholar 

  9. N Sandeep and C Sulochana, Ain Shams Eng. J. 7, 709 (2016)

    Article  Google Scholar 

  10. S A M Mehryan, M A Sheremet, M Soltani and M Izadi, J. Mol. Liq. 277, 959 (2019)

    Article  Google Scholar 

  11. S Qayyum, M I Khan, T Hayat and A Alsaedi, Results Phys. 7, 1907 (2017)

    Article  ADS  Google Scholar 

  12. M N Othman, A Jedi and N A A Bakar, Appl. Sci. 11, 8199 (2021)

    Article  Google Scholar 

  13. U Yashkun, K Zaimi, N A A Bakar, A Ishak and I Pop, Int. J. Numer. Methods Heat Fluid Flow 31(3), 1014 (2021)

  14. I Waini, A Ishak and I Pop, Appl. Math. Mech. 41, 507 (2020)

    Article  Google Scholar 

  15. U Khan, I Waini, A Ishak and I Pop, J. Mol. Liq. 331, 115752 (2021)

    Article  Google Scholar 

  16. N C Roy and I Pop, Eur. Phys. J. Plus 135, 768 (2020)

    Article  Google Scholar 

  17. A A A Arani and H Aberoumand, Powder Technol. 380, 152 (2021)

    Article  Google Scholar 

  18. N S Wahid, N Md Arifin, N S Khashi’ie, I Pop, N Bachok and M E H Hafidzuddin, Alex. Eng. J. 61(4), 3323 (2022)

    Article  Google Scholar 

  19. M Shoaib, M A Z Raja, M T Sabir, M Awais, S Islam, Z Shah and P Kumam, Alex. Eng. J. 60(4), 3605 (2021)

    Article  Google Scholar 

  20. M Shoaib, M A Z Raja, M T Sabir, S Islam, Z Shah, P Kumam and H Alrabaiah, Sci. Rep. 10, 18533 (2020).

    Article  Google Scholar 

  21. N A Zainal, R Nazar, K Naganthran and I Pop, Int. J. Numer. Methods Heat Fluid Flow 31(3), 858 (2021)

  22. P Sreedevi, P R Sudarsana and A Chamkha, Appl. Sci. 2, 1222 (2020)

    Google Scholar 

  23. A Jamaludin, K Naganthran, R Nazar and I Pop, Eur. J. Mech. B/Fluids 84, 71 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  24. H Berrehal, G Sowmya and O D Makinde, Int. J. Numer. Methods Heat Fluid Flow 32(5), 1643 (2022)

  25. S Tinker, S R Mishra, P K Pattnaik and R P Sharma, Proc. Inst. Mech. Eng. N: J. Nanomater. Nanoeng. Nanosyst., https://doi.org/10.1177/23977914211069021 (2022)

    Article  Google Scholar 

  26. R P Sharma, O Prakash, I Rashidi, S R Mishra, P S Rao and F Karimi, Eur. Phys. J. Plus 137, 297 (2022)

    Article  Google Scholar 

  27. B Nayak and S R Mishra, Pramana – J. Phys. 95, 29 (2021)

    Google Scholar 

  28. M M Bhatti, M A Yousif, S R Mishra and A Shahid, Pramana – J. Phys. 93, 88 (2019)

    Article  ADS  Google Scholar 

  29. B C Rout and S R Mishra, Pramana – J. Phys. 93, 41 (2019)

    Google Scholar 

  30. X J Yang, P T Qiu and G L Liu, Therm. Sci. 26(2A), 1025 (2022)

    Article  Google Scholar 

  31. X J Yang, M A Aty and M A A Khder, Therm. Sci. 26(2A), 1047 (2022)

    Article  Google Scholar 

  32. X J Yang, C Ping and J G Liu, Therm. Sci. 25(6B), 4505 (2021)

    Article  Google Scholar 

  33. X J Yang and J G Liu, Therm. Sci. 25(6B), 4561 (2021)

    Article  Google Scholar 

  34. J G Liu, X J Yang and Y Y Feng, J. Geom. Phys. 144, 190 (2019)

  35. X J Yang, L Geng and Y M Pan, Therm. Sci. 25(6B), 4577 (2021)

    Article  Google Scholar 

  36. X J Yang and Y R Fan, Therm. Sci. 25(6B), 4631 (2021)

    Article  Google Scholar 

  37. X J Yang, Fractals 30(3), 2250054-929 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  38. M Hussain, A Ali, M Inc, N Sene and Md Hussan, J. Math. 2022, 3233964 (2022)

  39. N Ali, M F Yassen, S A Asiri, R Nawaz, L Zada, Md M Alam and N Sene, J. Nanomater. 2022, 8370107 (2022)

    Google Scholar 

  40. I Waini, A Ishak and I Pop, Int. J. Numer. Methods Heat Fluid Flow 31(1), 216 (2021)

  41. N Bachok, A Ishak and I Pop, Int. J. Heat Mass Transf. 55, 8122 (2012)

    Article  Google Scholar 

  42. K Bhattacharyya and K Vajravelu, Commun. Nonlinear Sci. Numer. Simul. 17(7), 2728 (2012)

    Article  ADS  Google Scholar 

  43. M Q Brewster, Thermal radiative transfer and properties (John Wiley and Sons, New York, USA, 1992)

    Google Scholar 

  44. H Schlichting and K Gersten, Boundary layer theory (Springer-Verlag, Berlin, 2001)

    MATH  Google Scholar 

  45. A M Rohni, S Ahmad and I Pop, Int. J. Therm. Sci. 75, 164 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, JECRC University, Jaipur, 303 905, India

    Om Prakash & P S Rao

  2. Department of Mathematics and Computing, IIT (ISM), Dhanbad, 826 006, India

    Om Prakash

  3. Department of Mechanical Engineering, National Institute of Technology, Jote, 791 113, India

    Ram Prakash Sharma

  4. Department of Mathematics, Siksha O Anusandhan Deemed to be University, Khandagiri, 751 030, India

    S R Mishra

Authors
  1. Om Prakash
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P S Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ram Prakash Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S R Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S R Mishra.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Prakash, O., Rao, P.S., Sharma, R.P. et al. Hybrid nanofluid MHD motion towards an exponentially stretching/shrinking sheet with the effect of thermal radiation, heat source and viscous dissipation. Pramana - J Phys 97, 64 (2023). https://doi.org/10.1007/s12043-023-02533-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-023-02533-0

Keywords

PACS Nos

Search

Navigation