Skip to main content
Log in

MHD Carbon Nanotubes Gravity-Driven Flow Along a Thermal Sensitive Porous Surface

  • Research Article-Mechanical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

The main focus of this mathematical study is to explore the gravity-driven flow of Carbon (single and multi) nanotubes influenced by applied magnetic field towards a vertical thermal sensitive porous sheet. Moreover, heat transfer of nanofluid flow is explored taking into the account viscous dissipation and joule heating effect. The physical flow problem is mathematically modeled in Cartesian coordinate system. The coupled system of nonlinear partial differential equations is reduced to the ordinary differential equations system by implementing similarity analysis. Computational software MATLAB built in routine Bvp4c is employed to compute numerical solutions for assisting flow \((\sigma < 0)\) as well as opposing flow \((\sigma > 0)\). It is concluded that MWCNTs gives promising results in case of favorable buoyancy force. Moreover, presence of CNTs along with Biot number contribute to upsurge fluid temperature whereas thermal radiation influence fluid temperature in an opposite manner.

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.

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

Similar content being viewed by others

References

  1. Fulford, G.D.: The flow of liquids in thin films. Adv. Chem. Eng. 5, 151 (1964)

    Article  Google Scholar 

  2. Pop, I.; Watanabe, T.; Konishi, H.: Gravity-drive laminar film flow along a vertical wall with surface mass transfer. Int. Comm. Heat Mass Trans. 23, 687–695 (1996)

    Article  Google Scholar 

  3. Andersson, H.I.: Gravity-driven film flow with variable physical properties. Phys. Fluids 18, 83602 (2006)

    Article  Google Scholar 

  4. Liu, I.C.; Andersson, H.I.: Heat transfer in a liquid film on an unsteady stretching sheet. Int. J. Therm. Sci. 47, 766–772 (2008)

    Article  Google Scholar 

  5. Raees, A.; Wang, R.Z.; Xu, H.: A homogeneous-heterogeneous model for mixed convection in gravity-driven film flow of nanofluids. Int. Commun. Heat Mass Transf. 95, 19–24 (2018)

    Article  Google Scholar 

  6. Pop, I.; Ingham, D.B.; Lesnic, D.: Conjugate film flow down a heated vertical wall. J. Appl. Math. Mech. 77, 151–154 (1997)

    MathSciNet  MATH  Google Scholar 

  7. Huppert, H.E.; Woods, A.W.: Gravity-driven flows in porous layers. J. Fluid Mech. 292, 55–69 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  8. Andersson, H.I.; Dahl, E.N.: Gravity-driven flow of a viscoelastic liquid film along a vertical wall. J. Phys. D: Appl. Phys. 32, 1557 (1999)

    Article  Google Scholar 

  9. Wojnar, R.; Bielski, W.: Gravity driven flow past the bottom with small waviness. Modern Prob. Appl. Analy. 1, 181–202 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ullah, N.; Nadeem, S.; Saleem, A.: Impact of gravity-induced and Fourier’s heat flux on the nano-film flow over thermal sensitive surface. Appl. Nanosci. 10, 5253–5263 (2020)

    Article  Google Scholar 

  11. Choi, S.U.S.; Eastman, J.A.: Enhancing thermal conductivity of fluids with nanoparticles. In: The Proceedings of the 1995 ASME Int. Mech. Eng. Congress Exposition, ASME, San Francisco, USA, 1995, 99–105. FED 231/MD 66.

  12. Buongiorno, J.: Convective transport in nanofluids. J. Heat Transfer 128, 240–250 (2005)

    Article  Google Scholar 

  13. Raees, A.; Xu, H.; Sun, Q.; Pop, I.: Mixed convection in gravity driven nano-liquid film containing both nanoparticles and gyrotactic microorganisms. Appl. Math. Mech. 36, 163–178 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  14. Xu, H.; Pop, I.; You, X.C.: Flow and heat transfer in a nano-liquid film over an unsteady stretching surface. Int. J. Heat Mass Transf. 60, 646–652 (2013)

    Article  Google Scholar 

  15. Hsiao, K.L.: Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet. Appl. Thermal Engg. 98, 850–861 (2016)

    Article  Google Scholar 

  16. Lin, Y.; Zheng, L.; Zhang, X.; Ma, L.; Chen, G.: MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation. Int. J. Heat Mass Transf. 84, 903–911 (2015)

    Article  Google Scholar 

  17. Rahman, M.M.; Eltaye, I.A.: Radiative heat transfer in a hydromagnetic nanofluid past a non-linear stretching surface with convective boundary condition. Meccanica 48, 601–615 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Masuda, H.; Ebata, A.; Teramae, K.: Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles: Dispersion of Al2O3, SiO2 and TiO2 ultra-fine particles. Netsu Bussei 7, 227–233 (1993)

    Article  Google Scholar 

  19. Nadeem, S.; Ahmed, Z.; Saleem, S.: Carbon nanotubes effects in magneto nanofluid flow over a curved stretching surface with variable viscosity. Microsyst. Technol. 25, 2881–2888 (2019)

    Article  Google Scholar 

  20. Oke, A.S.; Mutuku, W.N.; Kimathi, M.; Animasaun, I.L.: Coriolis effects on MHD Newtonian flow over a rotating non-uniform surface. J. Mech. Eng. Sci. 1, 1–13 (2020)

    Google Scholar 

  21. Oke, A.S.; Animasaun, I.L.; Mutuku, W.N.; Kimathi, M.; Shah, N.A.; Saleem, S.: Significance of Coriolis force, volume fraction, and heat source/sink on the dynamics of water conveying 47nm alumina nanoparticles over a uniform surface, Chinese. J. Phys. 71, 716–727 (2021)

    Google Scholar 

  22. Oke, A.S.: Coriolis effects on MHD flow of MEP fluid over a non-uniform surface in the presence of thermal radiation. Int. Comm. Heat Mass Transf. 129, 105695 (2021)

    Article  Google Scholar 

  23. Oke, A.S.; Mutuku, W.N.: Significance of viscous dissipation on MHD Eyring-Powell flow past a convectively heated stretching sheet, Pramana. J. Phys. 95, 119–206 (2021)

    Google Scholar 

  24. Hayat, T.; Nadeem, S.; Khan, A.U.: Numerical analysis of Ag-CuO/ water rotating hybrid nanofluid with heat generation/absorption. Can. J. Phys. 97, 644–650 (2018)

    Article  Google Scholar 

  25. Cortell, R.: Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet. Phys. Lett. A 372, 631–636 (2008)

    Article  MATH  Google Scholar 

  26. Bhatti, M.M.; Zeeshan, A.; Bashir, F.; Sait, S.M.; Ellahi, R.: Sinusoidal motion of small particles through a Darcy- Brinkmann-Forchheimer microchannel filled with non-Newtonian fluid under electro-osmotic forces. J. Taibah Uni. Sci. 15, 514–529 (2021)

    Article  Google Scholar 

  27. Bhatti, M.M.; Zeeshan, A.; Asif, M.A.; Ellahi, R.; Sait, S.M.: Non-uniform pumping flow model for the couple stress particle-fluid under magnetic effects. Chem. Eng. Commun. 1, 1–12 (2021)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. N. Maraj.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maraj, E.N., Bibi, A., Ijaz, S. et al. MHD Carbon Nanotubes Gravity-Driven Flow Along a Thermal Sensitive Porous Surface. Arab J Sci Eng 47, 15875–15885 (2022). https://doi.org/10.1007/s13369-022-06775-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-022-06775-9

Keywords

Navigation