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Soret effects on simultaneous heat and mass transfer in MHD viscous fluid through a porous medium with uniform heat flux and Atangana-Baleanu fractional derivative approach

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Abstract.

The present paper is about the application of a non-local and non-singular fractional derivative to the unsteady flow of incompressible MHD viscous fluid with uniform heat flux through a porous medium. In addition the Soret, radiation, heat sink and chemical reaction effects were also applied to this physical model. The transport model of an ordinary derivative can be extended to the fractional model of a non-integer order derivative with non-local and non-singular kernel. The Laplace transform was used to obtain the expressions for temperature, concentration and velocity fields in non-dimensional form and numerical techniques were used to obtain the inverse Laplace transform for these expressions. At the end, influence of flow parameters on temperature, concentration and velocity fields have been discussed and explained graphically. As a result, the flow behavior can be enhanced with the non-integer order fractional parameter of non-local and non-singular kernel.

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References

  1. P.S. Ghoshdastidar, Heat Transfer (Oxford University Press, 2004)

  2. A.A. Kilbas, H.M. Srivastava, J.J. Trujllo, Thoery and Applications of Fractional Differential Equations (Elsevier, Amsterdram, 2006)

  3. R.L. Bagley, P.J. Trovik, J. Rheol. 30, 133 (1986)

    Article  ADS  Google Scholar 

  4. M. Caputo, F. Mainardi, Pure Appl. Geophys. 91, 134 (1971)

    Article  ADS  Google Scholar 

  5. R. Hilfer, Applications of Fractional Calculus in Physics (World Scientific, Singapore, 2000)

  6. M.A. Imran, I. Khan, M. Ahmad, N.A. Shah, M. Nazar, J. Mol. Liq. 229, 67 (2016)

    Article  Google Scholar 

  7. M.A. Imran, Nehad Ali shah, Ilyas khan, Maryam Aleem, Neural Comput. Appl. (2017) https://doi.org/10.1007/s00521-016-2741-6

  8. N.A. Shah, M.A. Imran, Fizza Miraj, J. Prime Res. Math. 13, 56 (2017)

    MathSciNet  Google Scholar 

  9. N. Shahid, Springer Plus 4, 640 (2015)

    Article  Google Scholar 

  10. D. Vieru, C. Fetecau, C. Fetecau, Therm. Sci. 19, 85 (2015)

    Article  Google Scholar 

  11. F. Ali, S.A. Alam, I. Khan, N.A. Shiekh, Eur. Phys. J. Pluse 131, 310 (2016)

    Article  Google Scholar 

  12. I. Khan, M. Ahmad, N.A. Shah, M.A. Imran, Effects of non-integer order time fractional derivative on coupled heat and mass transfer of MHD viscous fluid over an infinite inclined plane with heat absorption, in Int. J. Innov. Res. Sci., Eng. Technol., Vol. 6, (2017)

  13. M. Caputo, M. Fabrizio, Progr. Fract. Differ. Appl. 2, 73 (2015)

    Google Scholar 

  14. I.A. Mirza, D. Vieru, Comput. Math. Appl. 73, 1 (2017)

    Article  MathSciNet  Google Scholar 

  15. Asma R. Butt, M. Abdullah, N. Raza, M.A. Imran, Eur. Phys. J. Plus 132, 414 (2017)

    Article  Google Scholar 

  16. A. Atangana, B.S.T. Alkahtani, Entropy 17, 4439 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  17. A. Atangana, S.T.A. Badr, Adv. Mech. Eng. 7, 1 (2015)

    Google Scholar 

  18. M.A. Imran, N.A. Shah, Maryam, I. Khan, Eur. Phys. J. Plus 132, 340 (2017)

    Article  Google Scholar 

  19. F. Ali., M. Saqib, I. Khan, N.A. Sheikh, Eur. Phys. J. Plus 131, 377 (2016)

    Article  Google Scholar 

  20. I. Khan, N.A. Shah, M. Yasir, D. Vieru, Eur. Phys. J. Plus 132, 194 (2017)

    Article  Google Scholar 

  21. N.A. Shah, I. Khan, Eur. Phys. J. C 76, 1 (2016)

    Article  Google Scholar 

  22. L. Jorge, J.J. Nieto, Prog. Fract. Differ. Appl. 1, 87 (2015)

    Google Scholar 

  23. A. Atangana, D. Baleanu, J. Eng. Mech. 143, D4016005 (2016)

    Article  Google Scholar 

  24. J. Hristov, Therm. Sci. 20, 757 (2016)

    Article  Google Scholar 

  25. J. Hristov, Therm. Sci. 21, 827 (2017)

    Article  Google Scholar 

  26. A.A. Zafar, C. Fetecau, Alex. Eng. J. 55, 2789 (2016)

    Article  Google Scholar 

  27. A. Abdon, D. Baleanu, Therm. Sci. 20, 763 (2016)

    Article  Google Scholar 

  28. A.S. Nadeem, A. Farhad, S. Muhammad, I. Khan, S.A.A. Jan, S.A. Ali, S.A. Metib, Results Phys. 7, 789 (2017)

    Article  ADS  Google Scholar 

  29. A.S. Nadeem, A. Farhad, S. Muhammad, K. Ilyas, A. Syed, A. Jan, Eur. Phys. J. Plus 132, 54 (2016)

    Google Scholar 

  30. A. Khan, K.A. Abro, A. Tassaddiq, I. Khan, Entropy 19, 279 (2017)

    Article  ADS  Google Scholar 

  31. A. Atangana, I. Koca, Chaos, Solitons Fractals 89, 447 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  32. B.S.T. Alkahtani, A. Atangana, Chaos, Solitons Fractals 89, 566 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  33. M.A. Aziz, A.S. Yahya, J. Theor. Appl. Mech. 47, 25 (2017)

    Google Scholar 

  34. M. Abdullah, N. Raza, A.R. Butt, E.U. Haque, Can. J. Phys. 95, 472 (2017)

    Article  ADS  Google Scholar 

  35. M. Tahir, M.A. Imran, N. Raza, M. Abdullah, Maryam Aleem, Results Phys. 7, 1887 (2017)

    Article  ADS  Google Scholar 

  36. H. Sheng, Y. Li, Y.Q. Chen, J. Franklin Inst. 348, 317 (2011)

    Article  Google Scholar 

  37. D.K. Tong, X.M. Zhang, X.H. Zhang, J. Non-Newtonian Fluid Mech. 156, 75 (2009)

    Article  Google Scholar 

  38. Y. Jiang, H. Qi, H. Xu, X. Jiang, Microfluidics Nanofluidics 21, 7 (2017)

    Article  Google Scholar 

  39. H. Stehfest, Commun. ACM 13, 47 (1970)

    Article  Google Scholar 

  40. D.Y. Tzou, Macro to Microscale Heat Transfer: The Lagging Behavior (Taylor and Francis, Washington, 1970)

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Authors and Affiliations

  1. Department of Mathematics, University of Management and Technology Lahore, C-II Johar Town, 54700, Lahore, Pakistan

    Muhammad Imran Asjad & Fizza Miraj

  2. Basic Sciences Department, College of Engineering Majmaah University, P.O. Box 66, 11952, Majmaah, Saudi Arabia

    Ilyas Khan

Authors
  1. Muhammad Imran Asjad
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  2. Fizza Miraj
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  3. Ilyas Khan
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Correspondence to Muhammad Imran Asjad.

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Asjad, M.I., Miraj, F. & Khan, I. Soret effects on simultaneous heat and mass transfer in MHD viscous fluid through a porous medium with uniform heat flux and Atangana-Baleanu fractional derivative approach. Eur. Phys. J. Plus 133, 224 (2018). https://doi.org/10.1140/epjp/i2018-11857-7

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  • DOI: https://doi.org/10.1140/epjp/i2018-11857-7

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