MHD Three Dimensional Darcy-Forchheimer Flow of a Nanofluid with Nonlinear Thermal Radiation

  • Nainaru Tarakaramu
  • P. V. Satya NarayanaEmail author
  • B. Venkateswarlu
Conference paper
Part of the Trends in Mathematics book series (TM)


The numerical analysis of 3D magnetohydrodynamic Darcy-Forchheimer nanofluid flow with nonlinear thermal radiation is explored. Utilizing suitable similarity transformations, the governing PDEs are transformed into nonlinear ODEs. The resulting equations are then solved numerically by the most robust shooting technique with RK method of fourth order. The effect of various parameters like radiation, temperature ratio, Forchheimer and porosity parameters on θ(η) and ϕ(η), skin friction coefficient, and rate of heat transfer is discussed graphically. It is observed that the heat transfer rate reduces and skin friction coefficient increases for the rise of Fr and λ.


MHD Nanofluid Nonlinear thermal radiation Darcy-Forchheimer porous medium 


  1. 1.
    Choi, S.U.S.: Enhancing thermal conductivity of fluids with nanoparticles, USA ASME, FED 231/MD 66, 99–105 (1995).Google Scholar
  2. 2.
    Wang, X., Mujumdar, A. S.: A review on nanofluids part-I: Theoretical and numerical investigations. Braz. J. Chem. Eng. 24, 613–530 (2008).CrossRefGoogle Scholar
  3. 3.
    Wang, X., Mujumdar, A. S.: A review on nanofluids part-II: Experiments and applications. Braz. J. Chem. Eng. 24, 613–530 (2008).CrossRefGoogle Scholar
  4. 4.
    Ahn, H. S., Kim, M. H.: A review on critical heat flux enhancement with nanofluids and surface modification. J. Heat Transfer 134, 1–14 (2012).CrossRefGoogle Scholar
  5. 5.
    JCai, J., Hu, X. B., Xiao, B., Zhou, Y., Wei, W.: Recent developments on fractal based approaches to nanofluids and nanoparticle aggregation. Int. J. Heat Mass Transfer 105, 623–637 (2017).CrossRefGoogle Scholar
  6. 6.
    Kakac, S., Pramuanjaroenkij, A.: Review convective heat transfer enhancement with nanofluids. Int. J. Heat Mass Transfer 52, 3187–96 (2009).CrossRefGoogle Scholar
  7. 7.
    Das, K.: Flow and heat transfer characteristics of nanofluids in a rotating frame, Alexandria Eng. J. 1–9 (2014) Scholar
  8. 8.
    Satya Narayana, P. V., Akshit, S. M., Ghori, J. P., Venkateswarlu, B.: Thermal radiation effects on an unsteady MHD nanofluid flow over a stretching sheet with non-uniform heat source/sink. J. Nanofluids, 8, 1–5 (2017).Google Scholar
  9. 9.
    Satya Narayana, P. V.: Lie group analysis for the flow and heat transfer of a nanofluid over a stretching sheet with viscous dissipation, J. Nanofluids, 6, 1181–1187 (2017).CrossRefGoogle Scholar
  10. 10.
    Darcy, H.: Les Fontaines Publiques De La Ville De Dijon, Victor Dalmont, Paris, 1856.Google Scholar
  11. 11.
    Forchheimer, P.: Wasserbewegung durch boden, Zeitschrift, Ver D. Ing. 45, 1782–1788 (1901).Google Scholar
  12. 12.
    Khan, I.M., Hayat, T., Alsaedi, A.: Numerical analysis for Darcy-Forchheimer flow in presence of heterogeneous-homogeneous reactions. Results Phys. 7(7), 2644–2650 (2017).CrossRefGoogle Scholar
  13. 13.
    Muhammad, T., Alsaedi, A., Hayat, T., Ali Shehzad, S.: A revised model for Darcy-Forchhiemer three-dimensional flow of nanofluid subject to convective boundary condition. Results Phys. 7, 2791–2797 (2017).CrossRefGoogle Scholar
  14. 14.
    Hayat, T., Shah, F., Alsaedi, A., Hussain, Z.: Outcome of homogeneous and heterogeneous reactions in Darcy-Forchheimer flow with nonlinear thermal radiator and convection condition. Results Phys. 7, 2497–2505 (2017).CrossRefGoogle Scholar
  15. 15.
    Hayat, T., Shah, F., Alsaedi, A., Ijaz Khan, M.: Development of homogeneous/heterogeneous reaction in flow based through non-Darcy Forchheimer medium. J. Theoretical Comp. Chemistry, 16, 5, 1–21 (2017).CrossRefGoogle Scholar
  16. 16.
    Mahammad, T., Alsaedi, A., Ali Shehzad, S., Hayat, T.: A revised model for Darcy-Forchhiemer flow of Maxwell nanofluid subject to convective boundary condition. Chi. J. Phys., 55(9), 63–976 (2017).Google Scholar
  17. 17.
    Durga Prasad, P. Varma, S. V. K. Kiran Kumar, R. V. M. S. S.: MHD free convection and heat transfer enhancement of nanofluids through a porous medium in the presence of variable heat flux. J. Nanofluids, 6, 1–9 (2017).CrossRefGoogle Scholar
  18. 18.
    Gupta, S., Sharma, K.: Numerical simulation for magnetohydrodynamic three dimensional flow of Casson nanofluid with convective boundary conditions and thermal radiation. Eng. Comp. 1–32 (2017).Google Scholar
  19. 19.
    Yousif, M. A., Mahmood, B. A., Rashidi, M. M.: Using differential transform method and Pade approximation for solving MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet. J. Math. Computer Sci., 17, 169–178 (2017).CrossRefGoogle Scholar
  20. 20.
    Satya Narayana, P. V., Tarakaramu, N., Akshit, M.S., Jatin, Ghori, P.: MHD flow and heat transfer of an eyring - powell fluid over a linear stretching sheet with viscous dissipation - a numerical study, Frontiers Heat Mass Transfer, 9(9), 1–5 (2.017).Google Scholar
  21. 21.
    Tarakaramu, N., Satya Narayan, P. V.: Unsteady MHD nanofluid flow over a stretching sheet with chemical reaction, IOP Conf. Series: Mater. Science Eng., 263, 1–8 (2017) Scholar
  22. 22.
    Brewster, M. Q.: Thermal Radiative Transfer Properties, Wiley, New York, (1972).Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Nainaru Tarakaramu
    • 1
  • P. V. Satya Narayana
    • 1
    Email author
  • B. Venkateswarlu
    • 2
  1. 1.Department of Mathematics, School of Advanced SciencesVellore Institute of TechnologyVelloreIndia
  2. 2.Department of MathematicsMadanapalli Institute of Technology & ScienceMadanapalliIndia

Personalised recommendations