CNTS-Water–Based Nanofluid Over a Stretching Sheet

  • Abid Hussanan
  • Ilyas KhanEmail author
  • Mohammad Rahimi Gorji
  • Waqar A. Khan


This article mainly focuses on the energy transfer with the effects of carbon nanotubes (CNTs) of magnetohydrodynamic (MHD) nanofluids flow past a stretching sheet under thermal radiation and Newtonian heating. Single and multi-wall CNTs are considered in water as convectional based fluid. With the help of similarity transformations, the nonlinear ODEs are obtained from system of PDEs. Closed form analytic solutions are obtained for velocity, temperature, and concentration. These solutions are plotted and discussed for pertinent parameters. The results indicate that temperature of CNTs-water–based nanofluid is higher than CNTs-engine oil (or kerosene). Further, heat transfer rate increases due to suspension of CNTs.


MHD flow CNTs Stretching sheet Porous medium Newtonian heating 



strength of magnetic field


species concentration


nanofluid heat capacity


mass diffusivity of base fluid


nanofluid mass diffusivity


heat transfer coefficient




mean absorption coefficient


thermal conductivity of base fluid


carbon nanotubes thermal conductivity


nanofluid thermal conductivity


magnetic parameter


porosity parameter


Prandtl number


radiative heat flux


Schmidt number


temperature of the fluid


ambient temperature



nanofluid thermal diffusivity


conjugate parameter for Newtonian heating


base fluid dynamic viscosity


nanofluid dynamic viscosity


density of base fluid


carbon nanotubes density


nanofluid density


Stefan–Boltzmann constant


electric conductivity of base fluid


carbon nanotubes electric conductivity


nanofluid electric conductivity


dimensionless temperature


dimensionless concentration


nanoparticle volume fraction


Funding Information

The research is supported by China Postdoctoral Science Foundation (Grant No. 2018M643156).


  1. 1.
    Choi, S. (1995). Enhancing thermal conductivity of fluids with nanoparticles in developments and applications of non-Newtonian flows. In D. A. Siginer & H. P. Wang (Eds.), ASME (Vol. 66, pp. 99–105).Google Scholar
  2. 2.
    Pak, B. C. (1998). Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Experimental Heat Transfer: A Journal of Thermal Energy Generation, Transport, Storage, and Conversion, 11, 151–170.CrossRefGoogle Scholar
  3. 3.
    Eastman, J. A., Cho, S. U. S., Li, S., Soyez, G., Thompson, L. J., & Dimelfi, R. J. (1999). Novel thermal properties of nanostructured materials. Journal of Metastable and Nanocrystalline Materials, 2, 629–637.CrossRefGoogle Scholar
  4. 4.
    Qiang, L., & Yimin, X. (2002). Convective heat transfer and flow characteristics of Cu-water nanofluid. Science in China (Series E), 45, 408–416.Google Scholar
  5. 5.
    Xie, H., Lee, H., Youn, W., & Choi, M. (2003). Nanofluids containing multiwalled carbon nanotubes and their enhanced thermal conductivities. Journal of Applied Physics, 94, 4967–4971.CrossRefGoogle Scholar
  6. 6.
    Ding, Y., Alias, H., Wen, D., & Williams, R. A. (2006). Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids). International Journal of Heat and Mass Transfer, 49, 240–250.CrossRefGoogle Scholar
  7. 7.
    Shafahi, M., Bianco, V., Vafai, K., & Manca, O. (2010). An investigation of the thermal performance of cylindrical heat pipes using nanofluids. International Journal of Heat and Mass Transfer, 53, 376–383.CrossRefGoogle Scholar
  8. 8.
    Khan, W. A., Khan, Z. H., & Rahi, M. (2014). Fluid flow and heat transfer of carbon nanotubes along a flat plate with Navier slip boundary. Applied Nanoscience, 4, 633–641.CrossRefGoogle Scholar
  9. 9.
    Akbar, N. S., Raza, M., & Ellahi, R. (2015). Influence of induced magnetic field and heat flux with the suspension of carbon nanotubes for the peristaltic flow in a permeable channel. Journal of Magnetism and Magnetic Materials, 381, 405–415.CrossRefGoogle Scholar
  10. 10.
    Khan, W. A., Culham, R., & Haq, R. U. (2015). Heat transfer analysis of MHD water functionalized carbon nanotube flow over a static/moving wedge. Journal of Nanomaterials, 2015, 1–13.CrossRefGoogle Scholar
  11. 11.
    Ebaid, A., Mutairi, F. A., & Khaled, S. M. (2014). Effect of velocity slip boundary condition on the flow and heat transfer of Cu-water and TiO2-water nanofluids in the presence of a magnetic field. Adv. Math. Phys., 2014, 1–9.CrossRefGoogle Scholar
  12. 12.
    Haroun, N. A., Sibanda, P., Mondal, S., & Motsa, S. S. (2015). On unsteady MHD mixed convection in a nanofluid due to a stretching/shrinking surface with suction/injection using the spectral relaxation method. Boundary Value Problems, 24, 1–17.MathSciNetzbMATHGoogle Scholar
  13. 13.
    Chamkha, A. J., & Ismael, M. A. (2016). Magnetic field effect on mixed convection in lid-driven trapezoidal cavities filled with a Cu–water nanofluid with an aiding or opposing side wall. Journal of Thermal Science and Engineering Applications, 8, 031009–1–12.CrossRefGoogle Scholar
  14. 14.
    Tayebi, T., Chamkha, A. J., Djezzar, M., & Bouzerzour, A. (2017). Natural convective nanofluid flow in an annular space between confocal elliptic cylinders. Journal of Thermal Science and Engineering Applications, 9, 011010–1-9.Google Scholar
  15. 15.
    Ghafouri, A., Salari, M. M., & Jozaei, A. F. (2017). Effect of variable thermal conductivity models on the combined convection heat transfer in a square enclosure filled with a water–alumina nanofluid. Journal of Applied Mechanics and Technical Physics, 58, 103–115.MathSciNetCrossRefGoogle Scholar
  16. 16.
    Abro, K. A., Chandio, A. D., Abro, I. A., & Khan, I. (2018). Dual thermal analysis of magnetohydrodynamic flow of nanofluids via modern approaches of Caputo–Fabrizio and Atangana–Baleanu fractional derivatives embedded in porous medium. Journal of Thermal Analysis and Calorimetry.
  17. 17.
    Abdelsalam, S. I., & Bhatti, M. M. (2018). The impact of impinging TiO2 nanoparticles in Prandtl nanofluid along with endoscopic and variable magnetic field effects on peristaltic blood flow. Multidiscipline Modeling in Materials and Structures, 14(3), 530–548.CrossRefGoogle Scholar
  18. 18.
    Abdelsalam, S. I., & Bhatti, M. M. (2018). The study of non-Newtonian nanofluid with hall and ion slip effects on peristaltically induced motion in a non-uniform channel. RSC Advances, 8, 7904–7915.CrossRefGoogle Scholar
  19. 19.
    Qasim, M., Khan, I., & Shafie, S. (2013). Heat and mass diffusion in nanofluids over a moving permeable convective surface. Mathematical Problems in Engineering, 2013, 1–7.MathSciNetCrossRefGoogle Scholar
  20. 20.
    Anwar, M. I., Khan, I., Hussanan, A., Salleh, M. Z., & Sharidan, S. (2013). Stagnation-point flow of a nanofluid over a nonlinear stretching sheet. World Applied Sciences Journal, 23, 998–1006.Google Scholar
  21. 21.
    Khan, U., Ahmed, N., Asadullah, M., & Mohyud-Din, S. T. (2015). Effects of viscous dissipation and slip velocity on two-dimensional and axisymmetric squeezing flow of Cu-water and Cu-kerosene nanofluids. Propulsion and Power Research, 4, 40–49.CrossRefGoogle Scholar
  22. 22.
    Hussanan, A., Khan, I., Hashim, H., Mohamed, M. K. A., Ishak, N., Sarif, N. M., & Salleh, M. Z. (2016). Unsteady MHD flow of some nanofluids past an accelerated vertical plate embedded in a porous medium. Jurnal Teknologi, 78, 121–126.Google Scholar
  23. 23.
    Hussanan, A., Salleh, M. Z., Khan, I., & Shafie, S. (2017). Convection heat transfer in micropolar nanofluids with oxide nanoparticles in water, kerosene and engine oil. Journal of Molecular Liquids, 229, 482–488.CrossRefGoogle Scholar
  24. 24.
    Abro, K. A., Hussain, M., & Baig, M. M. (2017). An analytic study of molybdenum disulfide nanofluids using the modern approach of Atangana-Baleanu fractional derivatives. The European Physical Journal Plus, 132, 439–1-10.Google Scholar
  25. 25.
    Hussanan, A., Salleh, M. Z., & Khan, I. (2018). Microstructure and inertial characteristics of a magnetite ferrofluid over a stretching/shrinking sheet using effective thermal conductivity model. Journal of Molecular Liquids, 255, 64–75.CrossRefGoogle Scholar
  26. 26.
    Hamad, M. A. A. (2011). Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field. International Communications in Heat and Mass Transfer, 38, 487–492.CrossRefGoogle Scholar
  27. 27.
    Loganathan, P., Chand, P. N., & Ganesan, P. (2013). Radiation effects on an unsteady natural convection flow of a nanofluids past an infinite vertical plate. Nano, 8, 1350001–1350010.CrossRefGoogle Scholar
  28. 28.
    Nandkeolyar, R., Das, M., & Pattnayak, H. (2013). Unsteady hydromagnetic radiative flow of a nanofluid past a flat plate with ramped wall temperature. Journal of Orissa Mathematical Society, 32, 15–30.MathSciNetGoogle Scholar
  29. 29.
    Ebaid, A., & Sharif, M. A. A. (2015). Application of Laplace transform for the exact effect of a magnetic field on heat transfer of carbon nanotubes-suspended nanofluids. Zeitschrift für Naturforschung, 70, 471–475.Google Scholar
  30. 30.
    Turkyilmazoglu, M. (2014). Unsteady convection flow of some nanofluids past a moving vertical flat plate with heat transfer. Journal of Heat Transfer, 136, 031704–031711.CrossRefGoogle Scholar
  31. 31.
    Asma, K., Khan, I., & Shafie, S. (2015). Exact solutions for free convection flow of nanofluids with ramped wall temperature. The European Physical Journal Plus, 130, 1–14.CrossRefGoogle Scholar
  32. 32.
    Merkin, J. H. (1994). Natural convection boundary layer flow on a vertical surface with Newtonian heating. International Journal of Heat and Fluid Flow, 15, 392–398.CrossRefGoogle Scholar
  33. 33.
    Hussanan, A., Khan, I., & Shafie, S. (2013). An exact analysis of heat and mass transfer past a vertical plate with Newtonian heating. Journal of Applied Mathematics, 2013, 1–9.MathSciNetCrossRefGoogle Scholar
  34. 34.
    Hussanan, A., Anwar, M. I., Farhad, A., Khan, I., & Sharidan, S. (2014). Natural convection flow past an oscillating plate with Newtonian heating. Heat Transfer Research, 45, 119–137.CrossRefGoogle Scholar
  35. 35.
    Alkasasbeh, H. T., & Salleh, M. Z. (2014). Numerical solutions of radiation effect on MHD free convection boundary layer flow about a solid sphere with Newtonian heating. Applied Mathematical Sciences, 8, 6989–7000.CrossRefGoogle Scholar
  36. 36.
    Hussanan, A., Ismail, Z., Khan, I., Hussein, A. G., & Shafie, S. (2014). Unsteady boundary layer MHD free convection flow in a porous medium with constant mass diffusion and Newtonian heating. The European Physical Journal Plus, 129, 1–16.CrossRefGoogle Scholar
  37. 37.
    Hussanan, A., Salleh, M. Z., Tahar, R. M., & Khan, I. (2014). Unsteady boundary layer flow and heat transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating. PLoS One, 9, 1–9.CrossRefGoogle Scholar
  38. 38.
    Vafai, K., & Thiyagaraja, R. (1987). Analysis of flow and heat transfer at the interface region of a porous medium. International Journal of Heat and Mass Transfer, 30, 1391–1405.CrossRefGoogle Scholar
  39. 39.
    Komy, S. R., Barakat, E. S. I., & Abdelsalam, S. I. (2012). Hall and porous boundaries effects on peristaltic transport through porous medium of a Maxwell model. Transport in Porous Media, 94, 643–658.MathSciNetCrossRefGoogle Scholar
  40. 40.
    Mekheimer, K. S., Komy, S. R., & Abdelsalam, S. I. (2013). Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel. Chinese Physics B, 22(12), 124702–124701.CrossRefGoogle Scholar
  41. 41.
    Abdelsalam, S. I., & Vafai, K. (2017). Combined effects of magnetic field and rheological properties on the peristaltic flow of a compressible fluid in a microfluidic channel. European Journal of Mechanics - B/Fluids, 65, 398–411.MathSciNetCrossRefGoogle Scholar
  42. 42.
    Elmaboud, Y. A., Abdelsalam, S. I., Mekheimer, K. S., & Vafai, K. (2018). Electromagnetic flow for two-layer immiscible fluids. Engineering Science and Technology, an International Journal.

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Abid Hussanan
    • 1
    • 2
  • Ilyas Khan
    • 3
    Email author
  • Mohammad Rahimi Gorji
    • 4
  • Waqar A. Khan
    • 5
  1. 1.School of Mathematics and StatisticsShenzhen UniversityShenzhenChina
  2. 2.Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong province, College of Optoelectronic EngineeringShenzhen UniversityShenzhenChina
  3. 3.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  4. 4.Department of MathematicsGhent UniversityGhentBelgium
  5. 5.Department of Mechanical Engineering, College of EngineeringPrince Mohammad Bin Fahd UniversityAl KhoberSaudi Arabia

Personalised recommendations