Investigation of viscous dissipation in the nanofluid flow with a Forchheimer porous medium: Modern transportation of heat and mass

  • Sadaf MasoodEmail author
  • M. Farooq
  • S. Ahmad
  • A. Anjum
  • N. A. Mir
Regular Article


In this article, the motion of a viscous nanofluid over a shrinking/stretching sheet is analyzed. This study also focuses on the non-Darcian transport in the stagnation-point flow of a nanofluid. The nanofluid consists of Brownian motion and thermophoresis effects. A magnetic field is applied in the vertical direction under the assumption of low magnetic Reynolds number. The Cattaneo-Christov phenomenon is incorporated to investigate the characteristics of heat and mass transfer. The characteristics of heat transfer are evaluated for the first time by utilizing the viscous dissipation with the Cattaneo-Christov theory. The equations (PDEs) governing the flow, heat and mass transport are first derived and then transformed into the corresponding ordinary differential equations via using similarity solutions. A homotopic proceduce is addressed to obtain the solutions for the accomplished ordinary differential equations. The variation of the divergent involved parameters on the fluid temperature, velocity and concentration distributions is disclosed through graphs and analyzed in detail. The features of the skin friction coefficient is graphed in order to understand the flow processes. It is noted that an increase in the Darcy number results in the decrease in the velocity field. Further impacts of Brownian diffusion and Eckert number on the temperature are quite similar.


  1. 1.
    S.U.S. Choi, J. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, in The Proceedings of the ASME International Mechanical Engineering Congress and Exposition (ASME, 1995) pp. 99--105Google Scholar
  2. 2.
    T. Hayat, T. Muhammad, A. Alsaedi, B. Ahmad, Results Phys. 6, 897 (2016)ADSCrossRefGoogle Scholar
  3. 3.
    N. Muhammad, S. Nadeem, T. Mustafa, Results Phys. 7, 862 (2017)ADSCrossRefGoogle Scholar
  4. 4.
    L. Ahmad, M. Khan, W.A. Khan, Eur. Phys. J. Plus 132, 373 (2017)CrossRefGoogle Scholar
  5. 5.
    T. Hayat, S. Qayyum, S. Shehzad, A. Alsaedi, Results Phys. 7, 4145 (2017)ADSCrossRefGoogle Scholar
  6. 6.
    Hashim, M. Khan, Sharjeel, U. Khan, J. Mol. Liq. 272, 787 (2018)CrossRefGoogle Scholar
  7. 7.
    M. Khan, H. Sardar, Hashim, J. Mol. Liq. 272, 474 (2018)CrossRefGoogle Scholar
  8. 8.
    I. Uddin, M.A. Khan, S. Ullah, S. Islam, M. Israr, F. Hussain, Results Phys. 8, 160 (2018)ADSCrossRefGoogle Scholar
  9. 9.
    J.H. Merkin, N. Najib, N. Bachok, A. Ishak, I. Pop, J. Taiwan Inst. Chem. Eng. 74, 65 (2017)CrossRefGoogle Scholar
  10. 10.
    T.M. Agbaje, S. Mondal, Z.G. Makukula, S.S. Motsa, P. Sibanda, Ain Shams Eng. J. 9, 233 (2018)CrossRefGoogle Scholar
  11. 11.
    T. Hayat, M.I. Khan, M. Waqas, A. Alsaedi, M. Farooq, Comput. Methods Appl. Mech. Eng. 315, 1011 (2017)ADSCrossRefGoogle Scholar
  12. 12.
    R. Kumar, S. Sood, S.A. Shehzad, M. Sheikholeslami, Results Phys. 7, 3325 (2017)ADSCrossRefGoogle Scholar
  13. 13.
    P. Weidman, M.R. Turner, Eur. J. Mech.-B/Fluids 61, 144 (2017)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    A. Hamid, Hashim, M. Khan, Abdul Hafeez, Int. J. Heat Mass Transfer 126, 933 (2018)CrossRefGoogle Scholar
  15. 15.
    M.M. Bhatti, M.A. Abbas, M.M. Rashidi, Appl. Math. Comput. 316, 381 (2018)MathSciNetGoogle Scholar
  16. 16.
    D. Lu, M. Ramzan, M. Bilal, J.D. Chung, U. Farooq, Commun. Theor. Phys. 70, 071 (2018)ADSCrossRefGoogle Scholar
  17. 17.
    P. Forchheimer, Z. Ver. Deutsch. Ing. 45, 1782 (1901)Google Scholar
  18. 18.
    T. Hayat, T. Muhammad, S. Al-Mezal, S.J. Liao, Int. J. Numer. Methods Heat Fluid Flow 26, 2355 (2016)CrossRefGoogle Scholar
  19. 19.
    T. Hayat, F. Haider, T. Muhammad, A. Alsaedi, Int. J. Heat Mass Transfer 112, 248 (2017)CrossRefGoogle Scholar
  20. 20.
    M.I. Khan, T. Hayat, A. Alsaedi, Results Phys. 7, 2644 (2017)ADSCrossRefGoogle Scholar
  21. 21.
    D. Srinivasacharya, P.V. Kumar, Propuls. Power Res. 7, 147 (2018)CrossRefGoogle Scholar
  22. 22.
    C.J. Huang, Int. J. Therm. Sci. 130, 256 (2018)CrossRefGoogle Scholar
  23. 23.
    C. Cattaneo, Atti Sem. Mat. Fis. Univ. Modena 3, 83 (1948)Google Scholar
  24. 24.
    C.I. Christov, Mech. Res. Commun. 36, 481 (2009)CrossRefGoogle Scholar
  25. 25.
    N. Muhammad, S. Nadeem, T. Mustafa, Results Phys. 7, 862 (2017)ADSCrossRefGoogle Scholar
  26. 26.
    R. Malik, M. Khan, A. Shafiq, M. Mushtaq, M. Hussain, Results Phys. 7, 1232 (2017)ADSCrossRefGoogle Scholar
  27. 27.
    T. Hayat, F. Haider, T. Muhammad, A. Alsaedi, Results Phys. 7, 2663 (2017)ADSCrossRefGoogle Scholar
  28. 28.
    M. Waqas, T. Hayat, S.A. Shehzad, A. Alsaedi, Results Phys. 8, 908 (2018)ADSCrossRefGoogle Scholar
  29. 29.
    R. Malik, M. Khan, Results Phys. 8, 64 (2018)ADSCrossRefGoogle Scholar
  30. 30.
    A. Naseem, A. Shafiq, L. Zhao, M.U. Farooq, Results Phys. 9, 961 (2018)ADSCrossRefGoogle Scholar
  31. 31.
    M. Khan, A. Shahid, M.Y. Malik, T. Salahuddin, J. Mol. Liq. 251, 7 (2018)CrossRefGoogle Scholar
  32. 32.
    S.J. Liao, Homotopy Analysis Method in Non-Linear Differential Equations (Springer and Higher Education Press, Heidelberg, 2012)Google Scholar
  33. 33.
    S.J. Liao, Advances in the Homotopy Analysis Method (World Scientific, 2014)Google Scholar
  34. 34.
    N.A. Demekhina, G.S. Karapetyan, V. Guimarães, Eur. Phys. J. Plus 128, 28 (2013)CrossRefGoogle Scholar
  35. 35.
    T. Hayat, A. Naseem, M. Farooq, A. Alsaedi, Eur. Phys. J. Plus 128, 158 (2013)CrossRefGoogle Scholar
  36. 36.
    J. Sui, L. Zheng, X. Zhang, G. Chen, Int. J. Heat Mass Transfer 85, 1023 (2015)CrossRefGoogle Scholar
  37. 37.
    M. Waqas, T. Hayat, M. Farooq, S.A. Shehzad, A. Alsaedi, J. Mol. Liq. 220, 642 (2016)CrossRefGoogle Scholar
  38. 38.
    T. Hayat, S. Qayyum, M. Imtiaz, A. Alsaedi, Results Phys. 7, 126 (2017)ADSCrossRefGoogle Scholar
  39. 39.
    T. Hayat, M. Javed, M. Imtiaz, A. Alsaedi, Eur. Phys. J. Plus 132, 146 (2017)CrossRefGoogle Scholar
  40. 40.
    T. Hayat, M.I. Khan, S. Qayyum, A. Alsaedi, Colloids Surf. A: Physicochem. Eng. Aspects 539, 335 (2018)CrossRefGoogle Scholar
  41. 41.
    M.I. Khan, T. Hayat, M.I. Khan, A. Alsaedi, Int. Commun. Heat Mass Transfer 91, 216 (2018)CrossRefGoogle Scholar
  42. 42.
    T.R. Mahapatra, A. Gupta, Heat Mass Transf. 38, 517 (2002)ADSCrossRefGoogle Scholar
  43. 43.
    S. Pop, T. Grosan, I. Pop, Tech. Mech. 25, 100 (2004)Google Scholar
  44. 44.
    P. Sharma, G. Singh, J. Appl. Fluid Mech. 2, 13 (2009)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Sadaf Masood
    • 1
    Email author
  • M. Farooq
    • 1
  • S. Ahmad
    • 1
  • A. Anjum
    • 1
  • N. A. Mir
    • 1
  1. 1.Department of MathematicsRiphah International UniversityIslamabadPakistan

Personalised recommendations