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Convective heat transfer and MHD effects on Casson nanofluid flow over a shrinking sheet

  • Research Article
  • Published:
Central European Journal of Physics

Abstract

Current study examines the magnetohydrodynamic (MHD) boundary layer flow of a Casson nanofluid over an exponentially permeable shrinking sheet with convective boundary condition. Moreover, we have considered the suction/injection effects on the wall. By applying the appropriate transformations, system of non-linear partial differential equation along with the boundary conditions are transformed to couple non-linear ordinary differential equations. The resulting systems of non-linear ordinary differential equations are solved numerically using Runge-Kutta method. Numerical results for velocity, temperature and nanoparticle volume concentration are presented through graphs for various values of dimensionless parameters. Effects of parameters for heat transfer at wall and nanoparticle volume concentration are also presented through graphs and tables. At the end, fluid flow behavior is examined through stream lines. Concluding remarks are provided for the whole analysis.

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References

  1. M. V. Ochoa, Ph. D theses, Aug 2006

  2. S. Nadeem, R. U. Haq, C. Lee, Sci. Iran. 19, 1550 (2012)

    Article  Google Scholar 

  3. S. Nadeem, R. U. Haq, Noreen Sher Akbar, Z.H. Khan, Alex. Eng. J. 52, 577 (2013)

    Article  Google Scholar 

  4. R. Ellahi, A. Riaz, Math. Comp. Mod. 52, 1783 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  5. N. S. Akbar, S. Nadeem, R. Ul Haq, Z. H. Khan, Ind. J. Phy. 87, 1121 (2013)

    Article  Google Scholar 

  6. Sakiadis BC, J. Amer. Ins. Chem. Eng. 7, 26 (1961)

    Article  Google Scholar 

  7. Sakiadis BC, J. Amer. Ins. Chem. Eng. 7, 221 (1961)

    Article  Google Scholar 

  8. F. K. Tsou, E. M. Sparrow, R. J. Goldstein, Inter. J. Heat and Mass Tran. 10, 219 (1967)

    Article  Google Scholar 

  9. L. Crane, Zeit. für Ange. Math. Phy. 21, 645 (1970)

    Article  Google Scholar 

  10. O. D. Makinde, A. Aziz, Int. J. of Therm. Sci. 49, 1813 (2010)

    Article  Google Scholar 

  11. O. D. Makinde, Inter. J. of Phy. Sci. 5, 700 (2010)

    Google Scholar 

  12. S. Nadeem, S. Zaheer, T. Fang, Num. Alg. 57, 187 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  13. E. Magyari, B. Keller, J Phys D: Appl Phys 32, 577 (1999)

    Article  ADS  Google Scholar 

  14. B. Bidin, R. Nazar, Eur J Sci Res. 33, 710 (2009)

    Google Scholar 

  15. MA. El-Aziz, Can. J. Phys. 87, 359 (2009)

    Article  ADS  Google Scholar 

  16. A. Ishak, Sai. Malay. 40, 391 (2011)

    Google Scholar 

  17. X. Q. Wang, A. S. Mujumdar, Int. J. Therm. Sci. 46, 1 (2007)

    Article  MATH  Google Scholar 

  18. S.U.S. Choi, USA, ASME, FED 231/MD 66, 99 (1995)

  19. W.A. Khan, I. Pop, Int. J. Heat Mass Tran. 53, 2477 (2010)

    Article  MATH  Google Scholar 

  20. O. D. Makinde, A. Aziz, Int. J. Therm. Sci. 50, 1326 (2011)

    Article  Google Scholar 

  21. S. Nadeem, C. Lee, Nanosca. Rese. Lett. 94, 7 (2012)

    Google Scholar 

  22. J. Buongiorno, ASME J. Heat transfer, 128, 240 (2006)

    Article  Google Scholar 

  23. W.A. Khan, A. Aziz, Inter. Jour. Therm. Sci. 50, 1207 (2011)

    Article  Google Scholar 

  24. W.A. Khan, A. Aziz, Inter. Jour. Therm. Sci. 50, 2154 (2011)

    Article  Google Scholar 

  25. S. Nadeem, R. U. Haq, J. Aero. Eng. 10.1061 (ASCE) AS.1943-5525.0000299

  26. O. D. Makinde, W. A. Khan, Z. H. Khan, Int. J. Heat Mass Tran. 62, 526 (2013)

    Article  Google Scholar 

  27. W. Ibrahim, O. D. Makinde, Comp. Flu. 86, 433 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  28. W. N. Mutuku-Njane, O. D. Makinde, J. Comp. l Theor. Nano Sci. 11, 667 (2014)

    Article  Google Scholar 

  29. R. U. Haq, Z.H. Khan, W. A. Khan, Phys E: Low-dim. Sys. Nano Str. 63, 215 (2014)

    Article  ADS  Google Scholar 

  30. S. Nadeem, R. U. Haq, Zafar Hayat Khan, Alex. Eng. J. 53, 219 (2014)

    Article  Google Scholar 

  31. P. D. Weidman, D. G. Kubitschek, A. M. J. Davis, Int. J. Eng. Sci. 44, 730 (2006)

    Article  MATH  Google Scholar 

  32. A. Postelnicu, I. Pop, Appl. Math. Comput. 217, 4359 (2011)

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan

    Rizwan Ul Haq & Sohail Nadeem

  2. Mechanical and Materials Engineering, University of Western Ontario, Spencer Engineering Building, Room3055, London, Ontario, Canada

    Rizwan Ul Haq

  3. Department of Mathematics, University of Malakand, Dir (Lower), Khyber Pakhtunkhwa, Pakistan

    Zafar Hayyat Khan

  4. Department of Mathematics, Ondo State University of Science and Technology, Okitipupa, Nigeria

    Toyin Gideon Okedayo

Authors
  1. Rizwan Ul Haq
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  2. Sohail Nadeem
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  3. Zafar Hayyat Khan
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  4. Toyin Gideon Okedayo
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Correspondence to Rizwan Ul Haq.

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Haq, R.U., Nadeem, S., Khan, Z.H. et al. Convective heat transfer and MHD effects on Casson nanofluid flow over a shrinking sheet. centr.eur.j.phys. 12, 862–871 (2014). https://doi.org/10.2478/s11534-014-0522-3

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  • DOI: https://doi.org/10.2478/s11534-014-0522-3

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