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Chemical reaction, thermal relaxation time and internal material parameter effects on MHD viscoelastic fluid with internal structure using the Cattaneo-Christov heat flux equation

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Abstract.

In this article, the influence of thermal relaxation time and chemical reaction is studied on the MHD upper-convected viscoelastic fluid with internal structure using the Cattaneo-Christov heat flux equation for the first time in the literature. The flow-governing equations are formulated and are converted into their respective ordinary differential equations (ODEs) with the application of similarity functions. The resulting system of coupled nonlinear ODEs is solved along with the prescribed conditions at boundary using a finite-difference code in MATLAB. Influence of chemical reaction, thermal relaxation time and internal material parameter on the macroscopic and micropolar velocities as well as on the temperature and concentration profiles is examined along with other physical parameters (e.g., magnetic parameter, Eckert number, Prandtl number and fluid relaxation time). The accuracy of the obtained numerical solution is shown by comparing the physical parameters of interest with particular cases of existing results in the literature.

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References

  1. M. Renardy, J. Non-Newtonian Fluid Mech. 68, 125 (1997)

    Article  Google Scholar 

  2. A.D. Hobiny, I.A. Abbas, Eur. Phys. J. Plus 131, 424 (2016)

    Article  Google Scholar 

  3. N. Sandeep, M.G. Reddy, Eur. Phys. J. Plus 132, 147 (2017)

    Article  Google Scholar 

  4. C. Fetecau, D. Vieru, C. Fetecau, I. Pop, Eur. Phys. J. Plus 130, 6 (2015)

    Article  Google Scholar 

  5. M. Reddy, G. Reddya, Eur. Phys. J. Plus 129, 41 (2014)

    Article  Google Scholar 

  6. N.T. EL-Dabe, H.A. Attia, M.A.I. Essawy, Eur. Phys. J. Plus 131, 395 (2016)

    Article  Google Scholar 

  7. D. Srinivasacharya, G.S. Reddy, J. Egypt. Math. Soc. 24, 108 (2016)

    Article  Google Scholar 

  8. G.V.R. Reddy, N.B. Reddy, S.R. Gorla, Int. J. Appl. Mech. Eng. 21, 157 (2016)

    Article  Google Scholar 

  9. Mulolani, M. Rahman, J. Math. Math. Sci. 23, 319 (2000)

    Article  Google Scholar 

  10. A.J. Chamkha, A. Al-Mudhaf, J. Al-Yatama, Int. J. Fluid Mech. Res. 31, 529 (2004)

    Article  Google Scholar 

  11. H. Usman, I.J. Uwanta, S.K. Ahmad, MATEC Web of Conferences 64, 01002 (2016)

    Article  Google Scholar 

  12. S.M.M. EL-Kabeir, M. Modather M. Abdou, Appl. Math. Sci. 34, 1663 (2007)

    Google Scholar 

  13. S. Rawat, S. Kapoor, R. Bhargava, J. Appl. Fluid Mech. 9, 321 (2016)

    Article  Google Scholar 

  14. Ch. RamReddy, T. Pradeepa, Dr. Sirinivasacharya, Adv. High Energy Phys. 2015, 350813 (2015)

    Article  Google Scholar 

  15. P.K. Rout, S.N. Sahoo, G.C. Dash, S.R. Mishra, Alex. Eng. J. 55, 2967 (2016)

    Article  Google Scholar 

  16. S. Darbhashayanam, U. Mendu, Turkish J. Eng. Env. Sci. 38, 184 (2014)

    Article  Google Scholar 

  17. M.N. El-Fayez, J. Surf. Eng. Mater. Adv. Technol. 2, 100 (2012)

    Google Scholar 

  18. M. Ibrahim S., Chem. Process Eng. 19, 25 (2014)

    Google Scholar 

  19. Z. Uddin, M. Kumar, Int. J. Math. Model. Simul. Appl. 3, 155 (2010)

    MathSciNet  Google Scholar 

  20. A.D. Hobiny, I.A. Abbas, Eur. Phys. J. Plus 131, 424 (2016)

    Article  Google Scholar 

  21. T. Ariman, M.A. Turk, N.D. Sylvester, Int. J. Eng. Sci. 11, 905 (1973)

    Article  Google Scholar 

  22. T. Ariman, M.A. Turk, N.D. Sylvester, Int. J. Eng. Sci. 12, 9273 (1974)

    Article  Google Scholar 

  23. C. Cattaneo, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 3, 83 (1948)

    Google Scholar 

  24. C.I. Christov, Mech. Res. Commun. 36, 481 (2009)

    Article  Google Scholar 

  25. M.S. Khan, M. Hammad, S. Batool et al., Eur. Phys. J. Plus 132, 158 (2017)

    Article  Google Scholar 

  26. G. Lukaszewicz, Micropolar Fluids - Theory and Applications (Birkhäuser, Basel, 1999)

  27. J. Kierzenka, L.F. Shampine, ACM Trans. Math. Softw. 27, 299 (2001)

    Article  Google Scholar 

  28. M.Z. Salleh, R. Nazar, I. Pop, J. T. Inst. Chem. Eng. 41, 651 (2010)

    Article  Google Scholar 

  29. M. Qasim, I. Khan, S. Shafie, PLOS one 8, e59393 (2013)

    Article  ADS  Google Scholar 

  30. J.B.J. Fourier, Theorie Analytique De La Chaleur (Paris, 1822)

  31. S.R. Mishra, S. Baag et al., Eng. Sci. Technol. Int. J. 19, 1919 (2016)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Applied Mathematics & Statistic, Institute of Space technology Islamabad, 44000, Islamabad, Pakistan

    Sabeel M. Khan, M. Hammad & D. A. Sunny

Authors
  1. Sabeel M. Khan
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  2. M. Hammad
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  3. D. A. Sunny
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Correspondence to D. A. Sunny.

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Khan, S.M., Hammad, M. & Sunny, D.A. Chemical reaction, thermal relaxation time and internal material parameter effects on MHD viscoelastic fluid with internal structure using the Cattaneo-Christov heat flux equation. Eur. Phys. J. Plus 132, 338 (2017). https://doi.org/10.1140/epjp/i2017-11599-0

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  • DOI: https://doi.org/10.1140/epjp/i2017-11599-0

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