Skip to main content
SpringerLink
Log in

Flow of carbon nanotubes suspended nanofluid in stretchable non-parallel walls

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Analysis of the carbon nanotubes suspended nanofluids in a channel with non-parallel stretchable walls is presented. Water is taken as the base fluid for the analysis. The governing partial differential equations governing the flow are transformed to a set of nonlinear ordinary differential equations. Solution of the problem is obtained using a numerical scheme as well as an analytical procedure called the differential transform method. Two types of CNTs called the single-walled carbon nanotubes and multi-walled carbon nanotubes are considered for the analysis. To examine the influence of involved parameters on velocity and temperature profiles, graphical analysis is carried out coupled with comprehensive discussions. The expressions for skin friction coefficient and the Nusselt number are formulated, and variations in these two for different values of parameters are presented graphically. Results obtained in this study are compared with some of the already existing results in the literature and found to be in exceptional agreement.

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
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34
Fig. 35
Fig. 36
Fig. 37

Similar content being viewed by others

References

  1. Choi SUS (1995) Enhancing thermal conductivity of fluids with nanoparticle. In: Siginer DA, Wang HP (eds) Developments and applications of non-newtonian flows, ASME FED, vol 231/MD-vol 66, pp 99–105

  2. Choi SUS, Zhang ZG, Yu W, Lockwood FE, Grulke EA (2001) Anomalously thermal conductivity enhancement in nanotube suspensions. Appl Phys Lett 79:2252–2254

    Article  Google Scholar 

  3. Buongiorno J (2006) Convective transport in nanofluids. ASME J Heat Transfer 128:240–250

    Article  Google Scholar 

  4. Hamilton RL, Crosser OK (1962) Thermal conductivity of heterogeneous two component systems. Ind Eng Chem Fundam 1(3):187–191

    Article  Google Scholar 

  5. Maxwell JC (1904) Electricity and magnetism, 3rd edn. Clarendon, Oxford

    Google Scholar 

  6. Xue Q (2005) Model for thermal conductivity of carbon nanotube-based composites. Phys B 368:302–307

    Article  Google Scholar 

  7. Khan WA, Pop I (2010) Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf 53:2477–2483

    Article  Google Scholar 

  8. Sheikholeslami M, Hatami M, Ganji DD (2014) Nanofluid flow and heat transfer in a rotating system in the presence of a magnetic field. J Mol Liq 190:112–120

    Article  Google Scholar 

  9. Sheikholeslami M, Ellahi R (2014) A study of natural convection heat transfer in a nanofluid filled enclosure with elliptic inner cylinder. Int J Numer Methods Heat Fluid Flow 24(8):1906–1927

    Article  Google Scholar 

  10. Nadeem S, Haq RU (2013) Effect of thermal radiation for megnetohydrodynamic boundary layer flow of a nanofluid past a stretching sheet with convective boundary conditions. J Comput Theor Nanosci 11:32–40

    Article  Google Scholar 

  11. Ellahi R, Hassan M, Zeeshan A (2015) Shape effects of nanosize particles in Cu–H2O nanofluid on entropy generation. Int J Heat Mass Transf 81:449–456

    Article  Google Scholar 

  12. Mohyud-Din ST, Khan U, Bin-Mohsin B (2016) Numerical investigation of MHD flow and heat transfer of copper-water nanofluid in a channel with non-parallel walls considering different shapes of nanoparticles. Adv Mech Eng 8(3):1–9

    Article  Google Scholar 

  13. Anwar MI, Sharidan S, Khan I, Salleh MZ (2014) Magnetohydrodynamic flow of a nanofluid over a nonlinearly stretching sheet. Indian J Chem Technol 21:199–204

    Google Scholar 

  14. Khalid A, Khan I, Shafie S (2015) Exact solutions for free convection flow of nanofluids with ramped wall temperature. Eur Phys J Plus 130(57). doi:10.1140/epjp/i2015-15057-9

  15. Mabood F, Khan WA, Ismail AIM (2015) MHD boundary layer flow and heat transfer of nanofluids over a nonlinear stretching sheet: a numerical study. J Magn Magn Mater 374:569–576

    Article  Google Scholar 

  16. Ul Haq R, Nadeem S, Khan ZH, Noor NFM (2015) Convective heat transfer in MHD slip flow over a stretching surface in the presence of carbon nanotubes. Phys B 457:40–47

    Article  Google Scholar 

  17. Rashidi MM, Ganesh NV, Abdul Hakeem AK, Ganga B (2014) Buoyancy effect on MHD flow of nanofluid over a stretching sheet in the presence of thermal radiation. J Mol Liq 198:234–238

    Article  Google Scholar 

  18. Khan U, Mohyud-Din ST, Mohsin BB (2016) Convective heat transfer and thermo-diffusion effects on flow of nanofluid towards a permeable stretching sheet saturated by a porous medium. Aerosp Sci Technol 50:196–203

    Article  Google Scholar 

  19. Jeffery GB (1915) The two-dimensional steady motion of a viscous fluid. Phil Mag 6:455–465

    Article  Google Scholar 

  20. Hamel G (1916) Spiralförmige Bewgungen Zäher Flüssigkeiten. Jahresber Deutsch Math Verein 25:34–60

    MATH  Google Scholar 

  21. Motsa SS, Sibanda P, Awad FG, Shateyi S (2010) A new spectral-homotopy analysis method for the MHD Jeffery–Hamel problem. Comput Fluids 39:1219–1225

    Article  MathSciNet  Google Scholar 

  22. Sheikholeslami M, Ganji DD, Ashorynejad HR, Rokni HB (2012) Analytical investigation of Jeffery–Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method. Appl Math Mech Engl Ed 33:25–36

    Article  MathSciNet  Google Scholar 

  23. Dorrepaal JM (1993) Slip flow in converging and diverging channels. J Eng Math 27:343–356

    Article  MathSciNet  Google Scholar 

  24. Khan U, Ahmed N, Sikander W, Mohyud-Din ST (2015) A study of velocity and temperature slip effects on flow of water based nanofluids in converging and diverging channels. Int J Appl Comput Math 1(4):569–587

    Article  MathSciNet  Google Scholar 

  25. Asadullah M, Khan U, Manzoor R, Ahmed N, Mohyud-din ST (2013) MHD flow of a Jeffery fluid in converging and diverging channels. Int J Mod Math Sci 6(2):92–106

    Google Scholar 

  26. Hayat T, Nawaz M, Sajid M (2010) Effect of heat transfer on the flow of a second-grade fluid in divergent/convergent channel. Int J Numer Meth Fluids 64:761–776

    MathSciNet  MATH  Google Scholar 

  27. Hatami M, Ganji DD (2014) MHD nanofluid flow analysis in divergent and convergent channels using WRMs and numerical method. Int J Numer Meth Heat Fluid Flow 24(5):1191–1203

    Article  MathSciNet  Google Scholar 

  28. Khan U, Ahmed N, Sikander W, Mohyud-Din ST (2015) A study of velocity and temperature slip effects on flow of water based nanofluids in converging and diverging channels. Int J Appl Comput Math 1(4):569–587

    Article  MathSciNet  Google Scholar 

  29. Khan U, Ahmed N, Mohyud-Din ST (2015) Heat transfer effects on carbon nanotubes suspended nanofluid flow in a channel with non-parallel walls under the effect of velocity slip boundary condition: a numerical study. Neural Comput Appl. doi:10.1007/s00521-015-2035-4

    Article  Google Scholar 

  30. Turkyilmazoglu M (2014) Extending the traditional Jeffery–Hamel flow to stretchable convergent/divergent channels. Comput Fluids 100:196–203

    Article  MathSciNet  Google Scholar 

  31. Mohyud-Din ST, Khan U, Ahmed N, Hassan SM (2015) Magnetohydrodynamic flow and heat transfer of nanofluids in stretchable convergent/divergent channels. Appl Sci 5:1639–1664

    Article  Google Scholar 

  32. Khan WA, Khan ZH, Rahi M (2014) Fluid flow and heat transfer of carbon nanotubes along a flat plate with Navier slip boundary. Appl Nanosci. doi:10.1007/s13204-013-0242-9

    Article  Google Scholar 

  33. Rashidi MM, Erfani E (2011) The modified differential transform method for Investigating nano boundary-layers over stretching surfaces. Int J Numer Meth Heat Fluid Flow 21(7):864–883

    Article  MathSciNet  Google Scholar 

  34. Rashidi MM, Mohimanian Pour SA (2010) Analytic solution of steady three-dimensional problem of condensation film on inclined rotating disk by differential transform method. Math Probl Eng 2010:1–15

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt, Pakistan

    Umar Khan, Naveed Ahmed, Syed Tauseef Mohyud-Din & Waseem Sikander

Authors
  1. Umar Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Naveed Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Syed Tauseef Mohyud-Din
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Waseem Sikander
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Syed Tauseef Mohyud-Din.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khan, U., Ahmed, N., Mohyud-Din, S.T. et al. Flow of carbon nanotubes suspended nanofluid in stretchable non-parallel walls. Neural Comput & Applic 30, 2859–2871 (2018). https://doi.org/10.1007/s00521-017-2891-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-017-2891-1

Keywords

Search

Navigation