Skip to main content
Log in

Thermally stratified squeezed flow between two vertical Riga plates with no slip conditions

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

Abstract.

This paper demonstrates the mixed convective squeezing nanomaterials flow between two vertical plates, one of which is a Riga plate embedded in a thermally stratified medium subject to convective boundary conditions. Heat transfer features are elaborated with viscous dissipation. Single-wall and multi-wall carbon nanotubes are taken as nanoparticles to form a homogeneous solution in the water. A non-linear system of differential equations is obtained for the considered flow by using suitable transformations. Convergence analysis for velocity and temperature is computed and discussed explicitly through BVPh 2.0. Residual errors are also computed by BVPh 2.0 for the dimensionless governing equations. We introduce two undetermined convergence control parameters, i.e. \( \hslash_{\theta}\) and \( \hslash_{f}\) , to compute the lowest entire error. The average residual error for the k -th-order approximation is given in a table. The effects of different flow variables on temperature and velocity distributions are sketched graphically and discussed comprehensively. Furthermore the coefficient of skin friction and the Nusselt number are also analyzed through graphical data.

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

Similar content being viewed by others

References

  1. S.U.S. Choi, J.A. Eastman, in Enhancing thermal conductivity of fluids with nanoparticles, Development and Application of non-Newtonian Flows, FED Vol. 231/MD Vol. 66 (ASME, 1995) pp. 99--105

  2. M.F.L.D. Volder, S.H.T. Fick, R.H. Baughman, A.J. Hart, Sci. 339, 535 (2013)

    Article  ADS  Google Scholar 

  3. T. Hayat, M. Farooq, A. Alsaedi, AIP Adv. 5, 027130 (2015)

    Article  ADS  Google Scholar 

  4. M. Sheikholeslami, M.M. Rashidi, D.D. Ganji, Comput. Methods Appl. Mech. Eng. 294, 299 (2015)

    Article  ADS  Google Scholar 

  5. T. Hayat, K. Muhammad, M. Farooq, A. Alsaedi, PLoS ONE 11, e0152923 (2016)

    Article  Google Scholar 

  6. T. Hayat, M.I. Khan, M. Farooq, A. Alsaedi, T. Yasmeen, Int. J. Heat Mass Transfer 106, 810 (2017)

    Article  Google Scholar 

  7. R.U. Haq, S. Nadeem, Z.H. Khan, N.F.M. Noor, Physica B 457, 40 (2015)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Z. Iqbal, E. Azhar, E.N. Maraj, Physica E 91, 128 (2017)

    Article  ADS  Google Scholar 

  10. T. Hayat, M.I. Khan, M. Farooq, T. Yasmeen, A. Alsaedi, J. Mol. Liq. 224, 786 (2016)

    Article  Google Scholar 

  11. M. Farbod, A. Ahangarpour, Phys. Lett. A 380, 4044 (2016)

    Article  ADS  Google Scholar 

  12. T. Hayat, S. Ullah, M.I. Khan, A. Alsaedi, Results Phys. 8, 357 (2018)

    Article  ADS  Google Scholar 

  13. F. Rehman, M.I. Khan, M. Sadiq, A. Malook, J. Mol. Liq. 231, 353 (2017)

    Article  Google Scholar 

  14. T. Hayat, S. Ullah, M.I. Khan, A. Alsaedi, Q.M.Z. Zia, Results Phys. 8, 473 (2018)

    Article  ADS  Google Scholar 

  15. T. Hayat, M. Khan, M.I. Khan, A. Alsaedi, A. Ayub, PLoS ONE 12, e0180976 (2017)

    Article  Google Scholar 

  16. A. Ahmad, S. Asghar, S. Afzal, J. Magn. & Magn. Mater. 402, 44 (2016)

    Article  ADS  Google Scholar 

  17. T. Hayat, T. Abbas, M. Ayub, M. Farooq, A. Alsaedi, J. Mol. Liq. 222, 854 (2016)

    Article  Google Scholar 

  18. A. Ahmad, S. Asghar, S. Afzal, J. Magn. & Magn. Mater. 402, 44 (2016)

    Article  ADS  Google Scholar 

  19. M. Farooq, A. Anjum, T. Hayat, A. Alsaedi, J. Mol. Liq. 224, 1341 (2016)

    Article  Google Scholar 

  20. M. Ayub, T. Abbas, M.M. Bhatti, Eur. Phys. J. Plus 131, 193 (2016)

    Article  Google Scholar 

  21. M.A. Sheremet, S. Dinarvand, I. Popet, Physica E 69, 332 (2015)

    Article  ADS  Google Scholar 

  22. S. Nadeem, N. Muhammad, J. Mol. Liq. 224, 423 (2016)

    Article  Google Scholar 

  23. S. Elci, Limnology 9, 135 (2008)

    Article  Google Scholar 

  24. R. Ahmad, M. Mustafa, M. Turkyilmazoglu, Int. J. Heat Mass Transfer 111, 827 (2017)

    Article  Google Scholar 

  25. T. Hayat, M. Farooq, A. Alsaedi, Int. J. Numer. Methods Heat Fluid Flow 25, 724 (2015)

    Article  Google Scholar 

  26. S.J. Lio, Homotopy Analysis Method in Non-linear Differential Equations (Springer and Higher Education Press, Heidelberg, 2012)

  27. T. Hayat, M.I. Khan, M. Farooq, A. Alsaedi, M. Waqas, T. Yasmeen, Int. J. Heat Mass Transfer 99, 702 (2016)

    Article  Google Scholar 

  28. T. Hayat, M.I. Khan, M. Farooq, T. Yasmeen, A. Alsaedi, J. Mol. Liq. 220, 49 (2016)

    Article  Google Scholar 

  29. M.I. Khan, M. Waqas, T. Hayat, A. Alsaedi, J. Colloid Interface Sci. 498, 85 (2017)

    Article  ADS  Google Scholar 

  30. M. Turkyilmazoglu, Trans. Model. Comput. Simul. 27, 21 (2017)

    Google Scholar 

  31. M.W.A. Khan, M. Waqas, M.I. Khan, A. Alsaedi, T. Hayat, Colloid Polymer Sci. 295, 1201 (2017)

    Article  Google Scholar 

  32. T. Hayat, F. Shah, A. Alsaedi, M.I. Khan, J. Theor. Comput. Chem. 16, 1750045 (2017)

    Article  Google Scholar 

  33. N.B. Khan, Z. Ibrahim, M.I. Khan, T. Hayat, M.F. Javed, Int. J. Heat Mass Transfer 121, 309 (2018)

    Article  Google Scholar 

  34. T. Hayat, M.I. Khan, M. Imtiaz, A. Alsaedi, J. Therm. Sci. Eng. Appl. 10, 011002 (2018)

    Article  Google Scholar 

  35. M.I. Khan, M. Waqas, T. Hayat, A. Alsaedi, M.I. Khan, Int. J. Hydrogen Energy 42, 26408 (2017)

    Article  Google Scholar 

  36. M. Turkyilmazoglu, Int. J. Heat Mass Transfer 90, 781 (2015)

    Article  Google Scholar 

  37. M. Turkyilmazoglu, Phys. Fluid 28, 043102 (2016)

    Article  ADS  Google Scholar 

  38. M. Waqas, M.I. Khan, T. Hayat, A. Alsaedi, Results Phys. 7, 2489 (2017)

    Article  ADS  Google Scholar 

  39. M.I. Khan, A. Alsaedi, S.A. Shehzad, T. Hayat, Results Phys. 7, 2255 (2017)

    Article  ADS  Google Scholar 

  40. T. Hayat, M.I. Khan, A. Alsaedi, M.I. Khan, Int. Commun. Heat Mass Transf. 89, 190 (2017)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  42. Q.Z. Xue, Physica B 368, 302 (2005)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Ijaz Khan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Farooq, M., Mansoor, Z., Ijaz Khan, M. et al. Thermally stratified squeezed flow between two vertical Riga plates with no slip conditions. Eur. Phys. J. Plus 133, 152 (2018). https://doi.org/10.1140/epjp/i2018-11891-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2018-11891-5

Navigation