Skip to main content
SpringerLink
Log in

Impact of irreversibility ratio and entropy generation on three-dimensional Oldroyd-B fluid flow with relaxation–retardation viscous dissipation

  • Original Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

The study is concerned with entropy minimization on three-dimensional magnetohydrodynamic Oldroyd-B fluid flow with relaxation–retardation viscous dissipation and a mixed chemical reaction. A numerical solution of the nonlinear transport equations is obtained using an overlapping grid spectral collocation numerical scheme. We investigate strategies for entropy generation minimization in terms of system parameters such as the mixed convection parameter and changes in thermal and concentration fields under different conditions. Further, the findings on changes in the axial and transverse skin friction coefficients, the Nusselt number and the Sherwood number are presented.

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

Similar content being viewed by others

Abbreviations

(u, v, w):

Velocity components along (x, y, z) directions

\(B_0\) :

Uniform magnetic field strength

\(\lambda _1\) :

Relaxation time

\(\lambda _2\) :

Retardation time

\(\nu _f\) :

Kinematic viscosity

\(\varGamma _e\) :

Relaxation time for heat flux

\(\varGamma _c\) :

Relaxation time for mass flux

T :

Fluid temperature in the boundary layer

\(T_\infty \) :

Temperature of ambient fluid

\(T_w\) :

Surface temperature

C :

Fluid concentration in the boundary layer

\(C_\infty \) :

Concentration of ambient fluid

\(C_w\) :

Surface concentration

g :

Acceleration due to gravity

\(k_f\) :

Thermal conductivity

\(\rho _\mathrm{f}\) :

Density of the fluid

q :

Heat flux

V :

Velocity

\(\varGamma _1\) :

Deborah number in terms of relaxation time

\(\varGamma _2\) :

Deborah number in terms of retardation time

Sc:

Schmidt number

M:

Hartman number

\(\hbox {Gr}_x\) :

Thermal Grashof number

Re:

Reynolds number

Pr:

Prandtl number

J :

Mass flux

\(\varepsilon \) :

Thermal relaxation chemical reaction parameter

\(\phi \) :

Irreversibility ratio

\(D_\mathrm{B}\) :

Brownian diffusion coefficient

\(\gamma \) :

Chemical reaction parameter

\(\beta \) :

Ratio of stretching rates

\(\lambda \) :

Mixed convection parameter

N :

Concentration buoyancy parameter

\(\delta _\mathrm{e}\) :

Deborah number in terms of relaxation time of the heat flux

\(\delta _\mathrm{c}\) :

Deborah number in terms of relaxation time of the mass flux

\(\beta _\mathrm{T}\) :

Volumetric coefficient thermal expansion

\(\beta _\mathrm{T}\) :

Volumetric coefficient solutal expansion

EG:

Entropy generation

VBL:

Velocity boundary layer

HTR:

Heat transfer rate

TBL:

Thermal boundary layer

CPU:

Central processing unit

QLM:

Quasi-linearization method

References

  1. J Oldroyd Proc. R. Soc. Lond. 200 523 (1950)

    ADS  Google Scholar 

  2. R K Bhatnagar, G Gupta and K R Rajagopal Int. J. Nonlinear Mech. 30 391 (1995)

    Article  Google Scholar 

  3. C Fetecau and C Fetecau Int.J. Eng. Sci. 43 340 (2005)

    Article  Google Scholar 

  4. T Hayat, Z Hussain, M Farooq, A Alsaedi and M Obaid Int. J. Nonlinear Sci. Numer. Simul. 15 77 (2014)

    MathSciNet  Google Scholar 

  5. T Hayat, M Ijaz, Khan, M Waqas and A Alsaedi Nuclear Eng. Nuclear Eng. Technol. 49 1645 (2017)

    Article  Google Scholar 

  6. Y Zhang, M Zhang and Y Bai J. Mol. Liq. 220 665 (2016)

    Article  Google Scholar 

  7. M M Bhatti, A Zeeshan and M M Rashidi Int. J. Eng. Sci. Technol. 20 265 (2017)

    Google Scholar 

  8. Y Zhang, J Jiang and Y Bai Comput. Math. Appl. (2019)

  9. S S Ghadikolaei, K h Hosseinzadeh and D D Ganji World J. Eng. (2019)

  10. M Gholinia, K H Hosseinzadeh, H Mehrzadi, D D Ganji, and A A Ranjbar Case Stud. Therm. Eng. 13 100356 (2019)

    Article  Google Scholar 

  11. Kh Hosseinzadeh, A Jafarian Amiri, S Saedi Ardahaie and D D Ganji Case Stud. Therm. Eng. 10 595 (2017)

    Article  Google Scholar 

  12. T Hayat, T Muhammad, S A Shehzad and A Alsaedi Int. J. Therm. Sci. 111 274 (2017)

    Article  Google Scholar 

  13. C Cattaneo Atti Sem. Mat. Fis. Univ. Modena 3 83 (1948)

    Google Scholar 

  14. C I Christov Mech. Res. Commun. 36 481 (2009)

    Article  Google Scholar 

  15. K H Hosseinzadeh, M Gholinia, B Jafari, A Ghanbarpour, H Olfian, and D D Ganji Heat Transf. Asian Res. 48 744 (2019)

    Article  Google Scholar 

  16. M Gholinia, S Gholinia, K H Hosseinzadeh, and D D Ganji Results Phys. 9 1525 (2018)

    Article  ADS  Google Scholar 

  17. F M Abbasi, M Mustafa, S A Shehzad, M S Alhuthali and T Hayat Chin. Phys. B 25 147 (2015)

    Google Scholar 

  18. T Hayat, M Waleed, A Khan, A Alsaedi, M Ayub, and M I Khan Results Phys. 7 2470 (2017)

    Article  ADS  Google Scholar 

  19. K H Hosseinzadeh, A R Mogharrebi, A Asadi, M Paikar and D D Ganji J. Mol. Liq. 300 112347 (2020)

    Article  Google Scholar 

  20. T Hayat, M Imtiaz, A Alsaedi and S Almezal J. Magn. Magn. Mater. 401 296 (2016)

    Google Scholar 

  21. N Sandeep and C Sulochana Ain Shams Eng. J. 9 517 (2018)

    Article  Google Scholar 

  22. Z Shah, P Kumam and W Deebani Sci. Rep. 10 14 (2020)

    Article  Google Scholar 

  23. M I Sumaira, K Qayyum, T Hayat, M I Khan, A Alsaedi and T Khan Phys. Lett. A 382 2026 (2018)

    Google Scholar 

  24. A Saeed, S Islam, A Dawar, Z Shah, P Kumam and W Khan Symmetry 11 439 (2019)

    Article  Google Scholar 

  25. S A Shehzad, Z Abdullah, F M Abbasi, T Hayat and A Alsaedi J. Magn. Magn. Mater. 399 97 (2016)

    Article  ADS  Google Scholar 

  26. M Almakki, S K Nandy, S Mondal, P Sibanda and D Sibanda Heat Transf. Asian Res. 48 24 (2019)

    Article  Google Scholar 

  27. K H Hosseinzadeh, A Asadi, A R Mogharrebi, J Khalesi, S Mousavisani and D D Ganji Case Stud. Therm. Eng. 14 100482 (2019)

    Article  Google Scholar 

  28. W A Khan, M M Yovanovich and J R Culham Twenty-Second Annual IEEE Semiconductor Thermal Measurement and Management Symposium 78 (2006)

  29. M W Khan, M I Khan, T Hayat and A Alsaedi Phys. B Condens. Matter 534 113 (2018)

    Article  ADS  Google Scholar 

  30. S Huang, Z Ma, and P Cooper Energy Convers. Manag. 87 128 (2014)

    Article  Google Scholar 

  31. H Feng, J You, L Chen, Y Ge, and S Xia Eur. Phys. J. Plus 135 257 (2020)

    Article  Google Scholar 

  32. S A Shehzad, A Alsaedi, T Hayat and M S Alhuthali J. Taiwan Inst. Chem. Eng. 45 787 (2014)

    Article  Google Scholar 

  33. T Hayat, T Muhammad, S A Shehzad, M S Alhuthali and J Lu J. Mol. Liq. 212 272 (2015)

    Article  Google Scholar 

  34. W A Khan, M Irfan and M Khan Results Phys. 7 3583 (2017)

    Article  ADS  Google Scholar 

  35. A Hafeez, M Khan and J Ahmed Comput. Methods Prog. Biomed. 191 105342 (2020)

    Article  Google Scholar 

  36. A Bejan Second Law Anal. Heat Transf. 5 720 (1980)

    Google Scholar 

  37. R Bellman, R Kalaba and B Kotkin Math. Comput. 17 155 (1963)

    Google Scholar 

  38. L N Trefethen Spectral Methods MATLAB v.10 (2000)

  39. G Birkhoff and A Priver J. Math. Phys. 46 440 (1967)

    Article  MathSciNet  Google Scholar 

  40. D V Griffiths and I M Smith Numer. Methods Eng. (2006)

  41. B Fischer and R Freund J. Approx. Theory 65 261 (1991)

    Article  MathSciNet  Google Scholar 

  42. H E Salzer Math. Comput. 30 295 (1976)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the University of KwaZulu-Natal, South Africa, and Amity University Kolkata, India, for necessary support.

Author information

Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg, 3209, South Africa

    Z. M. Mburu & P. Sibanda

  2. Department of Physics, IHSE, Siksha O Anusandhan Deemed to be University, Bhubaneswar, Odisha, India

    M. K. Nayak

  3. Department of Mathematics, Amity University Kolkata, Newtown, West Bengal, 700135, India

    S. Mondal

Authors
  1. Z. M. Mburu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. K. Nayak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Mondal
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. Sibanda
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Mondal.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mburu, Z.M., Nayak, M.K., Mondal, S. et al. Impact of irreversibility ratio and entropy generation on three-dimensional Oldroyd-B fluid flow with relaxation–retardation viscous dissipation. Indian J Phys 96, 151–167 (2022). https://doi.org/10.1007/s12648-020-01950-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-020-01950-w

Keywords

Search

Navigation