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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

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Abstract

The present article is dedicated to analyze the flow and heat transfer of carbon nanotube (CNT)-based nanofluids under the effects of velocity slip in a channel with non-parallel walls. Water is taken as a base fluid, and two forms of CNTs are used to perform the analysis, namely the single- and multi-walled carbon nanotubes (SWCNTs and MWCNTs, respectively). Both the cases of narrowing and widening channel are discussed. The equations governing the flow are obtained by using an appropriate similarity transform. Numerical solution is obtained by using a well-known algorithm called Runge–Kutta–Fehlberg method. The influence of involved parameters on dimensionless velocity and temperature profiles is displayed graphically coupled with comprehensive discussions. Also, to verify the numerical results, a comparative analysis is carried out that ensures the authenticity of the results. Variation of skin friction coefficient and the rate of heat transfer at the walls are also performed. Some already existing solutions of the particular cases of the same problem are also verified as the special cases of the solutions obtained here.

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References

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

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  3. Goldstein S (1938) Modern developments in fluid mechanics. Clarendon Press, Oxford

    Google Scholar 

  4. Rosenhead L (1940) The steady two-dimensional radial flow of viscous fluid between two inclined plane walls. Proc R Soc A 175:436–467

    Article  MATH  Google Scholar 

  5. Fraenkel LE (1962) On the Jeffery–Hamel solutions for flow between plane walls. Proc R Soc A 267:119–138

    Article  MATH  Google Scholar 

  6. Batchelor K (1967) An introduction to fluid dynamics. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  7. Sadri R (1997) Channel entrance flow. PhD thesis, Dept. Mechanical Engineering, the University of Western Ontario

  8. 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 Methods Fluids 64:761–766

    MathSciNet  MATH  Google Scholar 

  9. 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 

  10. 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

  11. 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 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  16. 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 

  17. 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)

  18. Ali F, Khan I, Ulhaq S, Mustapha N, Shafie S (2012) Unsteady magnetohydrodynamic oscillatory flow of viscoelastic fluids in a porous channel with heat and mass transfer. J Phys Soc Jpn 81(6)

  19. 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 

  20. Sheikholeslami M, Ganji DD, Javed MY, Ellahi R (2015) Effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two phase model. J Magn Magn Mater 374:36–43

    Article  Google Scholar 

  21. 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 

  22. Khan U, Ahmed N, Khan SIU, Mohyud-din ST (2014) Thermo-diffusion and MHD effects on stagnation point flow towards a stretching sheet in a nanofluid. Propuls Power Res 3(3):151–158

    Article  Google Scholar 

  23. Ellahi R, Hameed M (2012) Numerical analysis of steady flows with heat transfer, MHD and nonlinear slip effects. Int J Numer Methods Heat Fluid Flow 22(1):24–38

    Article  Google Scholar 

  24. Sheikholeslami M, Ellahi R, Hassan M, Soleimani S (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 

  25. Nawaz M, Zeeshan A, Ellahi R, Abbasbandy S, Rashidi S (2015) Joules heating effects on stagnation point flow over a stretching cylinder by means of genetic algorithm and Nelder–Mead method. Int J Numer Methods Heat Fluid Flow 25(3):665–684

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  27. 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  MATH  Google Scholar 

  28. Mohyud-Din ST, Khan U, Ahmed N, Sikander W (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. doi:10.1007/s40819-015-0032-z

    MathSciNet  Google Scholar 

  29. Ganji DD, Hatami M (2014) Three weighted residual methods based on Jeffery–Hamel flow. Int J Numer Methods Heat Fluid Flow 24(5):1191–1203

    Article  MathSciNet  Google Scholar 

  30. Iijima S (1991) Helical microtubules of graphitic carbon. Nature 354:56–58

    Article  Google Scholar 

  31. Endo M, Hayashi T, Kim YA, Terrones M, Dresselhaus MS (2004) Applications of carbon nanotubes in the twenty-first century. Philos Trans R Soc Lond A 362:2223−2238

    Article  Google Scholar 

  32. Saito R, Dresselhaus G, Dresselhaus MS (2001) Physical properties of carbon nanotubes. Imperial College Press, Singapore

    MATH  Google Scholar 

  33. Murshed SM, Nieto de Castro CA, Lourenço MJV, Lopes MLM, Santos FJV (2011) A review of boiling and convective heat transfer with nanofluids. Renew Sustain Energy Rev 15:2342–2354

    Article  Google Scholar 

  34. Khan U, Ahmed N, Zaidi ZA, Asadullah M, Mohyud-Din ST (2015) Effects of velocity slip and temperature jump on Jeffery Hamel flow with heat transfer. Eng Sci Technol. doi:10.1016/j.jestch.2014.09.001

    Google Scholar 

  35. Khan WA, Khan ZH, Rahi M 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

  36. Ul R, Haq S, Nadeem ZH, Khan NFM (2015) Noor, 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 

  37. Akbar NS, Butt AW (2014) CNT suspended nanofluid analysis in a flexible tube with ciliated walls. Eur Phys J Plus 129(8):1–10

    Google Scholar 

  38. Motsa SS, Sibanda P, Marewo GT (2012) On a new analytical method for flow between two inclined walls. Numer Algorithms 61:499–514

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors are grateful to the anonymous reviewers for their comments and suggestions that really helped in improving the quality of the article.

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Authors and Affiliations

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

    Umar Khan, Naveed Ahmed & Syed Tauseef Mohyud-Din

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  1. Umar Khan
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  2. Naveed Ahmed
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  3. Syed Tauseef Mohyud-Din
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Correspondence to Umar Khan.

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Khan, U., Ahmed, N. & Mohyud-Din, S.T. 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 & Applic 28, 37–46 (2017). https://doi.org/10.1007/s00521-015-2035-4

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  • DOI: https://doi.org/10.1007/s00521-015-2035-4

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