Skip to main content
Log in

Dufour and Soret effect on heat and mass transfer with radiative heat flux in a viscous liquid over a rotating disk

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

Abstract.

Free surface flow of an incompressible viscous fluid over a porous rotating disk with heat and mass transfer with radiative heat flux is studied. The effect of the natural parameters such as Dufour number, Soret number, Prandtl number, radiation parameter, Suction parameter and Schmidt number on the fluid properties are determined and shown graphically. The corresponding skin friction coefficient, the Nusselt number and the Sherwood number are also calculated and displayed in tables showing the effects of various parameters on velocity profile. Individual averaged square residual errors as well as optimal values of converges control parameterconvergence control parameters are also discussed in detail. It is found that Dufour and radiation effects cause reductions in the fluid temperature. The effect of suction decreases the velocities, temperature and concentration profiles significantly in boundary layer. The total averaged squared errors and average squared residual errors are further reduced as the order of approximation is increased. This analysis was performed by means of the Homotopy Analysis Method (HAM) and for validity it is compared with the results of BVP4C numerical routine.

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.

Similar content being viewed by others

References

  1. T. Von Kármán, Z. Angew. Math. Mech. 1, 233 (1921)

    Article  Google Scholar 

  2. W.G. Cochran, Proc. Camb. Philos. Soc. 30, 365 (1934)

    Article  ADS  Google Scholar 

  3. E.R. Benton, J. Fluid Mech. 24, 781 (1966)

    Article  ADS  Google Scholar 

  4. K. Millsaps, K. Polhausen, J. Aeronaut. Sci. 19, 120 (1952)

    MathSciNet  Google Scholar 

  5. E.M. Sparrow, J.L. Gregg, J. Heat Transf. ASME 81, 249 (1959)

    Google Scholar 

  6. H.K. Kuiken, J. Fluid Mech. 47, 789 (1971)

    Article  ADS  Google Scholar 

  7. H.A. Attia, Int. Commun. Heat Mass Transfer 29, 653 (2002)

    Article  Google Scholar 

  8. H.I. Andersson, E. de Korte, Eur. J. Mech. B 21, 317 (2002)

    Article  Google Scholar 

  9. M. Turkyilmazoglu, Mediterr. J. Math. 13, 4019 (2016)

    Article  MathSciNet  Google Scholar 

  10. M.M. Ali, T.S. Chen, B.F. Armaly, AIAA J. 22, 179 (1984)

    Article  Google Scholar 

  11. T.M.A. El-Mistikawy, H.A. Attia, A.A. Megahed, The rotating disk flow in the presence of a weak magnetic field, in Proceedings of the 4th Conference on Theoretical and Applied Mechanics, Cairo, Egypt (Hindawi Publishing, 1990) pp. 69--82

  12. J. Rath, M.O.P. Iyengar, Proc. Natl. Inst. Sci. India A 35, 180 (1969)

    Google Scholar 

  13. K.T. Yang, J. Appl. Mech. 25, 421 (1958)

    Google Scholar 

  14. C.Y. Wang, J. Appl. Mech. 23, 579 (1976)

    Article  Google Scholar 

  15. S. Uchida, H. Aoki, J. Fluid. Mech. 82, 371 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  16. L.T. Watson, C.Y. Wang, Phys. Fluid 22, 2267 (1979)

    Article  ADS  Google Scholar 

  17. E.M. Sparrow, G.S. Beavers, L.Y. Hung, Int. J. Heat Mass Transfer 14, 993 (1971)

    Article  Google Scholar 

  18. Kh. Abdul Maleque, J. Heat Transfer 131, 082001 (2009)

    Article  Google Scholar 

  19. A. Afify Ahmed, Commun. Nonlinear Sci. Numer. Simul. 14, 2202 (2009)

    Article  ADS  Google Scholar 

  20. Beg Anwar, A.Y. Bakier, V.R. Prasad, Comput. Mater. Sci. 46, 57 (2009)

    Article  Google Scholar 

  21. M. Turkyilmazoglu, Phys. Fluids 28, 043102 (2016)

    Article  ADS  Google Scholar 

  22. R. Siegel, J.R. Howell, Thermal Radiation Transfer, 3rd ed. (Hemisphere, New York, 1992)

  23. M.F. Modest, Radiative Heat Transfer, 2nd ed. (Academic Press, New York, 2003)

  24. T. Hayat, M. Nawaz, M. Sajid, S. Asghar, Comput. Math. Appl. 58, 369 (2009)

    Article  MathSciNet  Google Scholar 

  25. M.S. Alam, S.M.C. Hossain, M.M. Rahman, Meccanica 49, 2439 (2014)

    Article  MathSciNet  Google Scholar 

  26. I.H. Lin, K.L. Hsiao, Am. J. Heat Mass Transfer 2, 127 (2015)

    Article  Google Scholar 

  27. M.S. Alam, Nayan K. Podder, M.M. Rahman, Vajravelu, Am. J. Heat Mass Transfer 3, 165 (2015)

    Google Scholar 

  28. M. Turkyilmazoglu, J. Heat Transfer 131, 691 (2009)

    Article  Google Scholar 

  29. S.P. Anjali Devi, R. Uma Devi, Commun. Nonlinear Sci. Numer. Simul. 16, 1917 (2011)

    Article  ADS  Google Scholar 

  30. M.H. Abolbashari, N. Freidoonimehr, F. Nazari, M.M. Rashidi, Powder Technol. 267, 256 (2014)

    Article  Google Scholar 

  31. S.J. Liao, Commun. Nonlinear Sci. Numer. Simul. 15, 2003 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  32. Y. Zhao, http://numericaltank.sjtu.edu.cn/BVPh2_0.htm (30.08.2014)

  33. M. Turkyilmazoglu, Phys. Scr. 86, 015301 (2012)

    Article  ADS  Google Scholar 

  34. M. Turkyilmazoglu, Filomat 30, 1633 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Muhammad Shuaib.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shah, R.A., Shuaib, M. & Khan, A. Dufour and Soret effect on heat and mass transfer with radiative heat flux in a viscous liquid over a rotating disk. Eur. Phys. J. Plus 132, 342 (2017). https://doi.org/10.1140/epjp/i2017-11632-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2017-11632-4

Navigation