Skip to main content
Log in

Unsteady boundary layer flow of a nanofluid over a stretching sheet with variable fluid properties in the presence of thermal radiation

  • Published:
Thermophysics and Aeromechanics Aims and scope

Abstract

In this paper, we investigated numerically an unsteady boundary layer flow of a nanofluid over a stretching sheet in the presence of thermal radiation with variable fluid properties. Using a set of suitable similarity transformations, the governing partial differential equations are reduced into a set of nonlinear ordinary differential equations. System of the nonlinear ordinary differential equations are then solved by the Keller-box method. The physical parameters taken into consideration for the present study are: Prandtl number Pr, Lewis number Le, Brownian motion parameter N b, thermophoresis parameter N t, radiation parameter N r, unsteady parameter M. In addition to these parameters, two more new parameters namely variable thermophoretic diffusion coefficient parameter e and variable Brownian motion diffusion coefficient parameter β have been introduced in the present study. Effects of these parameters on temperature, volume fraction of the nanoparticles, surface heat and mass transfer rates are presented graphically and discussed briefly. To validate our method, we have compared the present results with some previously reported results in the literature. The results are found to be in a very good agreement.

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.

Similar content being viewed by others

References

  1. W. J. Minkowycz, E. M. Sparrow, and J. P. Abrahim, Advances in numerical heat transfer, Nanoparticle Heat Transfer and Fluid Flow. CRC Press, Boca Raton, 2013.

    Google Scholar 

  2. S. U. Choi and J. A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, ASME Intern. Mechanical Engng Congress and Exposition, San Francisco, CA, 1995.

    Google Scholar 

  3. T. C. Chiam, Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet, Acta Mechanica, 1998, Vol. 129, P. 63–72.

    Article  MATH  Google Scholar 

  4. X. Wang, X. Xu, and S. U. S. Choi, Thermal conductivity of nanoparticle fluid mixture, J. Thermophysics and Heat Transfer, 1999, Vol. 13, No. 4, P. 474–480.

    Article  Google Scholar 

  5. M. J. Uddin, I. Pop, and A. M. Ismail, Free convection boundary layer flow of a nanofluid from a convectively heated vertical plate with linear momentum slip boundary condition, Sains Malaysiana, 2012, Vol. 41, No. 11, P. 1475–1482.

    MATH  Google Scholar 

  6. M. H. M. Yasin, N. M. Arifin, R. Nazar, F. Ismail, and I. Pop, Mixed convection boundary layer flow on a vertical surface in a porous medium saturated by a nanofluid with suction or injection, J. Mathematics and Statistics, 2013, Vol. 9, No. 2, P. 119–128.

    Article  Google Scholar 

  7. S. P. A. Devi and A. Julie, Laminar boundary layer flow of nanofluid over a flat plate, Int. J. Appl. Math and Mech., 2011, Vol. 7, No. 6, P. 52–71.

    MATH  Google Scholar 

  8. M. Ferdows, M. S. Khan, M. A. Mahmud, and S. Shuyu, MHD mixed convective boundary layer flow of a nanofluid through a porous medium due to an exponentially stretching sheet, Mathematical Problems in Engng, 2012, Vol. 2012, P. 408528–1-408528-21.

    MathSciNet  MATH  Google Scholar 

  9. R. S. R. Gorla and C. Ali, Natural convective boundary layer flow over a non isothermal vertical plate embedded in a porous medium saturated with a nanofluid, Nanoscale and Microscale Thermo-Physical Engng., 2011, Vol. 15, P. 81–94.

    Article  Google Scholar 

  10. F. M. Hady, F. S. Ibrahim, S. M. Abdel-Gaied, and R. E. Mohamed, Radiation effect on viscous flow of a nanofluid and heat transfer over a non-linearly stretching sheet, Nanoscale Research Letters, 2012, Vol. 7, P. 229–242.

    Article  ADS  Google Scholar 

  11. N. Bachok, A. Ishak, and I. Pop, Boundary layer flow over a moving surface in a nanofluid with suction or injection, Acta Mech. Sin., 2012, Vol. 28, No. 1, P. 34–40.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. J. Buongiorno, Convective transport in nanofluids, J. Heat Transfer, 2006, Vol. 28, P. 240–250.

    Article  Google Scholar 

  13. P. K. Kameswaran, P. Sibanda, and A. S. N. Murti, Nanofluid flow over a permeable surface with convective boundary conditions and radiative heat transfer, Mathematical Problems in Engng., 2013, Article ID 201219.

    Google Scholar 

  14. W. A. Khan and I. Pop, Boundary-layer flow of a nanofluid past a stretching sheet, Int. J. Heat and Mass Transfer, 2010, Vol. 53, P. 2477–2483.

    Article  MATH  Google Scholar 

  15. W. A. Khan and A. Aziz, Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux, Int. J. Thermal Sci., 2011, Vol. 50, P. 1207–1214.

    Article  Google Scholar 

  16. O. D. Makinde and A. Aziz, Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, Int. J. Thermal Sci., 2011, Vol. 50, P. 1326–1332.

    Article  Google Scholar 

  17. S. Nadeem and C. Lee, Boundary layer flow of nanofluid over an exponentially stretching surface, Nanoscale Research Letters, 2012, Vol. 7, P. 94–97.

    Article  ADS  Google Scholar 

  18. W. Ibrahim and B. Shanker, MHD boundary layer flow and heat transfer of a nanofluid past a permeable stretching sheet with velocity, thermal and solutal slip boundary conditions, Computers & Fluids, 2013, Vol. 75, P. 1–10.

    Article  MathSciNet  MATH  Google Scholar 

  19. S. Nadeem, R. U. Haq, N. S. Akbar, C. Lee, and Z. H. Khan, Numerical study of boundary layer flow and heat transfer of Oldroyd-B nanofluid towards a stretching sheet, PLoS ONE, 2013, No. 8, P. e69811.

    Article  ADS  Google Scholar 

  20. A. Remeli, N. M. Arifin, R. Nazar, F. Ismail, and I. Pop, Marangoni-driven boundary-layer flow in a nanofluid with suction and injection, World Applied Sci. J., 2012, Vol. 17, P. 21–26.

    Google Scholar 

  21. W. Ibrahim and B. Shanker, Boundary layer flow and heat transfer of nanofluid over a vertical plate with convective surface boundary condition, J. Fluids Engng, 2012, Vol. 134, P. 1–8.

    Article  Google Scholar 

  22. S. Kakac and A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, Int. J. Heat and Mass Transfer, 2009, Vol. 52, P. 3187–3196.

    Article  MATH  Google Scholar 

  23. D. Anilkumar, Nonsimilar solutions for unsteady mixed convection from a moving vertical plate, Communications in Nonlinear Sci. and Numerical Simulation, 2011, Vol. 16, P. 3147–3157.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. M. Kumari and G. Nath, Unsteady MHD mixed convection flow over an impulsively stretched permeable vertical surface in a quiescent fluid, Int. J. Non-Linear Mechanics, 2010, Vol. 45, P. 310–319.

    Article  ADS  Google Scholar 

  25. V. Kumaran, A. V. Kumar, and I. Pop, Transition of MHD boundary layer flow past a stretching sheet, Communications in Nonlinear Sci. and Numerical Simulation, 2010, Vol. 15, P. 300–311.

    Article  ADS  MATH  Google Scholar 

  26. A. Ishak, R. Nazar, and I. Pop, Boundary layer flow and heat transfer over an unsteady stretching vertical surface, Meccanica, 2009, Vol. 44, No. 4, P. 369–375.

    Article  MathSciNet  MATH  Google Scholar 

  27. A. Mahdy, Unsteady mixed convection boundary layer flow and heat transfer of nanofluids due to stretching sheet, Nuclear Engineering and Design, 2012, Vol. 249, P. 248–255.

    Article  Google Scholar 

  28. K. Vajravelu, K. V. Prasad, and N. Chiu-On, Unsteady convective boundary layer flow of a viscous fluid at a vertical surface with variable fluid properties, Nonlinear Analysis: Real World Applications, 2013, Vol. 14, P. 455–464.

    Google Scholar 

  29. A. E. Mohamed, Unsteady mixed convection heat transfer along a vertical stretching surface with variable viscosity and viscous dissipation, J. Egyptian Mathematical Society, 2013.

    Google Scholar 

  30. R. Cortell, Radiation effects in the Blasius flow, Applied Math. and Computation, 2008, Vol. 198, P. 333–338.

    Article  MathSciNet  MATH  Google Scholar 

  31. L. G. Grubka and K. M. Bobba, Heat transfer characteristics of a continuous stretching surface with variable temperature, Trans. ASME. Heat Transfer, 1985, Vol. 107, P. 248–250.

    Article  Google Scholar 

  32. F. M. Ali, R. Nazar, N. M. Arifin, and I. Pop, Mixed convection stagnation-point flow on vertical stretching sheet with external magnetic field, Appl. Math. Mech. Engl. Ed., 2014, Vol. 35, P. 155–166.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mitiku Daba.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Daba, M., Devaraj, P. Unsteady boundary layer flow of a nanofluid over a stretching sheet with variable fluid properties in the presence of thermal radiation. Thermophys. Aeromech. 23, 403–413 (2016). https://doi.org/10.1134/S0869864316030100

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0869864316030100

Keywords

Navigation